THE NATURE OF RESEARCH
Research can be defined as a systematic investigation undertaken to discover or establish facts and relationship i.e research is a systematic search for new information or knowledge.
METHODS OF ACQUIRING KNOWLEDGE
The development of human knowledge is generated in many ways some of these sources have very less defined rules other sources of acquiring new knowledge are highly structured and are generally defined by rules. Below are methods of acquiring knowledge:
1. UNSTRUCTURED SOURCES OF KNOWLEDGE
These methods are sometimes known as non scientific methods, those methods involving the following:
· Sensory experience
· Agreement with others
· Authority
(a) Sensory experience
The information/data that we take in from the environment through our senses is the most immediate way that we have of knowing something (smell, touch, see). Sensory knowledge is the information we get through senses that is its undependable and sometimes incomplete.
To obtain reliable knowledge we can’t rely on our senses alone we must check what we think we know with other sources and one such a source is opinion of others.
(b) Agreement with others
Not only can we share our sensations with others but also we can check on the accuracy and authenticity of the sensations for example if tea turns to test salty to us we can crosscheck with another person offered the same tea by asking “Does this tea test salty to you!” or ask is that Mathew out there? yet he walks or looks like Mathew or ask did you hear gunshots last night. It smells like fish doesn’t it?
(c) Authority
Sometimes we gain knowledge by consulting an expert on the issue, however no expert knows all there is to know in the given field all that the expert can tell if he/she doesn’t have current knowledge on the issue is to refer to another source/expert.
2. STRUCTURED SOURCES OF KNOWLEDGE
These include reasoning and empirical approach.
Its sometimes called logical or rationalistic approach. It allows us to use sensory information in order to develop a new kind of knowledge. There are 2 types of reasoning namely
(i) Deductive reasoning (Initiated by Greek philosopher Aristotle).
(ii) Inductive reasoning (Initiated by British Philosopher Francis Bacon).
i. Deductive reasoning
Here thinking proceeds from a general assumption (premise) to a specific application (conclusion) several pieces of general information are put together to produce a specific conclusion for example:
· All heavy cigarette smokers die from cancer.
· Peter smokes 5 packets of cigarettes a day.
· Peter will probably die of cancer.
First statement - major/general
Second statement - miner/example
Last - conclusion
NOTE: As long as the 1st & 2nd statements are true then the 3rd statement must also be true the question in this example. is Do all heavy smokers die of cancer?
Are 5 packets of cigars a day enough to cause cancer to Peter?
ii. Inductive reasoning
This approach of reasoning is the reverse of deductive reasoning here thinking or reasoning proceeds from the particular or specific instances, examples to a general premise (conclusion).
Example
· A headache is an altered level of health that is stressive.
· A fracture bone is an altered level of health that is stressful.
· Therefore all altered levels of healthy are stressful.
1st Bullet – particular
2nd Bullet – premise
3rd Bullet – conclusion
Research is necessary to test whether each of these specific instance is valid or accurate the testing of many altered levels of health in order to determine whether they are stressful is necessary to confirm the premise that all types of altered levels of health are stressful thus inductive reasoning is the creating a general rule be seeing/noticing similarities among several specific situations.
There are two kinds of induction namely; perfect and imperfect induction.
Perfect induction
Results in conclusions that are based on observations of selected characteristics of all members of a group or members of the population, this is frequently not possible in research particularly when groups are mainly large and scattered all over the country.
Imperfect induction
Results in conclusions that are based on observations of selected characteristics on a small specific number of members (sample) of the population. Most research is based on imperfect induction. The information obtained may not be absolutely perfect/true but is sufficient to make a fairly generalization provided the sampling used is appropriate.
Because of these faults in logical reasoning Charles Darwin integrated both deduction and induction methods analyzing problems and came up with an integrated method known as the scientific or empirical method.
SCIENTIFIC OR EMPIRICAL METHOD
Essentially this method of science involves the testing of ideas the answers of hypothesis, ideas, suggested answers in the public arena. When we identify our hypothesis or tentative explanations of what is happening we use the scientific method to check on our hypothesis. The scientific method consists of six broad steps and these steps contribute to what is called the research process.
These steps are: -
1. Identification and definition of the problem.
2. Reviewing available information on the problem.
3. Selecting the design of research methodology suitable to investigate the research questions or hypothesis.
4. Collecting the data.
5. Analyzing the data and stating the findings.
6. Drawing conclusions.
Any research in any discipline that uses the scientific method is technically called the empirical research methodology thus empirical research is an activity/process of finding first hand solutions to problems in a logical orderly and a systematic fashion.
Identification Of The Problem
Once the problem area of research has been decided upon then the problem should be defined even if only in broad terms. The researcher establishes a frame work in which to conduct the research is the identification on any necessary assumptions or conditions that are related to the research problems a well stated problem will imply a specific answer or conclusions.
Reviewing Available Information
The second step in the scientific approach is to gather the information about how others have approached or dealt with similar problems. The researcher showed profit from the work of others rather than trying to evaluate the will each time the research problem is attached. The research literate is the source of such information.
Selecting Research Method/Design
This step refers to the procedure and techniques that are employed in order to investigate the question or to test the hypothesis the steps involved is the set of decisions regarding the variables (factors) to be handled regarding participants in the study this is the stage to decide on the methods and techniques of data collection.
Collecting Data
In this stage, the study is arranged in such a way so as to test the hypothesis or to answer the research questions in other words the researcher will observe, test, weigh, measure, experiment the phenomenon of interest and collect data to refute the predicted outcome. Data collection should not be handled in hazardous manner the process requires proper organization and editing of instruments before they are used in the field.
Analysis Of Data
The collected data is now analyzed in a manner appropriate to the problem. An attempt is made to determine if the investigation or study answers the questions or confirms or refutes the hypotheses. In other words the question to keep in mind is to have the data give an answer to the question or has the data supported the predicted outcome, the researcher decides either to accept or reject the hypotheses.
Drawing Conclusions
The last step in scientific approach is the process of drawing conclusions; conclusions discuss the meaning of the research results and place them in a broader and more general context and perspectives often generalizing beyond the specific sample of the study.
Conclusions should not be restatement of the findings of the study but should be definite statement it concepts with the acceptance or rejection of each stated hypothesis. The conclusion should be based on the data and analysis with the frame work of the research study.
CHARACTERISTICS OF EMPIRICAL RESEARCH
The following characteristics are common to many types of empirical research.
1. Objectivity
2. Precision
3. Verifiability
4. Parsimony
5. Empiricism
6. Probabilistic thinking
1. Objectivity
Refers to data collection and analysis procedures from which only one meaning or interpretation can be made. It means a researcher’s bias is eliminated from the researching process.
2. Precision
Precision is expressed by extensive and detailed descriptions of concepts in order to convey the meaning by the researcher in that particular context for example concepts like classroom atmosphere, creativity leadership, organizational behavior. must be given precise meaning in that particular research and the meaning may defer in another context. In other words these concepts must be defined in technical research words/terms.
An operational definition of a concept is achieved by stating the operations or procedures that will be employed in order to under stand it well and them context in which its being used, It indicates how a concept shall be observed and measured during the research activity precise language describes the study accurately so that the study may be repeated by another researcher who is interested in checking the accuracy of the findings.
3. Verifiability
Research is a social enterprise and its information is open for public scrutiny. This characteristic of research called verifiability is related to the criteria of objectivity and precision its only through investigation or republication of studies where the results of any single study can be confirmed or revised through this process the body of knowledge is developed and new research questions are identified.
4. Parsimony
This means simplicity, the researcher attempts to explain relationships among phenomena and reduce explanation to the most simple statement is called parsimony.
Example
The theory that frustration leads to aggression is an explanation that predicts and it can be tested for verification thus the ultimate aim of any research is to reduce complex realities to simple explanations. This is called parsimony in research.
5. Empiricism
Research is characterized by a strong empirical attitude/approach
To a researcher a word empirical means being guided by evidence data or sources obtained from systematic objected procedures rather than by personal experience or authorities.
Empirical requires a temporary suspension of personal experience and beliefs.
6. Probabilistic thinking
One misconception of research is that the results that we get are absolute and therefore conclusions are true beyond a shadow of a doubt this is not the case as far as a research is concerned. Behavior science and research in general doesn’t offer certainty it doesn’t even offer relative certainty all it does offer is probabilistic knowledge
Example.
In behavior science we say if A is done then B will probably occur.
One way of defining research might be to say it’s a method of reducing uncertainty research can never tell us that something is so certain and no doubt exists it can however say something like this the odds are about 80-20 that its true. Probabilistic thinking then is central to research. The researcher often writes or presents the results tend to indicate that there is poverty in this village or the results “are suggestive” that…
IDENTIFICATION OF A RESEARCH TOPIC
Research problems or topics involve areas of concern to researchers they involve conditions that the research wants to improve, they involve the difficulties researchers want to eliminate and they involve questions for the researchers seeking answers topics.
Problems for research /Indicate a gap of knowledge
When searching for problem/topics for research. Its always those to keep a notebook with a little research ideas.
Whenever the interesting idea comes up in your reading makes a brief note of the idea which has crossed your mind. This approach not only produce potential dissertation problems but makes individual increasingly sensitive to possible topics for research.
The first step in locating a problem for research is to identify the broad problem area that is closely related interest area and to your professional goals example is typical broad topics of interest that may be considered include;
A short fall of teachers in Tanzania, HIV and AIDS epidemic, poor performance in science subjects in Tanzania.
A research problem is the term used for a topic that has been narrowed down and refined appropriately for research. The most important question is where does one begin to find even a broad topic for research. There are three sources that the individual can turn to a research problem or research topic these sources include:-
1. Personal experience
2. Deduction from existing theories
3. Review of literature sources.
Personal experience
Among the most fruitful sources for the beginning researchers are here own experiences and observation as professional practitioners example Decisions are always made by government or other agencies regarding probably effects of professional practices such a policy decisions may generate some research topics.
If these decisions are to be sound then they must be based on research areas.
Deduction from existing theories
Theories are general principles whose applicability to specific problems are unknown until empirically tested its only through research that one determine whether example (organizational theories, counseling theories, personalities) can be translated into specific recommendations for practice.
Review of literature
Existing literature in an area of specialization is an excellent source of ideas for research nearly all the literature available including unpublished dissertations conclude with recommendation for further research is advised to turn to these pages of recommendations.
Particularly good research would be achieved through replicating a study with a modification there are valid reasons for carrying out replicated studies which include;
1. To check the findings of the major study occasionally a study is reported that either produces new and surprising results or a study that reports findings that conflict or disagree strongly with a previous research. The replication of studies of this kind is very useful because these studies help or disconfirm the validity of the new evidence if supported by replication such studies often open up a new area of investigation or will offer a major impact upon professional practice.
2. To check trends or change one time.
Many research results in behaviour science depend on part of the environment in which the individual functions thus research findings on tribal attitudes or ratio that was valued 20 to 10 years ago may be invalid today replication in such circumstances is a useful tool for checking such earlier finding in order to check if there any trends or does other time.
3. To correct faulty methodology
Reviewing previous research studies may result in the researchers dissatisfaction with methods, instruments to collect data or with the statistical analysis that was used etc.
These studies may be replicated using more appropriate methodology or measuring and data collection instruments or using more appropriate statistical methods.
4. To check on generalize ability or previous findings
Review of previous research may stimulate a researcher to see whether the procedures/measures that were employed in that study can be adapted in solving problems or whether a similar study could be conducted in a different field subject area or with different groups of participants example a study involving secondary school students might serve as a guide to the research who is interested in determining whether the same relationships between variables(factor) prevailed at the primary school level.
Similarly reviewing research studies previously undertaken in other cultures may be worth indicating in another culture in order to check the applicability generalize ability of that research to another culture.
CONSIDERATIONS IN SELECTING A RESEARCH TOPIC
The researcher should bear in mind certain consideration when trying to decide if a certain research problem/topic is appropriate for a research study. Some of these considerations include the following;
1. Personal interest in the research topic
The research should have personal motivation in the research topic that he/she is selecting if the experience is to be a rewarding one researcher topic antiques or the researcher is one the researcher associates with pleasant experiences or unpleasant concern whatever the case without interest the research process is going out to be tedious or may not be completed in time or not at all.
2. Importance of the research topic
Any topic selected for study should be of significant for the group the research cares for or should add to the fund of the existing knowledge, the significance of the problem can best be judged by assessing the problems within terms of a number of criteria including the following;
(i) Does the problems address issues to affect large number of people or many institutions.
(ii) With the outcome, findings improve the quality of life of individuals or groups.
(iii) Does the problem address issues in my area of (specialty).
(iv) Will results be suitable for use practically for use to improve……
3. Newness of research topic.
The newness of the research topic may affect the researcher enthusiasm and satisfaction although there is repeating or value in replacing previous research to validate methods and see if findings hold true overtime the researcher is likely to find it much more existing to explore newer topics where he/she has an opportunity to bring new information to right seniors review of literature available and dialogue with knowledgeable colleagues and alert the research to trivial and over worked/researched problem.
4. Time availability
In selecting a research topic time is always the factor to be considered. Its wise to analyze or compare the amount of time the topic will require against what you have available it will be unrealistic to select a topic that could not be finished comfortable within time the researcher has available.
You must give attention, more time than seems to be given because an planned delays normally occur.
5. Difficulty researching on the topic.
The researcher should always reflect on the difficulty of researching the topic many extremely interesting research topics are difficult or impossible to research on for a number of reasons example you would probably find it impossible to do research into what happens to the students brain cells as they learn mathematics point before is always select a research topic that is within your means and ability to investigate.
6. Costs involved
The researcher should always consider the monetary costs incurred in investigating the research topic if the investigation of the research topic would require costly supplies materials and travel expenses and such a topic should be put a side. There are many other research topics that can be handled with minimum costs.
7. Ethical issues
A final consideration for determining the research topic which has to do with ethics. Its un ethical and illegal to conduct pain to participants involved in the study.
REVIEW OF LITERATURE
Once the researcher has picked a topic that is researchable topic its now time to get familiar with what has been researched on. There are 3 basic sources that researchers can turn to for information related to the topic, these sources are;
1. General sources
2. Secondary sources
3. primary sources
(i) General sources
These are the references the researcher refers to first, these sources tell the researcher where to look in order to locate other relevant sources such as articles published, monographs, books and others. Most general sources are either indexes which simply make a list of the author, the title of the article and the place of publication of the article.
Another general source is abstract which give a brief summary of various publications as well as the author, title of the article and place of publication.
{In psychology the index that should be referred to should be called socio-science citation index (SSCR) and common abstract for psychology is called psychological abstracts}.
(ii) Secondary sources
These refer to publication in which authors describe the work of others the most common secondary source are textbooks others include encyclopedias then also you can consult research reviews in psychology, sociology and other areas interest.
(iii) Primary sources
There are publications in which researchers report the results of these studies the researcher communicates his/her findings directly to the reader most primary sources are dissertations; thesis and journals start with latest journals.
Reviewing And Evaluating Literature
Several steps are involved these steps include;
1. Define the research problem as precisely as possible.
General questions like what sorts of learning strategic work well in special studies lesson or the question how can an administrator be more of an effective leader. These questions are too vague and for broad to be of much help to the researcher accordingly they should be narrowed down to a single specific area of concern we can state the previous questions as follows;-
- Do students taught by a team of teachers learn more than students taught by an individual teacher on a social studies programme?
- What kind of strategies do administrators use to judge effectiveness by their staff to improve the staff morality?
2. Formulate key words of phrases contained in your research topic
Once you have a clear topic or problem with clear research hypothesis, its now time to formulate some key words or phrases that can help in locating the relevant literature.
3. Search the general references for relevant primary sources
The following procedure is used by many researchers in searching the general references sources for relevant for primary sources.
(a) Find the most recent book/issue/publication.
(b) Look to see if they are any articles listed under each of your search terms in that current publication.
(c) As you find the names of articles that seem relevant to your research its then useful to list them on note cards usually the author, title, pages, publication, date and source are listed. Use a separate card for each reference, the important thing is to take care and record the bibliographical date accurately and completely.
4. Read the relevant primary sources.
Once you have searched the general references you should have a list of bibliographical note cards the next step is to locate each of the sources you have listed and read and take notes on those that are relevant to the programme.
5. Take notes and summarise the key points in the sources
When you have the general articles you intend to search put together how you can now begin your review. Its advisable to begin to review with the most recent articles and work back words the reason is recent articles often rely on earlier articles as a foundation and thus can give the researcher a quicker understanding of previous work to summarize the key points of the key sources located. The, for researcher should follow the following steps;
1. Read the abstract or the summary this will tell the research is worth reading further if it is recorded the bibliographical data at the top of the note cards; as you take notes concentrate on the following reports.
· Problem
List that problem as it is given verbatim don’t paraphrase.
· Hypothesis/objectives/questions
List them exactly how they are stated in the article.
· Procedure
Here describe the methodology that was used (i.e. the research design that was used; experimental, case study indicate the number of participants in that study and how they were selected. Also indicate the instruments which were used to collect the data example questionnaire interviews.
· Make a note of any an usual techniques that were used or make a note of any flows or imperfections committed by the researcher.
· Results/findings of the study
List the major findings as given by the researcher indicate the objectives or questions or hypothesis of the study which were realized. Often the findings will be summarized in a table and this table the researcher can photocopy and paste them to the back of the card
Conclusions
2. Describe the authors conclusions note any disagreements that you may have with the author regarding the results and your reasons for such disagreements note any strength or weakness of the study that make the results particularly applicable or limited with regard to your objectives/questions or hypothesis.
NOTE: The scope of literature review
Beginning researchers seem to have difficulty in determining how broad there literature review should be they seem to understand that all literature directly related to the problem should be revealed and as a result they don’t know how quit the exercise they seem to have trouble determining which articles are related enough to have problem and therefore to be included in the review unfortunately there is no statistical formula that can be applied regarding the scope of the literature review the decisions of the researcher must be based on judgment. These judgments become easier as one acquires experience but in case of a beginning researcher the supervisor will guide regarding the scope of the literature review here are general guidelines which can assist the beginning researcher these guidelines are:
1. Avoid the temptation to include everything you find, bigger review doesn’t mean better. A smaller well-organized review is preferred to a review containing many studies that are more or less related to the problem.
2. Heavily researched topics or areas usually provide enough references directly related to a specific problem to eliminate relying on less peripheral targential.
3. New and little researched problem areas usually required review of any study that is related in some meaningful way to the problem at hand this is useful in order to develop a logical frame work for the study and a sound of rationale for the research problem.
VARIABLES IN RESEARCH
A variable is any characteristic or attribute that can take a variety or values or forms. The values of variables can be expressed in numbers and we normally call these numerical/quantitative variables.
The forms of variables can be expressed in categories these then are called categorical (qualitative) variables an example of numerical variables is the age of a the variable age can have different values example a person at the age of 30-40 they defer in other numerical values may include weight, distance between place can defer, heights, monthly income defers. Then different forms of a variable that are expressed in terms of categories which may include; colour of eyes, main type of staple food, marital status, research incomes studying variables and the relationships example of relationship between motivation and learning, personality of teacher in his or teaching subjects, administrative policies and the affection to morals, relation between age and attractiveness.
There are many variables in the world that can be investigated by the researcher.
There Is Yet Another Way For Categorizing Variables For Research Namely Independent Variable, Dependent Variable, Extraneous Variables.
(I) INDEPENDENT VARIABLE
An independent variable (IV) represents the conditions that the researcher controls in an effort to test the variables affect on some out come its what the reseacher chooses to study, In other words the (IV) is independent variable what the researcher chooses to study and often the researcher manipulates or varies the levels, in order to assess its possible effect on one or more other variables.
There are two types of IV’s namely;
- Treatment variable
- Organism variable/attribute
a) Treatment/intervention variables
These are variables the researcher actually manipulates or assigns participants in the study example offering different levels of alcohol to different participants.
b) Organism/attribute and variables
Are those characteristics of participants that are relatively natural and permanently endowed in an individual and can’t be altered or manipulated by the researcher e.g. age gender cannot be altered experimentally?
(ii) Dependent variable
The independent variable is presumed to affect is what is technically called the dependent variable sometimes it is called outcome variable in other words independent variable is presumed to cause an effect technically called dependent variable i.e. a result of boozing outcome of what is done.
(iii) Extraneous variable
A basic problem in research there are many possible independent variable that could have an effect on the outcome dependent variable (D.V). Once a researcher has decided which variables to study he/she must be concerned about the influence or the effect of other variables which exist and can interfere/confound with the outcome. Such other variables that the research is not interested to consider or take in account but can confound the outcome of the study are called extraneous variables.
The task of the researcher therefore is to control these variables in his/her research example supposing the researcher is interested in the extent to which the teaching ability of teachers affect the students academic performance.
SOURCES OF EXTRANEOUS
In any type of research several sources of extraneous variables are possible among these are the following;
1. Physical environment
2. Attributes of the participants
3. Variations in procedure
4. Social nature of the research situation
1. Physical environment
A variety of variables that may affect the outcome of the study dependent variable D.V are always present in the physical environment the research is conducted for example the behavior which is exhibited while doing a task or may be affected by the environmental variations in temperature (it may affect your performance) time of debate, background noise, lighting.
2. Attributes of participants
People have a variety of attributes that might be related to the behaviour differences in behaviour may be associated with organismic behaviours like age, gender intelligence, weight, Boredom, motivation (you need optimal).
3. Variations in procedure
If all aspects in the procedure of the study except for the administration of the independent variable are not held constant across the participants then extraneous variables may be introduced into the study for example the researcher may vary instructions slightly from participants to the instructions to participants then they become extraneous variable in research i.e. variation of the explanation of what to do, the instructions should be uniform to all participants Sometimes a researcher may give a participant more time than to some other participants.
4. Social nature of the research situation
A research environment is fundamentally a social situation in which the researcher and participant interact thus whenever an individual knows that he is participating in a study a person may react to many aspects of the research situation that may not be actively manipulated by the research the participant for example may respond as he/she thinks the researcher demands based on some cues that researcher displayed during the study.
Technically we call these factors emanating from a research situation the demand characteristics. Sometimes the extraneous variable may come from the researcher herself. She may enter into a research with some expectations regarding how the participants will behave and what the results will be these expectations are called the experimenter effects or the experimenter (bias).
CONTROL OF THE EFFECTS OF EXTRANEOUS VARIABLES IN A STUDY
Extraneous variables interfere with obtaining a clear understanding of the relational that or causal of dynamics within a study situation. The extraneous variable will make it possible to have an alternative explanation of that results accordingly they must be controlled. Controlling extraneous variables is to be able to identify balance minimize or eliminate there effects. A good research design should be able to control extraneous variable rather than confounding the effects with those of the independent variable of interest in other words the strategy of designing a good study is mainly one controlling extraneous variables.
There are eight procedures for controlling extraneous variables;
1. Randomizing extraneous variables
2. Eliminating or excluding extraneous variables completely from the study.
3. Holding extraneous variables constant.
4. Matching/equating participants on an extraneous variable.
5. Making the extraneous variable also an independent variable in the study.
6. Balancing the effects of extraneous variable.
7. Counter balancing the extraneous variables in the study.
8. Statistical adjustment for extraneous variables in the study.
1. Randomizing extraneous variables
In randomization first we carry out random selection of participants to be included in our sample for our study. This random selection is carried out using the target population. Random selection means every member of the target population of interest has an equal chance to be selected to be a member of the sample.
Then having selected a random sample of participants of the study we then randomly assign each of those participants to different conditions in our study if the researcher has included difficult conditions to be studied.
Randomization is effective in creating equivalent representative groups that are essentially the same on all variables thought by the researcher to be influencing the dependent variable.
The rational of randomization, therefore is that, participants are selected randomly from the target population (and are assigned at random to groups) there is no reason to believe that the groups are greatly different in any systematic way at the start of the study.
2. Eliminating or excluding extraneous completely from the study
Where possible the influence of extraneous variables can be entirely removed from experiences in both experiment or control conditions for example extraneous variables of noise or interruptions or changes in the environmental conditions where the study is being conducted can be avoided by the researcher by excluding them from the environment an example is a sign outside the door research in progress. Similarly than encountering possible confounding from participants asking questions while filling in the questionnaire may be eliminated by not explaining out, the entire questionnaire is about.
3. Holding extraneous variables constant
In many research situations important variables may be so hard to eliminate all together and since they may influence the amount of variation in the dependent variable the researcher must find some alternative of controlling the extraneous variables possibly is to hold them constant (let them be the same across all conditions) for example if gender is suspected to influence the dependent variable the overcome of the study then the researcher can bold this variable constant different conditions in the study e.g. males or females only can be used.
Similarly the intelligence is suspected to be an extraneous variable that can influence the outcome of the study the researcher can hold the intelligence constant by using a sample of participant whose intellectual level is nearly the same.
4. Equating/matching participants on the extraneous variable
If larger groups of participants are used in a study simple random assignment to different conditions in the study is likely to yield groups that are comparable on all variables.
However when working with small groups of participants researchers often use the process of matched pairs to make sure that the groups are initially comparable on the identified extraneous variable example is assume intellectual quotient is an extraneous variable identify the irrelevance to the study, The first thing the researcher does is to obtain measures of intelligence for each participants by administering an intelligence test. Having scored the intelligence test responses of the participants the participants are ranked in terms of their levels of their intelligence beginning from the highest scoring individuals to the lowest then the researcher takes the names of the participants with 2 highest score
There researcher then takes the names of participants which 2 the highest score and assigns one of them to group A and the other to B these 2 participants constitute the first pair who have been matched on there extraneous variable of intelligence the researcher then takes the next pair and so on until he or she gets the required number who are to participate in a study.
5. Make extraneous variable an independent variable of interest.
If an extraneous variables can’t be eliminated the researcher can build it in the design as another independent variable of interest example supposing researcher is interested in carrying out a study dealing with effects of alcohol on typing errors committed then the researcher goes to the stores and finds there are 2 types of typewriters and are few of them namely; 10 electric typewriters and 10 manual typewriters.
Here there different kinds of computers may influence the number of correct words a person can type so this variable can be controlled by including it in the study and therefore a second independent variable or design of the study before this variable was included in the study would look like this.
GROUP A GROUP B
No Alcohol Alcohol
20 Participants 20 Participants
Using same make of typewriter
t = test
= Average or mean
Holding extraneous constant;
The design incorporating the type of typewriter as an IV (independent variable) how it can be taken into account.
Group A Group BNo Alcohol (control conditioning) Alcohol experimental
Electrical 10 participants 10 participants
Manual 10 participants 10 participants
To check the extraneous variables and averages compared for a conclusion, the researcher can now look at the effect of the typewriter to the number of participants who used electrical typewriter and those who used the manual and then find the average.
Interaction effect: he researcher will also be interested in finding the joint effect of two effects on the amount of eras committed which is called an interaction effect. We use the statistical analysis of variance (ANOVA).
6. Balancing the effects of extraneous variable
If an extraneous variable can not be held constant or if the researcher chooses to hold it constant then the effects of the variable can be held constant by balancing this, balancing is achieved by having different levels of an extraneous variable equally represented in the study treatment conditions so that its effects are evenly distributed (balanced) across the research conditions or treatments example is when a researcher realizes that social, economic status (SES) is an extraneous variable and may affect the dependent variable he will make an effort to balance its effects in the study example, supposing he has the class of 30 students to participate in his students of the 30, 6 out of 30 come from low economic status 16 from middle economic status and 8 from high economic status. The researcher has 2 conditions to assign these participants.
Low Middle High n = 30
6 16 8
Experimental (E) condition. L M H
3 8 4
Control ( C) Condition 3 8 4
By distributing these participants according to SES you are spreading the effect across the conditions of the study.
After intervention you then compare the experimental group with the control group on the dependent variable usually compute the averages of each group separately using it for independent groups. Equally important researcher may want to compare SES in different conditions.
7. Counter Balancing Extraneous Variables
If the researcher suspects that there is likely to be a carry over effect (order effect) where a single group of participants is exposed to 2 or more tasks. In this case the limited sample is divided into 2 and each will be exposed to the tasks in a reverse order as follows;
Tasks Group 1 Group 2
B
Here counter balancing involves reversing the order of 2 tasks.
t - test for dependent or same or correlated groups.
8. Statistical Adjustments For Extraneous Variables
More often participants in a study defer on an extraneous variable even before a study is conducted these differences that might exist should be controlled through statistical adjustment.
Statistical adjustments (control) when used is achieved through computational procedures that are applied when data is analysed but the extraneous variable to be controlled must be planned for at the beginning of the study. This means the researcher must get an assessment of the level of assessment on each participant therefore for example intelligence can be tested by administering and intelligence test to each and scores removed statistically by using either Analysis Convariance (ANCOVA) or partial correlations.
DEVELOPING A FRAME OF REFERENCE
Once the researcher is familiar with the existing literature then a framework must be established in which to place the study both quantitative and qualitative require the use of a frame of reference.
A frame of reference (in brief framework) for a particular study is an abstract conceptualization (frame) that places the study within a context of meaning this is called reference this forms away of viewing the phenomenon the framework or way of viewing a phenomena must be clearly developed within a study the development of framework involves identification of its basic elements namely;
- Concepts/variables and relationships among those concepts/variables in other words in a frame work all concepts/variables that are used within a study must be related or linked together the direction of these relationships must also be indicated [usually using arrows if a diagram is used example. ].
Relationships in a frame work are clarified using a model which is a pectoral demonstration using arrows to show the relationships or mathematical formulas things that can be seen visually often help the researcher to pull together ideas that are more difficult to understand from written explanations.
Two types of framework in study that can be used;
1. A theoretical framework
This term is more appropriate for research which is based on identified theory.
2. Conceptual framework
This draws on concepts from various theories and research findings (literature review) in order to guide the study.
NOTE: Sometimes these two 2 frame works are interchangeable.
Basic Features In A Theoretical/Conceptual Frame Work
They are five items that should be incorporated in any theoretical or conceptual frame work;
1. A schematic diagram/model; this should be given so that the reader can see and easily comprehend the theorized relationships.
2. The variables consider the relevant to the study should be clearly identified and also described clearly and briefly in a discussion.
3. The discussion should state how two or more variables are related to one another. This should be done for the important relationships that are theorized to exist among variables.
4. If the nature and direction of the relationships can be theorized on the basis of the findings from previous research there should be an indication in the discussion if the relationships would be positive or negative.
5. There should be a clear explanation of why the researcher would expect these relationships to exist the arguments could be drawn from the previous research findings.
FORMULATION OF A STATEMENT OF A PROBLEM
After sharpening a problem through literature review and conceptual or theoretical frame work there is still a task of formulating or stating a specific problem in a form that is available to investigate. It contains what will be examined by the researcher or the content of the study in other words its useful to define a problem as any situation where a gap exists between the actual and the desired ideal state thus a good state must contain the following;
1. Clarify exactly what it is to be solved or determined;
It must identify an area of concern; a doubt, uncertainty or difficulty in other words must identify a gap of knowledge.
2. Contain the variables and the population that is to be studied.
3. It should restrict the scope/delimitation of the study to the specific situation or hypothesis.
NOTE:The formulation of the problem can be in the form of the declarative statement or a question. Many researchers prefer the question form but either form is acceptable.
The problem of the study is to evaluate available options of coping with smoking in (B.O.T) Bank of Tanzania.
FORMULATING THE PURPOSE OF THE STUDY
In the research process the purpose of the study is usually stated after the problem is stated the statement of the purpose of study is generated from and it supports the problem statement and clarifies the knowledge to be generated in other words the research purpose is a statement of what needs to be done in the study or the aim of the study.
The research purpose should be stated objectively or a way it doesn’t reflect particular biases or values of the research as the research problem and purpose increase in clarity and conciseness. The researcher has greater direction in determining the physibility of a study.
Example;The purpose of the study is to provide employer in BOU with guidelines to initiate or improve smoking policies in the work place.
FORMULATING RESEARCH QUESTIONS
Whereas the purpose statement explains the general direction of the study the research questions expand on these by providing details this is a crucial stage in research because if the research does not ask appropriate questions he/she will not be able to collect suitable data and arrive at sensible conclusions.
N.B. Research questions should be listed and numbered in the order of priority that is which is the most important or the less important.
Research questions may be descriptive questions or relationship questions or difference questions.
§ Descriptive research question
These describe “what are or what was or what is or what were” these types of questions involve survey type of research.
NOTE: These terms however are not always used directly in the wording of the research questions example
1. What available options are effective for coping with smoking in BOT?
2. What are the attitudes of youth in Nyamagana district towards AIDS?
3. What is the knowledge level of youth in Nyamagana on AIDS?
4. What is the extent of exposure of AIDS information to youth in Nyamagana district?
· RELATIONSHIP QUESTIONS
These ask the relationship of two or more variables.
NOTE: This does not mean that the exact words what is relationship between variable A/B in a specific population always appear in your question statement for example
What is the effect of available options of coping with smoking on performance in BOT or is there a relationship between performance and available options for copying with smoking in BOT.
· DIFFERENCE QUESTIONS
These in research typically ask if there a difference between variable A and B example is there any difference in performance between workers provided with adequate and those provided with inadequate options for copying with smoking in BOT.
Good Research Questions Should Posses;
1. Physibility
The being researcher should plan to investigate studies that are physical meaning should focus on the question requiring participants from whom the data can be collected with a relatively expenditure of time, money and energy.
2. Clarity
The nature of a research study needs to be clear to all those concerned i.e. most people should agree as to what the key questions mean.
3. Significance
The questions that are being asked should be worth getting answers too in the light of its contribution to the important knowledge in that area.
4. Ethicality
The question should be ethical i.e. it shouldn’t involve any physical or psychological damage to the participants example; Are you HIV positive? how much do you earn? Why are you ugly?
FORMULATING RESEARCH OBJECTIVES
Another way of detailing the purpose of the study is in the form of objectives like the research questions objectives are formulated by the researcher to explain in detail what the study is expected to achieve.
Research objectives like questions are listed and numbered in order of importance or priority usually following the order of the research questions example The objectives of the study are an attempt to identify the effects of different options on productivity in BOT.
1. Improvement of ventilation
2. Segregation smokers from non smokers
3. A total ban on smoking
FORMULATION OF HYPOTHESIS
A hypothesis is a prediction regarding the outcome of the study in terms of the variables being investigated i.e. an hypothesis is a formal tentative statement of the expected relationship between the independent and the dependent variable. The hypothesis translates the research purpose or objectives of the study into a clear explanation of the prediction of the expected outcome of the study.
TYPES OF HYPOTHESIS
There are two types the researcher can choose from;
(i) A statistical hypothesis
(ii) Research hypothesis
· A statistical hypothesis
This is also called the Null hypothesis, this is a statement claiming that individuals in the target population involved in a study do not defer with respect to the variable under investigation in other words the null hypothesis is a statement of equality example as follows.
· There is no difference in the average scores of P.7 students and the average scores of S.3 students on digit memory test i.e. no one knows than others.
· There is no relationship between personality type introvert or extravert and job success.
· There is no difference in performance between workers provided with in adequate and those provided within adequate options for coping with smoking in Bank of Tanzania.
NOTE:
1. What these null hypotheses have in common is that they all contain a statement of two or more variables being equal.
2. Researchers invariably carry out studies with hope that a null hypothesis will turn out to be incorrect. Rarely does a research hope to confirm a null hypothesis.
RESEARCH HYPOTHESIS
While a null hypothesis is a statement of equality a research hypotheses is a definite concrete statement of inequality between two variables or two groups. There are 2 types of research hypothesis namely;
- None directional
- Directional
· None directional
A none directional hypothesis does not make a specific prediction regarding what direction of the study will take. In other words a none directional research hypothesis reflects a difference between groups/variables but the direction of that difference is not specified.
Examples:
· There is difference in the average scores of P.7 students and the average scores of S.3 students on digit memory test;
· There is a relationship between personality types and job success
· There is difference in performance between workers provided with adequate and those provided within inadequate options for coping with smoking in BOT.
NOTE: When the review of literature shows conflict in findings then a researcher should take the safe side by formulating none directional hypothesis.
· Directional
This is one that indicates the specific direction (e.g. higher, lower more, better etc) that a researcher expects to emerge in a study. The particular direction that is expected by the researcher is based on what the researcher has found in personal experience or in experience of others such as that revealed in the literature review, In other words a directional research hypothesis affects a difference between the groups and the direction of the groups is specified.
Examples;
(i) S.7 students perform better than F.3 students in a digit memory test.
NOTE:
1. Normally when there is a scarcity of literature on topics normally a researcher formulates a research question.
2. In survey research we normally formulate research questions or when the research is qualitative.
3. In research topics where there is plenty of research available on the topic or when the topic is an experimental one we normally formulate a hypothesis.
SELECTING A SAMPLE FOR THE STUDY
Researchers collect data from a representative sub-set or sample selected from the target population. Researchers do this under the assumption that what they learn from studying the representative sample more or less generalises other individuals in the target population only if we have a representative sample we draw accurate appearances about the target population characteristics from data obtained on the sample.
Sampling Techniques Are Grouped Into Two Categories Namely;
- Probability Sampling
- None – Probability Sampling
· Probability Sampling
This is also called random sampling, it is a sampling technique which uses some form of random selection when choosing a sample from the population. It occurs when each individual has an equal independent chance of being included in the sample.
Random selection of individual to be included in the sample should not be confused with random assignment of individuals. Random assignment refers to the assignment or distribution of individuals once randomly selected from the target population to either a control group or to different conditions in the study on a purely random basis.
Probability sampling is more likely to result in a more representative sample and the four commonly listed are;
(i) Simple Random Sampling
(ii) Stratified Random Sampling
(iii) Cluster Sampling
(iv) Systematic Sampling
1. Simple Random Sampling
SRS is done in such a way so as to afford each individual in the target population on equal chance of being selected to obtain a simple random sample, the researcher must have a sampling frame.
This is a listing of each member of the target population from which the this sample will be drawn. Then participants/individuals included in the sampling frame are chosen randomly from the list. There are two methods of selecting a sample using simple random techniques.
(a) Lottery method (simple bowel method)
In this method individuals from the sampling frame are identified on a piece of paper then pieces of paper put in a container they are mixed up or shaken up to avoid bias then pieces of paper one at a time are picked from the container one at a time until the desired number of participants are obtained.
Those individuals whose identity is on the papers now make up the sample also called Fish bowel method.
NOTE: When a piece of paper is recorded and picked should be put back in the container to have the same chances with the others left.
(b) Using a table of random numbers.
NOTE: To use this table the researcher would follow the following steps;
(i) Each member of the target population is assigned a number example if there is a target population of 70 individual members and a researcher wants to select only 30 to participate in her study each member of the population of 70 people will be assigned a number from 01 up to 70.
(ii) The table of random numbers is now consulted the researcher may begin getting the sample either using any rows or columns to locate your sample.
(iii) Then any two digit numbers between 01and 70 are selected either usingthe first two digits of each set in the row or column using any last two digits in a row or column of each set of numbers if a number is between 01 and 70 its included in the sample if its beyond its ignored. If however the same digit is met again its ignored since it has been selected.
(iv) The process is carried on until the 30 participants are selected from the target population
NOTE: The starting point is selected randomly with eyes closed. If your numbers have 2 digits example 12, 70 then 2 if 123, 350 then 3 digits.
2. Stratified random sampling
SRS is more suitable for handling a larger population which can be put into groups (strata) each group to be represented in the study. Example: if the researcher wants to take both male and female as a sample the target population is stratified into male and female, married or unmarried.
After grouping then according to areas of interest then each member in that group is given an identity number then a random sample; using random sampling technique. Until the required individuals are selected to participate in each group, the researcher is interested in this method because he will analyze the data according to the groupings.
Usually they are two;
(i) Proportionate Stratified Sampling
(ii) Dis-Proportionate Stratified Sampling
i) Proportionate Stratified Sampling
In proportionate stratified sampling members of the target sampling are put into groups and then random sampling is used to get proportional number of participants from each group.
Example:365 post graduate students to choose from out of these, there are 219 females and 140 males.
365
219Females 146 Males
60% of 365 40% of 365
Researcher randomly
Selects a stratified sample
131 60% of 219 58 40% of 140
189 Final sample
i) Dis-proportionate Stratified Sampling
In dis-proportionate stratified sampling a larger percent of participants is taken from sum -strata than others this is a useful technique when a characteristic of interest of research occurs in frequently in the target population making it likely that a simple random sample or a proportionate sample will too have members with characteristic to allow full analysis of data.
In other words in dis-proportionate stratified sampling [DSS] the researcher selects a larger percentage of members from groups likely to be represented in the target population.Sometimes a researcher avoids this issue by selecting unequal number from each strata.
3.CLUSTER SAMPLING
This is particular appropriate in situations where a researcher can not’ obtain a list of the members of the population and has little knowledge of these characteristics and also the area of interest is scattered in a wide geographical area. Frequently also a researcher may not be able to select a random sample of individuals because of administrative or other restrictions of the institution. This is especially true in schools for example if a researcher target population is only or all S.6 students enrolled in economics in a district its unlikely that the headteachers of the schools in district would allow the researcher to select randomly a certain number of individuals from each class of economics for the study the best, the researcher could do, would be to select a number of intact classes i.e. classes which are already in existence in schools the selection of groups of classes (cluster) of individuals rather than individuals themselves is called cluster sampling sometimes this is area sampling and once an intact class has been selected randomly all individuals will participate in the study.
NOTE: The researcher might want to go further after selecting a cluster by moving mult stage cluster sampling. After cluster sampling you will use random sampling.
Systematic (Interval) sample(ing)
This method of sampling is done when all members of the population are listed in the sampling frame but this listing doesn’t indicate any systematic order that could create a bias in the sample.
Then this method is much easier than the simple random method to use this method to different procedure is followed;
1. Establish a number of individuals on the list or the sampling frame (e.g. 1000).
2. The researcher should decide how many participants he would want on that list e.g.
3. The researcher should establish the internal for selecting participant from the list. This is computed as follows;
Interval = 1000/100 = 10.
That means you will pick individuals who are the tenth on the list starting from a randomly selected individual who is between 1 and 10 and the 1st, individual is selected randomly , 2, 3, 4, 5, 6, 7, 8, 9, 10, ………
The first randomly and then jump 10 and 50 on.
· None probability sampling
Samples that are not selected at random are none probability samples they are four types of this
1. Convenience sampling
2. Purposive sampling
3. Network sampling
1. Convenience sampling
This is also called accidental sampling this sampling techniques uses groups of individuals that simply happen to be available. Individuals are chosen until the sample of the desired size is obtained without any regard to its representativeness.
The results obtained in such studies can be generalized to the population with great caution.
2. Purposive sampling
This is also judgmental sampling. It is used to select certain individuals from certain population for a study the researcher uses his/her judgmental to which participant of the population should be included in the sample.
e.g. the researcher might want views on poverty alleviation in village.
The researcher uses her judgment that the best people to include who should be knowledge about what is happening are the L.C Committee members we call such people key informers
NOTE: If they are many after purposive sampling you can use random sampling to select a few.
QUOTA SAMPLING
This ensures that certain groups are adequately represented in the study through group generally a quota which is fixed for each group is based on the total number of each sub-group in the population.
Questions can be considered as a form of proportionate stratified sampling in which a pre-predetermined proportioned are sampled from different groups but on a convenience basis e.g. lets assume that work attitudes of junior workers in an organization are quite different from those of senior workers. If there 60% of junior workers and 40% of senior workers in this organization and if the researcher wants a total of 30 people to be interviewed to find the answer on attitudes or other things then a quota of 18 junior workers and 12 senior workers will form the sample because these numbers represent 40% and 60% of the sample size required in other words questions ensures that all sub-groups in the sample are represented to note that the questions are basically stratified ______________where participants are selected randomly.
NETWORK SAMPLING
This is also referred to as the snow ball sampling its a strategy that is used for locating samples that are difficult or impossible to locate in other ways this sampling takes advantage of social networks and the tact that friends tend have characteristics in common when the researcher has found people with the needed criteria they area asked for the assistance in getting in tough in others with similar characteristics this strategy is useful for finding participants for the study which aims at those who are socially in deviled populations such as street children e.g. sex offenders, drug addicts criminals, sex workers.
These individuals are seldom willing to participate except to the intact groups in summary show ball sampling approach resembles the individual approach (convenience approach). It begins by identifying a single or a small number of individuals then asked to willing to participate in a study. None probability sampling techniques are heavily used while probability sampling are used in qualitative.
Sample size
The number of participants is called the sample size and its represented by the later case n while reserving the capital letter N for the target population the research must determine the size of the sample that will provide sufficient data to answer the research questions i.e a sample of adequate size will be one which permits the study to be sensitive enough to determine a statically significant if in fact it exists and to be able to properly generalize the results to general rule than in determining sample size is to use the largest sample possible. The larger sample the more representative it will be from which it will be drawn. The determination of sample size should take into consideration the following which include;
1. The type of research
2. The number of variables to be studied
3. The methods of data collection
4. The methods of data collection
5. The degree of accuracy needed
6. The importance of the results
7. The financial constraints of the researcher.
1. Type of research
As a rule larger samples are always necessary the larger the sample the more to rep the population from which it comes provided its randomly selected it general therefore the minimum number of participants believe to be acceptable for the study depends upon the research involved e.g. for survey research there should be a list of 100 participants from each major sub-group and 20 –50 in each minor sub-group whose responses are to be analyzed.
2. Research hypothesis
If the researcher expects to find suit relationships its desirable to have large sample as possible in order to detect the effect if the sample is not large the wrong decision may be made concerning the validity of the hypothesis.
3. Number of variables being studies
The larger sample is needed for the studied that have many in the independent many extraneous variables are present.
4. Methods
If not accurate or consistent (reliable) men a larger number of participant will be needed to offset the sampling environment inherent in the data collection.
5. Degree of accuracy needed
The degree of confidence that can be placed in a statement that the sample data reflects the characteristics of the population is greater as the sample size increases.
6. Importance of the study results
In exploratory research a small sample size is acceptable because the researcher is willing to tolerate a larger margin of error in the results however in research that is not exploratory its imperative for the researcher to attain a sample larger enough so that sampling error is minimized.
Financial constraints faced by the researcher
Obviously the cost of conducting a study will limit the number of participants to be included in the sample it is the based to estimate the necessary sample size of the study.
NB: Although these are guidelines for obtaining a sample size required for the study there are other vigorous size for study for obtaining. These involve statistical computations however they are available some statistically computed tables which can be used by the researcher effectively.
SELECTING THE RESEARCH APPROACH
Research strategies are sometimes called the research designs the term research design has a general and specific meaning.
General
It refers to the presentation of the plan for the studies methodology i.e. data collection and analysis plans for analysis.
Specific
Refers to the type of the study broadly the study could be quantitative or qualitative. In quantitative the variable are pre-selected and defined by the investigator and data are collected and quantified i.e. translated into numbers and statistically analyzed with a view to establishing calls and effect relationships among the variables.
In qualitative research the investigator seeks to identity the qualitative (none numerical) aspects of the phenomenon under study from the participants point of view (emic) and not from the researchers point of view (etc).
The qualitative type of study refers to the methods and techniques of observing, analyzing and interpreting attributes patents, characteristics and meaning of specific contextual features of phenomena under study. Common specific types of studies/designs under quantitative type of study include, survey research, conditional research, cast study experimental research.
Under qualitative study, historical researcher, ethical graphic research case study research phenomenological research and grounded theory research.
Once again under qualitative study we can break it further in experimental Vs none experimental studies.
Experimental research studies
They manipulate variables that can reveal cause and effect. The knowledge of the enables to predict and control events. Experimental researchers are carefully designed to control all variables except those whose relationships is being explored.
None experimental research studies
Are used to;
(a) Describe and explain events and situations as they exist or they once existed.
(b) Evaluate products or they once existed.
(c) To develop innovations to obtain the most valid and accurate answers possible to research questions or hypothesis the researcher should make a choice of a relevant research design or method certain problems require experimentation. Others may be attached by one of the experimental strategies and yet others by the qualitative strategies.
The choice of the research design or method than influences the detail of the study design and the procedures for measuring variables.
The instruments for measuring instruments may be already available for adoption on the research may have to develop.
NOTE:
VALIDITY OF A STUDY
The term validity means the degree to which scientific explanations of a phenomenon i.e. findings of the study. Much the realities of the word in other words the validity of the study describes the soundness of the results or conclusions reached from the study.
There are 2 types of a study/evidence;
1. Internal validity
2. External validity
Internal validity of the study is the extent to which results can be interpreted to which the results of a study the degree are due to the independent variable that was manipulated or of interest in the study and not to other factors (i.e. extraneous variables). On the other hand external validity of the study is the extent to which results of the study can be generalized to other populations or to other situations or to other conditions in other words are the findings of the research study unique to the conditions under which the study was conducted or do the results apply to other situations or conditions. Thus the validity of a study deals with the accurate interpretability of the results (this is in malvalidity) and the generalizability of the results this is external validity.
EXPERIMENTAL RESEARCH METHODS/STRATEGIES
The purpose of an experimental study is to examine cause and effect relationships between variables in highly controlled settings involves selecting a dependent variable and men one or more independent variables that are predicted to be closely related to it. The independent variable also frequently referred to as the experimental or treatment variable is then manipulated by the researcher under carefully controlled conditions to determine any changes in the dependent variable (also known as the criteria or outcome variable.
True experimental designs/methods
These are in which a researcher has a great deal of control over the research situation only with the use of true experimental designs can cause interfered with any degree of confidence i.e. with these types of designs the researcher can have some confidence that the independent variable was the cause of the observed in the dependent variables. There are 3 essential ingredients of a true experimental designs.
(a) The researcher manipulates the IVS.
(b) At least one experimental and one control (comparison) groups are included in the study for comparison purposes.
(c) Participants in the study are randomly selected from the target population and then randomly assigned and either be experimental or the control group.
In discussing these true experimental designs we use the following symbol system letter
R = Random assignment of participants to groups or area.
E = Experimental group
C = The control group
X = Exposure of a group to an IV
- = No exposure of a group to an IV
O = Observation or measure of the D.V
(where subscripts would mean);
O1 = 1st measure/observation
O2 = 2nd observation/measure
The following are examples of true experimental designs.
1. Prretest - postest control group design.
3. Postest - only control group design.
4. Solomon – four group design.
5. Facprial - design
1. Pretest – post test control design
This design (also called between groups) design can be diagrammed as follows
Group Pretest IV Post test
R E O1 X O2
R C O1 __ O2
Procedure
i. Participants/subjects are selected randomly from the target population and assigned randomly to groups (i.e. experimental groups or control group)
ii. A pretest is given to both groups to check on the baseline of IV.
iii. Experimental group receives the treatment (IV intervention) and control group/comparison does not receive the treatment but may receive normal routine treatment or no treatment at all a post test is then given to both groups later after the intervention.
NOTE:
1. This research design is used if the researcher has some concern differences between groups still do exist even after randomization and therefore these initial differences will go undetected and may actually explain any differences in post test scores between the 2 groups refer that difference being due to infects of the treatment (IV)
2. This design is used also when the sample size is small (less than 40 participants in each group).
3. This design is useful in controlling any extraneous variable the researcher didn’t put into account.
4. Generalizability of results obtained from this design. Only apply to situations where a pretest is also administered to comparison group.
STATISTICAL ANALYSIS
If this design is use the researcher should handle data in the following ways;
1. If the groups are found to be equivalent as reflected in their scores on the pretest from comparison of the post test means for the two groups will be handled using a statistical test called the t - test for independent groups.
2. If the groups are not equivalent as reflected in the scores of the pretest from the posttest scores can be statistically adjusted to groups this statistical adjustment can be done in two ways;
(a) Get the differences of scores for each individual i.e. subtract the pretest score from post test score from each individual get the average score for each group its the mean difference scores that are compared using a key pretest for the independent groups.
(b) By using a statistical test called analysis of convenience (ANCOVA)
2. Post test only concern to group design
This is often used when the researcher is unable to locate or construct an appropriate pretest or when there is a concern that the pretest might sensitize the participants. This design can designed or illustrated as follows diagrammatically.
Group IV Post test
R E X O1
R C __ O2
Procedure
i Participants are selected randomly from the target population and assigned to groups or conditions randomly.
ii The experimental group is exposed to treatment or intervention while control group is not exposed to IV or may receive normal treatment.
iii A post test is given to both groups after intervention.
STATISTICAL ANALYSIS
You total up the scores obtained for each individual in each group and find the average its the average of the experimental group and average for the control test that are compared using at test for independent groups.
SOLOMON FOUR – GROUP DESIGN
Usually this design is used when the researcher suspected the pretest experience as an influence on the treatment (IV) and therefore the researcher wishes to test that suspicion.
The Solomon four group design is a stronger design than the post test only design but it requires more participants to be included in the study. The design can be diagrammatically represented as follows;
Group Pretest Treatment IV Post test
R E1 O1 X O2
R C1 O1 _ O2
R E2 _ X O1
R C2 _ _ O1
Procedure
1. Randomly choose participants from target population are randomly assigned to 4 groups.
2. Two of these groups are pretested and two are not pretested.
3. One pretested group and non pretested group receive the intervention i.e. xx.
4. The other 2 groups receive no treatment or no intervention.
5. All the 4 groups are post tested.
STATISTICAL ANALYSIS OF DATA COLLECTED
Results may be compared in 3 ways,
1. To test the effectiveness of the treatment (IV) for intervention the researcher compares the mean post test scores of the experimental group one with the mean post test scores of the control group one since the only thing that defers is the intervention or inclusion of the treatment.
i.e
using at - test
2. To test the effect of the treatment on groups that they didn’t receive the pretest but only receive the treatment or intervention the researcher would compare the results of the mean post test score of the experimental group 2 with the mean post test score of group 2.
i.e.
3. To test the influence of the pretest on later post test out comes a comparison or mean post-test scores of the control group one.
i.e.
Factorial design
The word factor is another name for the independent variable accordingly the word factional means more than one IV is being used in a study through a factorial design is used by the researcher when he/she wishes to study two or more variables simultaneously in the same study in order to study or understand the independent effect of each variable on the DV as well as the effects due to interactions among the 2 or more.
If e.g. the researcher is interested in investigating two teaching methods x & x2 and the researcher was interested in the gender whether males and females achieve differently under these two teaching methods the researcher would randomly selected the participants from the target population and randomly assign them to a group or a teaching method after exposing the groups to various teaching methods they are given a test on what they were taught and the score obtained give an indication of the result score (DV). This situation diagrammatically shown as follows.
1st IV (Teaching methods)
2nd IV (Gender: males Vs Female) M F M F
Here we have the groups altogether in the study another way of representing the same design is to represent on IV on the top and the other on rows (columns).
Teaching method
X1 X2
Gender Male
Female
Here in this diagram we have a 2x2 factorial design.
STATISTICAL ANALYSIS
1. Analysis of variance (ANOVA) is the most appropriate technique for a factorial design.
2. If the researcher wishes to control for possible initial differences. The researcher may employ a statistical technique called analysis of co-variance (ACONVA).
QUASI EXPERIMENTAL DESIGNS
These are those that are “almost true” except that the researcher studies the effect of the treatment (IV) on “intact groups” rather than being able to randomly assign individual participants to the experimental or control groups.
There are 3 common designs called Quasi ED’s namely;
- Non equivalent control group design
- Counter balanced design.
- Timer series design
Non equivalent control group design
This design is the most frequently used when randomization is not possible. It works because there is some control over the influence of extraneous variables through the use of control group. The design can be represented diagrammatically as follows;
Group Pretest Treatment (IV) Post test Gain scores
Randomizing E O1 X O2
O1 - O2
This design is similar to pretest, post test control group design of the 2 statements except there is no random selection of individuals from the population and the researcher simply uses intact groups who are put to experimental or control groups.
Procedure
1. No random selection of participants but the researcher can assign intact groups not individual.
2. Pretest is given to both groups to determine how nearly equivalent they are before the study begins.
3. The experimental group receives the intervention while the control group doesn’t.
4. Both groups are post tested after the intervention.
NOTE:
In the none equivalent control group design a pretest is quite essential and must be employed to provide any control for selection bias arising from the lack of random assignment of individual to either experimental group or control group.
STATISTICAL ANALYSIS
1. In order to a certain the effect of the intervention the 2 groups are compared on gains scores using a t-test for independent groups.
2. If this scores for the 2 groups on the pretest are grossly not equivalent then the researcher should proceed with the study and then use “ANCOVA” to which will remove these initial differences in the groups.
Counter balanced design
This design is also used with intact groups particularly while several treatments (IV’s) or interventions are to be administered to the same participants and these participants are very few although they can be broken into 2 groups if there are 3 groups to be studied etc.
The purpose of this design is to avoid any carry over effects i.e. any effects of exposure either to the 1st intervention involving to the 2nd intervention and the 3rd interventions.
NB: Each person in this ltd sample has to be exposed to each of the intervention and there might be some carry over effect from one tasks to another and there balancing the sequence being exposed to this intervention will eliminate any carry over effect.
The design can be diagramed as follows;
Experimental treatment (IVs)
Session X1 X2 X3
1st Half: Group A Group B Group C
2nd half: Group B Group A
Mean: 1 2
Procedure
1. Obtaining intact groups that are equivalent on other possible on any extraneous variables.
2. For the 1st half of the experiment half of the intact group is exposed to only one treatment.
3. For the next half the groups are rotated now being exposed to the other treatment that they were not exposed during the 1st half of the experiment.
STATISTICAL ANALYSIS
1. Compute the mean performance scores for all the groups on each treatment.
2. The mean scores on treatment are now compared for significance using a t-test for dependent (same intact group) groups. If there are more than 2 treatments to be exposed to the group then the researcher should use ANOVA.
Time series design
This design is useful when you have intact groups and you have one intervention to study and when you don’t need a control group for the study design is as follows;
Group Pre-observations Treatment(IV) Post-observation
E O1 O2 O3 O4 X O5 O6 O7 O8
Time series Time series
C O1 O2 O3 O4 ___ O5 O6 O7 O8
Procedure
1. Intact group is used for one individual is observed at a time.
2. Usually one group is necessary to the experimental group but sometimes we can include a control group.
3. Intervention is now introduced for the experimental group.
4. Postal observations are now made until there is no more.
Statistical analysis
1. The researcher may compare the pattern before intervention and after intervention.
x x x x x
x
x
x
D.V
x
O1 O2 O3 O4 X O5 O6 O7 O8
Observations
2. Compute the average of the 1st observations and average of the post observation and the t-test for each group.
NB: If the researcher has both experimental and control then the post observations are compared using a t-test for a dependent groups. If pre-observations are the same for both groups however if the pre-pose are not equivalent for both groups then gain observations are computed for each before at-test for independent groups is applied.
NON EXPERIMENTAL RESEARCH METHODS
Here there is no manipulation of no variations of conditions rather the describe something that has occurred for the researcher makes observations of what is happening.
There are 2 main approach to no experimental researcher namely;
- Ex post facto researcher
- descriptive researcher
EX POST FACTO RESEARCH DEVELOPMENT
There are many research situations or research problems in which its desirable to study cores and effect relationship but the experimental approach is not needed because manipulation of conditions and random assignment of individuals is impossible/can’t be handled/not acceptable.
The type which is more used is the ex-post facto design (Latin for “after the fact”). Another name for ex-post facto design is causal comparative design or re-trospective design. The purpose of ex-post facto design is to investigate whether one or more pre-existing conditions have possibly caused subsequent differences in the group of individuals in other words the researcher observes right at the outset that groups are different on some variable and then attempts to identify the major factors that have led to this difference i.e. both the affect (D.V) and the alleged cause (IV) have already occurred and there, the researcher attempts to study these relationship in retrospect e.g.;
As a possible explanation on the apparent difference in social adjustment among P.1 pupils a researcher might hypothesis that participation in a nursery school education was the contributing major factor the researcher would then select one of pupils who attended nursery and group who had not then observe their behaviour and look at indicators .___________then compare 2 groups on social adjustments if the pupils who were in nursery show/exhibited a higher level of social than those who did not go for nursery education then the researchers hypothesis would be supported.
NOTE:
Any interpretations of ex-post facto findings are tentative at based because the researcher doesn’t know whether a particular factor or variable is the cause of the behaviour pattern being studied. What this design does it to identify possible causes regarding the variations in behaviour patterns being observed these tentative causes can be verified in subsequent rigorous experimental studies.
STATISTICAL/DATA ANALYSIS
Usually the following analysis is carried for data collected for experiment.
1. Descriptive analysis
The researcher may compute the averages and standard variations of the data of various groups so long the data is quantitative or the data will be described/analyzed by computing and for comparison purposes these frequencies are changed into percentages.
2. If the researcher is testing a hypothesis from can be undertaken. If they are 2 groups and data is quantitative then the t-test is used for independent groups. If they are more than 2 groups to be compared from (analysis of) ANOVA will be used.
If the researcher has displayed frequencies and percentages for his researcher then to test for the significance of hypothesis he will use the Chi-square test.
3. If the study involves the relationships between variables then the researcher will use correlation analysis and there is a variety of them depending on the data being collected.
DESCRIPTIVE RESEARCH
The purpose of this is to describe the current state of affairs at the time of the study e.g. if you want to know how many teachers use a particular teaching method than you did simply ask a group of them to complete a questionnaire regarding the methods they use or interview them face to face or you simply walk into lecture room and observe.
The most significant difference between descriptive and ex-post facto or experimental research is that;
Descriptive research doesn’t include treatment (IV) or a control group. In D.R there we are not trying to show influence of variable in another all that the researcher is trying to do while using this strategy is to try to paint a picture or draw a picture of what is happening in other words the researcher is trying to describe things the way they are;
Categorization of D.R.
1. Correlational research
2. Survey research
3. Case study research
4. Exploratory research
CORRELATIONAL RESEARCH
When a researcher is interested in exploring relationship between a little variables then he will use a correlational research design.
One group of participants is involved in this type of design and each participant has data on each variable either already available e.g. UNEB results or the researcher at the ministers instruments to participants and scores responses into title to find level of standing on level of participant on each then the results are correlated is the researcher is handling 2 variables then he can choose correlation methods like two variable problems.
Pearson product moment correlation co-efficient
Spearman rank - order “ “
Point – beserial
Phic co-efficient
Contingency co-efficient
Cramer Phi co-efficient
If you have < two variable problems
Partial corr efficient
Multiple corr efficient
NOTE:
1. Sometimes a researcher may use a correlational design for prediction purpose i.e. having found the relationship between 2 variable the researcher may use this relationship to turn this _________ in the future for this purpose the researcher will use regression analysis.
2. Whenever the researcher finds the 2 variables related he/she should not hurry to conclude that one variable is cause of the other because correlation doesn’t mean causation the two variables may be related because a 3rd variable is related to both of them z related to both x & y.
z
3. A correlation co-efficient the value never goes beyond 1 (one) it can be less.
SURVEY RESEARCH
In a survey we handle a big number of participants and purpose is to find a sizable amount of information such as attitudes towards an issue beliefs opinions practices perceptions etc. usually in such survey questionnaires or interviews are used as instruments for collecting required information if the researcher wishes to generalize the results than the sample should be randomly selected from the samples. There are 2 types of survey;
Cross-sectional S.R
Longitudinal S.R
Cross-section survey research
Here the researcher first identify the criteria of obtaining a cross-section of the participants e.g. the criteria for obtaining a cross-section may be in terms of gender and in that case the researcher must identify a section of males and females then he randomly selects participants from each strata category of males and females all may be in terms of age e.g 18yrs olds 21 24 27 reaching appreciable gap.
Years in a programme 1st 2nd 3rd 4th selected randomly and administer the questionnaire and instruments and information is obtained at once with everybody.
Longitudinal survey research
This is meant to assess any design in the characteristics of interest taking the same participants and making observations of the same participants at more than one point in time the study may last a few years or more years depending on the topic of interest. There are 3 designs of research in this longitudinal survey research namely;
Panel design,
Trend design
Cohart design
Depending on the topic.
Panel design
Here after selecting participants randomly from the target population the same individuals are observed. Many names are studied at different points of time such as after intervals of a year , months e.g. after every month, year or week to see if there are any design from the time an intervention was given.
Trend design
First the researcher identifies the target population of interest and this target population design. It is not constant e.g. the researcher may be interested in 1st year entrantrants in university and in each year there is a group of 1st year coming and there changes then at one point in time (when students have reported for studies in 1st year researcher takes a random sample of 1st year he surveys them on the topic of interest e.g. regarding there views to 1.5 points to gins.
The researcher would then analyze the results of that sample, then when the next year comes a researcher again selects a sample from that new group of 1st year he analyses the results of that second group and compares them to see if there is any trend regarding the issue of interest. If the trend has not been emerged he can continue to 3rd years.
Cohort design
Select 1st year then again sample the same 1st years but a different sample i.e. those that you had not interviewed and it continues even in 3rd year that is if you are not satisfied or want more information.
Samples
SURVEY DATA ANALYSIS
If the richer has collected frequency counts regarding interest then those frequencies can Des into percentages but if the researcher is simply describing the characteristic the analysis stops at percentages however the researcher has put forward hypothesis then the significance of those frequencies will be tested using a statistical analysis called Chi-square (x2) test.
On the other hand if the researcher had numerical information obtained through scales questionnaires like agree, disagree then the appropriate statistics to use could be the mean, medium and the mode they must vary with the standard deviation you must give quota simply record the range.
CASE STUDY
A case study is always called for when the researcher want to study in detail a characteristic or an attribute in a group of individuals or an organization or an institution the focus is on a group although individuals make up the group and usually like this some unusual characteristic has been observed in that organization e.g. dropout of students in a district or if the company is always in debts i.e. low production in an industry or why a district performs best in UNEB exams.
NOTE:
In case studies the researcher normally uses as many methods of data collected on to cross check the authenticity of the data collected using one instrument. Also an interview or observations or document analysis for focus groups in addition. This tendency of using more than one method is called triangulation.
DATA ANALYSIS
Data may be handled basing on instruments like frequency counts therefore percentages if its a quantitative study the researcher may sort out information according to categories or themes.
Exploratory research
This can be viewed as being preliminary research into an area where little is known the aim is to paint a picture being studied its sometimes called community studies or needs assessment studies or baseline studies from these exploratory studies more vigorous studies are planned.
The data can be collected using questionnaire interviews or observation methods and analysis used should be appropriate to the methods of data collection.
QUALITATIVE RESEARCH
In the questionnaire methodology the researcher seeks to identify the qualitative (non numerical) aspects of the phenomenon understudied from the participants. Point of view (Emic) in order to interpret the totality of the meaning associated with experience or event or phenomenon in other questionnaire is characterized by findings that can be expressed and described verbally in other words questionnaire researchers tend to be concerned with quality and textual of explanatory rather than what identification of calls and effect relationship.
The objective of questionnaire is to describe and explain events and explanations but never to predict. Questionnaire as study people in there own locality or territory within naturally occurring settings such as the home, schools, organization etc these are open systems where conditions continuously develop and interact with one another to give raise to a process on going change.
Participants and researchers interpretation of events itself contributes to this process therefore prediction of outcomes is not a meaningful for qualitative researchers instead they ask questions about process such as what do people do when they form groups? How do people manage ______ in the work place or how people live with chronic pain what, how are questions used in questionnaire.
HISTORICAN RESEARCH METHOD (HISTORIOGRAPHY)
Here the research systematically investigates and analyses documents and other sources of information about a given problem behaviour or event in the past.
The researcher does so principally to answer the question what is the nature of events that have happened in the past this broad question may be narrowed down to determine how such history influenced current practice or to suggest ways in which current practices should be modified in the light of events of history.
Modern historical research tends to emphasis interpret of questions rather than there reporting. There are 2 types of sources of historical information;
Primary and secondary
Primary sources
Are original artifacts, documents interviews with those people who lived that time and records of the eyewitnesses of events oral histories diaries etc. The more informed the primary sources are the more reliable and valuable they are to the historical researcher.
Secondary sources
Are second hand information such as people who may have knowledge about the events but didn’t experience it themselves.
EVALUATION OF HISTORICAL SOURCES
The data for historical research should be subjected to two types of evaluation namely;
External criticism (validity of data)
Internal criticism (Reliability of data)
External criticism
Is concerned of authentically and genuineness of the data (validity of data) during this _________ many questions are asked by the researcher regarding the author of the document time and place in which the document was written the prevailing conditions of the environment in which it appears and where or not the document is forgery e.g. external criticism would seek to know whether the letter was actually written by the person whose sign appears there. The writing paper might be examined to know whether that type of paper was in existence during the life time of the letter writing.
Various methods including common dating can be used to determine the age of substances like the paper through false documents can be uncovered through the process of external criticism.
Internal criticism (data reliable)
Examines the credibility of the data or accuracy collected during research or it examines how trustworthy the source is as a true reflection of what happened actually in other words internal criticism asks the following questions.
- Did the event actually happen as it was described.
- How consistent is the writers account with other reports about the same events etc.
The findings of the historical study are presented as a well sensitized chronically i.e. a range in order of time happening. The entire manuscript is a verbal description of findings.
ETHNOGRAPHIC RESEARCH
This is investigation of cultures through an in depth study of the members of the culture.
It attempts to tell the story of people’s daily lives and to describe the culture of which they are apart.
The goal of the researcher using this method is to understand the indigenous view of their world (Emic view).
The insiders or ethnic view is contrasted to the outsiders (researchers) view called ethic view. The ethnographer is sensitive to the meanings that behavour, actions, events and contexts have in the eyes of the people involved.
Sampling and data collection
An ethnographic study begins with a planning phase in which general research questions are identified.
The researcher then enters the word of the participants in the study by becoming a part of the groups setting in order to gather the data. This method is called participant observation. Once the researcher has gained entry into the participant’s word he introduces a rappel with the participants. Once fully emerged the group the researcher chooses the appropriate method of data collection like participant observation or in depth interviewing or document analysis or a combination of these techniques as a check of the information collected. This method is called triangulation.
These activities of collecting data is also called filled research or naturalistic research and it requires the taking extensive norms of what it observes and the quality of notes taken will depend on expertise. Experienced or skilled researcher in quality researcher techniques will be able to dis-concern or notice more easily what observations need to be noted.
During observation the research will be bombarded with a lot of information institution plays an important role in determining which data to collect typically in ethnographic research the researcher selected site for a length period of time such as weeks, months even years in order to understand fully the phenomenon that is being studied.
ANALYSIS OF DATA
Its essentially analysis of the filled notes and interviews the notes may be in many cases superficial however during the processes of analysis of the notes the most appropriate method is content analysis.
Content of analysis involves identifying coherent and important themes and clear patterns or categories in the data i.e. the researcher looks for observation that tend to go together that are examples of the same underlying ideas or issue or concept.
Sometime this involves pulling together all the data that addressed a particular question.
Labeling the data and establishing data index are the first steps in content analysis. The contents of the data are being classified a classification system is critical because without it there is likely to be cause in handling the data.
Organizing and simplifying the completely of data into some meaningful and manageable themes of categories in the purpose of content analysis.
Content analysis may involve counting the frequency with what various categories occur the abstract throughout processes like institution, introspection and reasoning are involved in this process of data analysis interpretations of the meaning of the information collected is usually checked out with the informants and this is a process of migration.
NOTE:
A variation of ethnographic research is the case study where the research tries to capture the interest in a short period of time e.g. unemployment, law salaries in an institution, absenteeism in an organization prevalence of pregnancies, defilement or indeed where there is a concern which need some policy then a case study is unbroken both quantitative and qualitative methods of data collection.
S1 Tally f
35-39
31-34 ////
26-30 //// //// /
20-25 ////
NOTE
REAL (EXACT) AND APPARENT SCORE LIMITS
A grouped F.D may have score intervals containing whole numbers in called apparent limits because they allow gaps between the limits of each score intervals.
S1 f
35-39 3
30-34 5
25-29 11
20-24 1
Sometimes in research we may have data that is not whole numbered and cannot be placed in a grouped F.D with apparent limits instead we have construct the real or the exact score limit F.D.
To construct exact limits we take the average of he decimal numbers namely point 5 (.5).
To construct the real limits we subtract point 5 from the lower apparent limit of the score internal and men add points 5 to the upper apparent limit of the same scare interval this is done for all the apparent score limits that are given.
e.g in our e.g (pervious) we have the ff real SI limits.
REAL S1 LIMITS Tally f
34-5-39.5 /// 32
29.5-34.5 //// 54
24.5-29.5 //// //// 10
19.5-24.5 // 2
n =
Where you have the score e.g 24.5 let it fall on one line but not both lines i.e the decision is yours which line to put it but not twice.
GRAPHIC PRESENTATION OF DATA
More easily be conceptualized if its depicted graphically we can gain important information concerning a set of data merely looking at the visual display of the data.
Visual display of data can be handled for both qualitative and quantitative data.
RULES FOR GRAPHING F.Ds
There are conventions followed when graphing/constructing graphs for data these conventions are;
1. Graphs in research are called figures
2. The number of the figure under level is always found below the graph
3. Frequency (D (dependent .V(variable)) is indicated on the ordinate (y axis) fy Lx and values of the IV are on the abscissa (the x axis) L abscissa (x)
4. The ordinates should be ¾ as long as the abscissa (x)
i.e
3cm
4cm longer by 1cm
5. Break any axis whose number or values do not begin at zero.
15 25
10 20
5 15
0 20 0 1 2 3
gap is left to pull the line
6. Numbers or values are placed at equal intervals along the ordinate and the abscissa
GRAPHS FOR QUALITATIVE DATA
For qualitative data there’re two graphs that the researcher can choose from namely
(i) Bar graph
(ii) Pie chart
N.B. A researcher should choose one and only to represent the data.
ORGANISATION OF DATA
Once a researcher has corrected new data he/she is faced with task of arranging that now into some meaningful formal data before its analysed or arranged its called raw because its un processed statistical methods.
There are 2 basic ways of organsing raw data for ease of comprehension understanding;
By tables and by graphs.
TABULAR PRESENTAITON OF DATA
Row data can be organized in a table to form a frequency distribution. A frequency is the number of times un even occurs in a table therefore a frequency distribution is organized showing a number of times event (e.g) each category, each row score) occurred in the collected data.
Frequency distribution can be organized for both qualitative and quantitative data.
Frequency distribution for qualitative data
When observation are described in the form of words or labels or numbers that indicate class category (counts) or membership or attribute or characteristic then the data are called qualitative another name for such data is categorical data or nominal data.
Such observations only differ in kind not in amount.
Example of qualitative data are:
· Marital status-they differ in kind
· Political party affiliation
· Blood type
· Gender
· Socio econ status
To construct a frequency distribution categories are listed in the 1st column then a tally (number of times each category appears).
A tally is made for each nun appearance.
Then in the 3rd column tallies are added up for each category to give a frequency value for that category.
Example
A researcher asked a group of 50 university undergraduates each the indicate his/her religious affiliation the ff key was used by the researcher.
Key
C = Catholic
P = Protestant
M = Muslim
O = Other
The following were the results
Table 1: Religious Affiliation of university undergraduate
Religious Affiliation Talley
Protestant //// //// ////
Catholic //// //// //// ////
Muslim //// ////
Others ////
Frequency (f)
NOTE 1: Table 1 is called a one way table because it involves only one variable namely
religious affiliation this one way table is sometimes called a uni variate table
NOTE 2: Usually for research purposes frequency are changed into percentages and percentages are useful when comparing two groups or more an more groups have differing number of participants in them.
One may have so and another to participants.
To compute a percentage you use
n = number in that group.
NOTE 3: In reporting results of research we don’t show tallies we only show frequency and percentage.
For the preceding example we therefore have the following;
Table 2: Religious affiliation of university
Religious affiliation f %
Protestant 15 30
Catholic 20 40
Moslem 10 20
Other 5 10
NOTE: Sometimes a researcher may show the results of 2 variables on the same table we call this a 2 way table or cross tabulation table or a bivariate table.
Example:
Religious affiliation of males and females in a hall of residence.
Religious affiliation of two groups of university undergraduates
Religious affiliation f % f %
Protestant 15 30 21 35
Catholic 20 40 15 25
Muslim 10 20 9 15
Other 5 10 15 25
n = 50 n = 60
NOTE 5: Always percentage your results on the columns contains to independent
Variable.
FREQUENCY DISTRIBUTION FOR QUANTIATIVE DATA
For quantitative data there are 2 basic types of frequency distribution namely;
1. Ungrouped F.D
2. Grouped F.D
Ungrouped F.D
Simple, absolute FD for quantitative data first;
Identify the smallest and largest raw scores in the collected data.
Then make a table with scores arranged in order in higher to lower magnitude all potential row scores within the range must be included on tod score or column regardless of whether or not they were actually collected.
A tally is made for each raw collected the frequency count is then made.
Example
15 students obtained the ff scores in a statistics test as follows;
19 24 23 25 22 19 15 18 23 15
17 21 22 21
Construct a F.D for this set of scores.
Score
(x) Tally f
25 25 / 1
24 24 / 1
23 23 // 2
23
22 22 ///
22 3
22
20 20 0
21 21 // 2
21
20 0 because its absent
19 19 2
1 19
18 18 / 1
17 17 / 1
16 16 0 because its absent
15 15 2
total scores
NOTE: Sometimes the researcher would like compare scores distributions from 2 or more groups of participants of the study particularly with different sizes . The researcher does not compare them directly using frequencies instead he converts those frequencies to relative frequencies.
2 v=
There are 2 versions of relative frequencies which is got by dividing
(i) Proportion
(ii) Percentage
N.B normally we work to 2 decimal places.
Example
Score Relative frequency
X f Prop f: Percentage f
25 1 = 0.07 7
24 1 0.07 7
23 2 = 0.13 13
22 3 0.20 20
21 2 0.13 13
20 0 0.00 00
19 2 0.13 13
18 1 0.07 7
17 1 0.07 7
16 0 0.00 00
15 2 0.13 13
n = 15 add = 1:00 100 while added total
N.B
Sometimes the researcher would live to know the number of scores which fall at or below a given score such information is called cumulative frequency.
To construct a cumulative frequency distribution we begin adding the frequency of each score from the lowest score to the total of frequency below it, don’t these until we go to the top score.
Example
Cumulative frequency (cf)
25 1 15
24 1 14
23 2 13
22 3 11
21 2 8
20 0 6
19 2 6
18 1 4
17 1 3
16 0 2
15 2 2
n = 15
Score Rel CF
x f cf Prof cf % c.f
25 1 15 1:00 100
24 1 15 0:93 93
23 2 13 0.87 87
22 3 11 0.73 73
21 2 8 0.53 53
20 0 6 0.40 40
19 2 6 0.40 40
18 1 4 0.27 27
17 1 3 0.20 20
16 0 2 0.13 13
15 2 2 0.13 13
prop
GROUPED FREQUENCY DISTRIBUTION FOR QUANTITIVE DATA
F.D for ungrouped data are match more informative when the number of possible values of the variable is smaller (less than about 20).
Under this circumstances they serve as a straight forward method for organizing data other ways if the data are more than 20 then its better grouped frequency.
HOW TO CONSTRUCT A GROUPED F.D
The ff steps should be followed when constructing a grouped F.D
1. Decide how may class intervals (score) are needed, as a rule o thumb the large the number of observation then the more score intervals are needed however for research purposes we usually have score intervals ranging from 4-10 these are considered manageable. If they are more than 10 they become less manageable.
2. Find the lowest and the highest score than compute the range.
2. Find range
3. Divide the range by proposed score interval in order to get score width which is later added
Divide R by proposed SI in order to get internal (size score width)
N.B - I should always be connected to an odd number so that the middle score is
a whole number.
4. Begin listing score interval from the lowest score that you’ve collected or making sure the lowest score is included up to the highest score collected.
5. Beginning tallying your obtained score into their appropriate score interval.
6. Add the tally’s for each score interval to obtain the frequency.
Example
Consider the following scores obtained in statistics test
22 19 24 23 25 22 19 15 18
23 15 17 21 22 21
Construct a grouped frequency for this data.
Solution
(i) Let score (SI) intervals = 4
(ii) Compute the range
(iii) How many scores in the SI
Begin now grouping your scores
SI Tally f
24-26 // 2
21-23 //// // 7
18-20 //// 4
15-17 // 2
n = 15
E.G II
28* 29* 28* 27* 25 33* 29* 21* 36*
32* 33* 22* 29* 39 35 25* 31* 28*
27* 28*
1. SI = 4
2.
The lower score the lowest score interval must divisible by i without a reminder you can go the lower score.
Si Tally f
38-39 / 1
35-37 // 2
32-34 //// 4
29-31 //// 4
26-28 //// 5
23-25 // 2
20-22 // 2
n= 20
N.B
This can be separate by the i = i.e 20-25.
BAR GRAPH
This is a graph which displays qualitative data in the form of bars or rectangles separate bars represent each category of the variable height of the bar represents the frequency with which each category occurred.
How the construct
The following steps are followed;
1. The possible frequencies are always marked of on the vertical axis and categories are marked on the horizontal axis.
Categories
2. A rectangle (bar) is constructed over each category with the height corresponding with the frequency of that category.
3. Since the bars represented categories they are drawn separate from each other i.e not drawn joint to the others.
4. All bars (rectangles will have the same with or trickiness and distance between them should be half the briskness of a bar.
Should be equal
e.g
Religious affiliation f
Catholic 20
Protestant 15
Moslem 10
Others 5
The above results can be represented as bar graph as follows.
Figure 1: Religious affiliation of undergraduates at Makerere University
NOTE: When drawing a bar it should be drawn in ascending order or descending order i.e from highest to lowest.
PIE CHART
Sometimes the researcher may not be interested in using a bar graph instead he prefers a pie chart.
A pie chart is a circular graph which displays data as pieces of a pie that represent proportion of cases of categories of available these proportions add up to 100%.
Example
Taking up the previous e.g’s we have the following;
Religious affiliation f % out of 360 degrees
Catholic 20
Protestant 15 30 108o
Muslim 10 20 72o
Others 5 10 36o
either we go anticlockwise by starting with the lowest to highest but clockwise begin with the biggest to lowest.
NOTE
In case you are to highlight or comment on you remove it or isolate it from the rest this is called a split pie chart.
For research purposes there are 2 common methods for graphing quantitative data these are;
i. Histogram
ii. Frequency polygon
N.B: Both types of graphs can be used for ungrouped and grouped frequency data.
Histogram
This is similar to the bar graph except the vertical bars re constructed with no gaps between them and indicate that the data re quantitative each score (for ungrouped data) or each class interval for grouped data is represented by a vertical bar whose height corresponds with frequency of observations in the score or in the score intervals.
Examples (ungrouped data)
Consider the ff scores obtained by 11 students in a statistics test.
X f
25 1
24 1
23 2
22 3
21 2
20 0
19
Draw a histogram for the above scores.
3
f 2
1
0
19 20 21 23 24 25
Figure 1: scores obtained in a statistics test.
Example 2
Consider the ff scores obtained by 20 students in an introductory test
GROUPED FREQUENCY
S1 f
35-39 3
30-34 5
25-29 11
20-24
Figure 2 scores in introductory pre- test
12
10
8
6
4
2
0
20 - 24 25 - 29 30 – 34 35 - 39
Figure 2 scores in introductory pre-test.
Frequency Polygon
This is sometimes called a line graph its a variation of a histogram where to plotted points are joined by a line.
NOTE
Where the lines hanging space its always advisable to bring those hanging points down to the X axis.
Example.
X f
25 1
24 1
23 2
22 3
21 2
20 0
19
N.B at 18 and 26 since they are out of range they have no star to indicate the score try just help the line graphs not the hang.
Example 2
S1 f
35-39 3
30-34 5
25-29 11
20-29
e.g
Consider the ff data on introductory pretest for male and female students construct a frequency polygon from
S1 Male Female
f f
35-39 3 2
30-34 5 4
25-29 11 8
20-24
Fig. Introductory pre-test scores for males and females.
MEASURES OF CENTRALITY
When any a summary of data is required the entire distribution is not necessary instead a statistical measure that reflects a typical or an average characteristic of a frequency distribution is computed such an average is referred to as a measure of central tendency or simply a measure of centrality.
Averages for Quantitative data
For quantitative data the 3 commonly used measures of central tendency or averages are;
- The mean
- The median
- The mode
The mean
This can be computed for both ungrouped and grouped data mean for ungrouped listed data;
For ungrouped listed data the mean is obtained by adding up all observations and men dividing that sum by the number of observations collected. Mathematically is represented as follows :-
Mean = Sum of all data conservations
Total number of data (observation)
i.e = mean also called X-bar
sigma
total number of observations
= scores
Example 1
X
7
7
6
5
4
4
4
i.e
Example II
25
25
23
22
22
22
21
20
19
The mean for data in ungrouped frequency distribution.
NOTE
Quit often the data are listed with the frequency of accuracy in such a case a slightly modified formula for the mean is used namely.
The previous example modified
6 1 6 Here
5 1 5
4 3 12
3
MEAN FOR DATA IN A GROUPED FRQUENCY DISTRIBUTION
NOTE: There are many formulas that can be used to compute the mean when data in a grouped frequency distribution however to easiest formula to use is to take the mid point of each score interval as a representative score for that score interval when this is done the same formula used for listed frequency distribution is used to compute the mean.
X – get the lower score interval the rest add 5 to get the rest.
i = 20 21 22 23 24 = 5
Example
S1 f Xmpt FXmpt
35-39 4 37 148
30-34 6 32 192
25-29 11 27 297
20-24 22
Another
where
where
.
Example II
S1 f Xmpt FXmpt
24-26 2 25 50
21-23 7 22 154
18-20 4 19 76
15-17 ef =n 16
where
Example III
X f Xmpt FXmpt
25-29 2 27 54
20-24 2 22 44
15-19 4 17 68
10-14 1 12 12
5-9 0 7 7
0-4 1 0 0
ef=n= 10 187
THE MEDIAN
It’s the point or score that divides to distribution into two halves/halfs
Median for ungrouped listed data
To find the median for ungrouped listed data first make sure that the data are listed in order from the highest to the lowest score the by inspection the median is the middle score in the distribution.
Examples I Example II
7 7 7
5 re-arranged 6 3 re-arranged 76
3 5 median 4
4 4
6 3 5 4
6 3
4
Median for ungrouped and grouped frequency distributions for both ungrouped and grouped frequency distribution of data the median is computed by using the following formula:-
Mdn =
Where L = exact lower limit of a score or a score interval containing median
i = score width or a number of scores in the score interval
n = Total frequency
= a locater where the median lies
= cumulative frequency below the score or below the score interval containing
the media
fw = the frequency for the score the frequency with in the score interval
containing the media.
Example
SI (score interval)
X f cf
16 2 8
15 1 6 (if found here at the cf)
14 2 5 medium lies here
13 1 plus 3
12 2
Example
Score f cf
10 3 19
9 1 16
8 2 15
7 2 13
6 5 11
5 6
Exercise
X f cf S1 f cf
7 2 7 35-39 4 25
6 1 5 30-34 6 21
5 1 4 25-29 11 15
4 3 3 20-24 4 4
3 1 1 25 28.36
THE MODE
This is the most frequent occurring score in the distribution.
Mode for listed scores
This is found through inspection of the scores them identifying the score which appears more than others.
(They can be more than one) e.g i
X
7
7
6
5 mode = 4
4
4
4
3
e.g ii
5
5 MO = 5, 4
4
3
3
Mode for ungrouped frequency distribution;
To find the mode of this F.D type inspect the column of the frequency located the highest frequency the score corresponding to this highest frequency the score corresponding to this highest frequency is the mode.
X f
7 2
6 1
5 1 Mo = 4
4 3
3 1
Mode for grouped f.D
For a grouped f.d there are 2 types of modes namely;
Crude mode
Exact mode
Crude mode
To find this first locate the highest frequency in the distribution and a score interval corresponding to that highest frequency is called the model score interval.
The mid point of that score interval is the crude mode.
E.g
S1 f
Post modal
Score interval 35-39 4
30-34 6 Crude mode =
modal score interval 25-29 11
Pre-modal score
interval 20-24 4 Crude Mo= 27
Exact mode
Its computed than obtained through inspection.
Exact mode =
Where;
L = Exact lower limit of score interval where the mode fall
i = is the score width or size number of scores in a score interval.
d1= is he difference between the frequency of the modal score interval and the
frequency of the pre-score modal score interval
d2 = is the difference between frequency of the modal score interval and the
frequency of the post modal score interval.
Exact mo=
E.g II
SI f SI f
24-26 2 25-29 2
21-23 7 20-24 2
18-20 4 15-19 4
15-17 2 10-14 1
5-9 0
0-4 1
Crude 22 =
Crude 17
Exact 15.5
Mode =
E.g
i exact lower limit of the si where to mode falls
di to difference between the frequency of the mode to press.
Which measure of central tendency to use
Researcher should used the most appropriate measure of central tendency when reporting when reporting results the appropriate measure of central tendency depends on shapes of the data distribution.
e.g when you graph the collected data.
Symmetrical
f distribution
normal
distribution
(or before shaped)
0 Scores
mean, median, mode.
With this shape what you are likely to find mean, median, mode when instead because it comes into further computations where the researcher may want to like the variance analysis.
Skewed distribution (abnormal)
f (positively skewed distribution )
Scores
Median
Mode
Mean
Skewed
Distribution
f negatively
Skewed
distribution
0
0 Scores
Mode
Mean Median
The median is one position i.e the middle its reliable.
A second method of deciding which
The quickest is when using a computer is to compute 2 measures of central tendendecy namely;
- The mean of the median and perform the following operations.
(i)
The first thing out of this test is the distribution is normal, use the mean.
(ii)
It means the mean is higher i.e distribution is positively skewed therefore use to median.
(iii)
The median has a higher volume compare to the median i.e the distribution is negatively skewed use the median.
NOTE:
The mode is the most appropriate measure the report if the researcher handling quantitative data.
Example
Religious affiliation f
Protestant 15
Catholic 20
Moslem 10
Others 15
MEASURE OF VARIABILITY
While measures of central tendency tell as what value is most common or typical in distribution measures of variability are needed to tell us how different most scores or cases are from the typical score measures for variability for quantitative data include the following;
1. Range
2. Quartile Deviation
3. Standard deviation
RANGE
The range may be defined as the difference between the two most extreme scores in the distribution the range thus defined is called to exclusive range or the crude range.
Range Crude
NOTE: There is also inclusive range which is obtained.
NOTE: The range is always reported in research together with the mode.
Interpreting the range
There are many ways of interpreting the range but the following is the simplest.
A range that covers about quarter or less of the total raw score scale generally reflects homogeneous distribution of scores.
Example:
In the following examples computer the crude and inclusive range for each and interpret your results
E.g 7 7 6 5 4 4 4 3
RC = 4
7-3+1 inclusive range = 5
Hence the inclusive range is homogenous.
Example 2
X f
7 2
6 1
5 1
4 3
3 1 (here only bother about frequency)
Example 3
28 25 36 29 31 28 34 33 32
38 26 28 28 29 24 35 27
30 27 21 32 37 28 23 22
Find both crude and inclusive ranges and interpret the results.
Crude range
Inclusive = 38-21
= 17+1
= 18
There is heterogeneous distribution of scores.
RANGE FOR GROUPED FREQUENCY DISTRIBUTION
For grouped frequency distribution the range is computed as follows
1. RC= upper apparent limit of the highest score intelia minus lower apparent limit of the lowest score interval.
Ri = inclusive range = or Ri = Real upper limit of the highest score interval
minus real.
Lower limit of the lowest score interval example.
S1 f
35-39 4
30-34 6
25-29 11
20-24 4
= 19
Ri = RC + 1
19+1= 20
39.5-19.5 = 20
Interpretation
distributed heterogeneous.
QUARTILE DEVIATION (QD)
Its also known as semi inter quartite range (SIR)
Score here are coild out liers
25%
- Q3
- Q2 Medium
75% - Q1
50%
25%
Where
We use the same pattern of formula as for to median.
Example
X f cf
7 2 8
6 1 6
5 1 5
4 3 4
3 1
QD is a most table measure of variability than the range and is appropriate whenever the median is reported as a measure of central tendency.
The Standard Deviation (SD)
SD is a measure that indicate the average deviation of all scores in the distribution from each individual score the difference is deviation score.
NOTE: SD is a useful index for measuring a degree of variability in a distribution or for campaigning vain ability in different distribution.
NB. 4. SD in research is always reported together with the mean of the distribution.
Examples
E.g
SD for ungrouped listed data we use the definitional formular of SD.
i.e
X Deviation scores Deviation score squared
5 5-4= 1 12=1
5 5-4= 1 12 = 1
3 3-4= -1 -12 = 1
3-4= -1 -12= 1
(Si) X Deviation score Deviation score square
7 7-5=2 2- = 1-4
7 7 7-5=2 22 = 1-4
6 6 6-5 = 1 12 = 1
5 5 5-5 = 0 02 =0
4 4 4-5= -1 -12 =1
3 4 4-5= -1 -12 = 1
4 4-5= -1 -12 = 1
3-5=-2 -22 =
SD for ungrouped listed scores with these frequencies
We use a modified formula of the preceding example which is
E.g
X f fx
5 2 10 5-4=1 1 2
3 3-4= -1 1
X X f- fx
7 7 2 14 7-5=2 4
7
6 6 1 6
5 5 1 5 5-5=
4 4 3 12 4-5= -1 1
4 3 3-5= -2 4
3
SD for grouped frequency distribution.
When scores have been put into groups the 1st thing the researcher does is to compute the mid points score for each score interval its this mid score that will be used to subtract the mean in order to get the deviation scores. To formula then for SD becomes
Example
ST f Xmpt fxmpt Xmpt
35-39 4 37 148 31-29=8 82 =64
30-34 6 32 192 32-29=3 32 = 9
25-29 11 27 297 22-29=2 -22 = 4
20-24 4 22 88 25-29 = 2 = 49
N = 55
4 ( 64 ) = 256
6 ( 9 ) = 54
11 ( 4 ) = 44
4 (49 ) = = 550
SD =
=
=
SD = 4.69
Interpreting the SD
Two factors influence the size of the SD namely;
The range and the distribution of scores with the range and because both range and the SD are measures of a groups variability then larger or bigger ranges will produce larger SD’s. a wide range and a wide SD both reflect Heterogeneous ones reflect a homogenous distribution of scores to decide whether to SD reflects homogenous or heterogeneous distribution of scores the researcher should inspect the following;
(i) First compute the range of the distribution.
(ii) Compute the SD of the distribution if the computed SD is or less of the range (i.e SD ) then this indicates that most scores are clustered within the area i.e. homogenous distribution of scores.
Comparing variability between sets of data
At times the researchers needs to compare the variability of different sets of data , this data may or may not be in the same units in such cases/circumstances the SD of the group must first be divided by the meaning that group the resulting measure is called the co-efficient of variation
i.e. CV =
It’s the CV’s that are directly compared.
NOTE:
Sometimes CV is expressed as a percentage CV x 100 = .
In that we now call this percentage of CV the co-efficient of relative variation which is CRV.
In terms of proportion
Example
Performance of school X at A’ level examinations in 2 subjects is as follows;
SD
Maths 50 15
Literature 80 20
Which subject indicates more variation in performance.
= = .
NOTE:
Measures of variability for Qualitative data
For Qualitative data we use the mode as a measure of ontral tendency accompanying this measure we use either
(i) variation ration (VR)
(ii) or index of qualitative variation (IQR) as a measure of variability.
Variation ratio
Variation ratio measure the extent to which observations are clustered together round the mode its computed by looking at the proportion of observations that lie at the modal category or class.
When we subtract these proportion from one then we have a measure of variation.
i.e. VR = 1 -
Where fm = frequency at the modal category
n = total number of observations.
Example
Consider the e.g. of University Undergraduates religious affiliation.
Rel Affiliation f
Protestant 15
Catholic 20 - mode (Catholic)
Muslim 10
Other 5
n = 50
VR = 1 -
=
=
= 0.6
or 60%.
Interpretation
Our Vr indicates that 60% of the observations are not in the modal category hence there is more variability in distribution (heterogeneity) among university undergraduates.
INDEX OF QUALITATIVE VARIATION
The index of Qualitative variation is sometimes simply called index of dispersion (ID). It measures the degree of homogeneity or heterogeneity of attributes or qualities possessed by a given number of elements IQV or ID can be interpreted more readily because its value varies from zero (meaning no variation to the value of one meaning maximum amount of variation possible).
Formula of IQV is given by;
IQR =
Where K = number of categories of the variables
n = number of observations in all categories
= sum/total of squared frequencies for categories.
Example
Religious Affiliation f f2
Protestant 15 400
Mode Catholic 20 225
Muslim 10 100
Others 5 25
n = 50 .
IQV =
IQV =
IQV =
=
= 0.93.
Measuring relationship between variables
Very often researchers are interested in the extent where two or more variables are related an index that describes the extent to which two or more sets of data are related is called correlation co-efficient. This index is expressed as a number which ranges between -1.0 and +1.0 any the beyond 1 something is wrong.
Interpretation of a correlation co-efficient
There are 2 ways to interpret a correlation co-efficient namely;
1. Verbal description
2. Co-efficient of determination.
Verbal description
Its also called the eyeball method of interpretation and it describes the ranges of a correlation co-efficient.
Example
Value of corr efficient Verbal description
.80 & 1.00 Very strong (very high)
.60 & .79 Strong (or high) relationship
.40 & .59 Moderate
.20 & .39 Weak (low)
:00 & .19 Very weak (negligible)
NOTE I:
A positive value of a correlation co-efficient means that the two variables go hand in hand in the same direction i.e. if one variable increases the other also increases if the decreases it also decreases.
NOTE II:
If there is negative correlation co-efficient, it means two variables vary or go in the opposite direction i.e. when one increases the other decreases.
Zero correlation where the two variables are not related at all.
NOTE III:
The degree of the relationship is indicated by the magnitude indicated.
Co-efficient of determination
A sounder method of interpreting a correlational co-efficient is to square its value this squared value is known as the co-efficient of determination. It tells us how strongly two variables are related or associated with each other by indicating the proportion or percentage of variation in one variable that can be accounted for by the other.
Example
Suppose the relationship between academic achievement and motivation is 0.40 its moderate.
Co-efficient Det: (0.40)2 = 0.16 - proportion or percentage
16%.
Motivation here is 16 percent to academic performance.
The remaining proportion is called correlation of alienation or co-efficient of none determination i.e. 1.0 - 0.16 = 84.
The 84% are the extraneous variables. Other factors that influence test or academic performance.
Correlation co-efficient between 2 variables both quantitative
When a researcher collects data from each participant from each of the two variables which are both continuous can be represented qualitatively from the appropriate correlation co-efficient use is the Pearson product moment correlation co-efficient and its represented by the small letter r. Sometimes we call this correlation Pearson r.
There are many formulae to use for computing this correlation co-efficient;
One of the formulae is;
Where X 1st variable
Y 2nd variable
n number of scores being handled
E.g.
The mathematics achievement (X) of 5 students whose social economic status (y) was also measured.
Was as follows;
Student Maths SEs
X Y
A 3 4
B 5 2
C 6 5
D 9 8
E 12 6
Is there any relationship between SEs and achievement in mathematics
X Y X2 Y2 XY
3 4 9 16 12
5 2 25 4 10
6 5 36 25 30
9 8 81 64 72
12 6 144 36 72
.
Therefore;
Or
=
196-175
= 21
Interpretation
Description
There is high positive relationship between social, economic status and performance in mathematics.
= 0.4409 or 44%.
The contribution of social, economic status is 44% the remaining 56 is other factors.
Although there is a high positive relationship between SEs and performance in maths the contribution of SEs is only 44% the performance in maths.
Spearman’s rank – order correlation eo-efficient
Spearman rank order correlation co-efficient is a special form of Pearson correlation co-efficient. Its appropriate when data has been already been ranked.
It can also be used if the researcher can rank the data collection
The formula is given by
Where D = the difference between a pair of ranks
n = number of pairs of ranks
6 = is constant
How 6 is obtained
NB:
To use this formula if the formulas are not ranked first rank the score.
When ranking we give the highest score rank number one.
NB 2:
If there are scores which are the same they are given an average rank each is given an average rank the difference is between the paired ranks is obtained then squared these values and substituted in the formula.
Example
Maths (SEs)
X Y Rank x Rank y
3 4 5 4 1
5 2 4 5
6 5 3 3 0
9 8 2 1 1
12 6 1 2
1
1
0
1
65%
64% of SEs effect on maths performance is 64% the remaining percentage is accounted for other extraneous variables.
E.g.
7 12 1.5 1 1 25
7 7 1.5 2 0 0
5 8 3 3 9
4 3 4 5 1 1
2 5 5 4 9
NOTE:
Row P = meaning
Spearman
can be computed using the Pearson r formula.
Pearson formula is;
Maths SEs
X Y
3 4 5 4 25 16 20
5 2 4 5 16 25 20
6 5 3 3 9 9 9
9 8 2 1 4 1 2
12 6
= 10
Point - Biserial correlation co-efficient
Sometimes a researcher has 2 variables which he wants to find the relationship, these 2 variables however are quite different;
(i) Quantitative and can be expressed in numerical terms e.g. academic achievement in a subject in school.
(ii) A category variable/normal variable which can be expressed exactly at 2 levels in other words that category variable is a dichotomous.
Examples of a dichotomous variables are;
Gender - male, female
Smoking - a smoker Vs non smoke
Virginity - either you are or not.
This dichotomous variable can be represented or expressed as numbers where one category will be given a zero and another one.
O = male
I = female
(NB): It doesn’t matter how you code this.
Once a relationship has been found point by serial (rpb), then the sign of rpb (+ or -) will indicate which level was given a one and which one has given a zero.
A positive rpb is always associated with a (one) 1.
(NB): There are many formulae for computing rpb but for simplicity we can still use the formula for Pearson r.
E.g
The following are grades on an English language achievement at O’level
Candidate Grade (Eng. Ach)
John 1
Peter 2
Joseph 2
Moses 1
Jane 1
Sarah 2
Ann 4
Rose 5
Susan 2
Agnes 5
Determine the relationship between gender and English language achievement and interpret your results.
Let gender = X
Achievement = Y
Gender male = 0
Female = 1
Gender Grade
X Y X2 Y2 XY
0 1 0 1 0
0 2 0 4 0
0 2 0 4 0
0 1 0 1 0
1 1 1 1 1
1 2 1 4 2
1 4 1 16 4
1 5 1 25 5
1 2 1 4 2
= = 0.54
Interpretation
0.544 is a moderate positive relationship between gender and performance in English more specifically, female tend to do better than males in English. Performance in English can only be attributed to either being male or female to the extent of 30% other factors account for the remaining percentage.
In correlational researcher you should always have a minimum of 30.
The Phi co-efficient
Sometimes a researcher wants to find out the relationship between a truly dycortomous categorical variables both of them are the dichotomous.
e.g. the relationship between gender, male, female, smoking, smoking or non smoker.
The relevant correlation co-efficient is Phi co-efficient in order to compute this correlation the researcher makes a code for each dichotomous variables namely he gives a zero and one to each level of the dichotomous variables.
Then the Pearson formula can be used to compute the Phi correlation co-efficient.
Example
A researcher interviewed people who had just completed their chakamchaka course to indicate their preference for either the movement or the multiparty type of governance in Uganda.
The following results were obtained;
Gender Political preference
Sarah Movement
Marga Movement
James Multiparty
Peter Movement
John Multiparty
Rose Multiparty
Mark Movement
Dorothy Movement
Joseph Multiparty
Determine the relationship between gender and political inclination interpret you results.
Let X = gender, Y = political preference
Female = 1, Male = 0, movement = 1 multiparty = 0.
X Y X2 Y2 XY
1 1 1 1 1
1 1 1 1 1
0 0 0 0 0
0 0 0 0 0
0 1 0 0 0
0 0 0 0 0
1 1 1 1 1
0 1 0 1 0
1 1 1 1 1
=
=
=
= 0.44%
Interpretation
Their moderate positive relationship between gender and political preference.
Thus indicating that females tend to be inclined towards movement while males are inclined multiparty.
Co-efficient of determination
Which is
o.17 or 17% of the preference to movement can be accounted by gender specifically female the remaining are other factors that make people prefer movement.
Partial correlation co-efficient
PCC measures the amount of association between 2 variables after the effects of the 3rd variable on the 1st 2 have been removed (partialed out).
The formula for PCC is;
NOTE:
In order to use this formula 1st the researcher must first find a correlation co-efficient between 2 variables at a time being handled at a time.
Correlation between variable 1 and variable .
Correlation between variable 1 and variable
Correlation between variable 2 and variable using Pearson correlation co-efficient.
NOTE: 12.3
This means the number before the dot means remained from the correlation.
NOTE: Interpretation of a partial correlation
The interpretation is the same as the Pearson .
Example
The researcher found out the following; relationships between the variables
· Correlation between achievement (1) and intelligence (IQ) (2): = Corr = .50.
· Correlation between Achievement (1) and study time (3): corr = .40
· Correlation between IQ (2) and study time (3):
What is the relationship between achievement and IQ controlling for the effect of study time.
Interpret your results.
=
=
= =
Interpretation
Pure relationship has gone up its positive and high relationship. This indicates that if study times is held constant (i.e. every student in the sample studied the same number of hours) to the relationship between achievement and iQ becomes positively higher than when students are heterogeneous with respect to study time. More specifically iQ contributes 50% of its effect to the performance or achievement.
Assignment;
(a) What is the relationship between achievement and study time controlling for the effect of iQ (i.e. ).
(b) What is the relationship between iQ and study time controlling achievement
( i.e. )
Interpret your results
=
TESTING HYPOTHESIS
The testing of a hypothesis provides a means of testing whether the difference is in a dependent variable should be attributed to an effect of the independent variable.
BASIC CONCEPTS
In testing hypothesis there are some basic concepts which are used which include;
1. Null and Research hypothesis
Much research start out with the idea that according to some practice or theory certain results should be expected to appear in the study which is called a prediction of the out come of the study but technically called a hypothesis.
Null hypothesis (chance hypothesis)
This predicts that if there is any difference in the outcome between groups in the study this difference is due to chance factors due to extraneous variables.
It predicts no differences between groups or relationship between variables.
NOTE:
Usually in testing a hypothesis the researcher indirectly handles the null hypothesis because all statistical tables are based on the null hypothesis the reasoning behind is once the null hypothesis is rejected them the researcher accepts the researcher hypothesis. The researcher hypothesis states that the outcome of the study is a result of the independent variable handled and therefore no chance factors have entered into the results.
A research hypothesis could be directional or non-directional.
2. Level of significance
In testing a hypothesis a decision is made between now and a research hypothesis this is done by calculating the probability of the obtaining results in a sample occurring the chance if the null hypothesis were true.
This probability is called level of significance. For researchers the following levels are acceptable.
(i) P = .05
(ii) P = .01
(i) P = .05 has of existing hence more extraneous variables.
(ii) P = .01 has chance of existing hence few extraneous variables.
3. Degrees of freedom (df)
The interpretation of a statistical test is dependent on the degrees of freedom degrees of freedom concerns the number of values that are free to vary. Procedures to calculate the degrees of freedom for a particular test are usually included in the description of the test.
The concept of degrees of freedom can be illustrated with the following example. Suppose you are told that a set of three scores adds up to 18.
X Total is a fixed value and therefore in statistics its called a constraint
Y placed on the problem.
+Z
18 Question: What are those numbers XYZ that add up to 18.
We are free to choose any numbers provided the total is 18.
e.g. X = 5, Y = 6,
you can choose any 1st 2 number but the last number is fixed because of the total.
=
.
n = total observations
1 = restrictions
df = degrees of freedom
4. One tailed Vs Two Tailed Test
NOTE:
When the researcher predicts the direction of the results, she makes one tailed test of significance i.e. the results are expected to go in one direction either left or right.
For the diction result on the left the hypothesis (researcher) may be as once, slower, lower etc. when the direction is on the right the researcher will use words like faster higher better.
On the other hand when the researcher doesn’t not make a prediction he makes a two tailed test which is non dictional test though it doesn’t suggest that there is going to be a difference.
Variance
When you take the mean from a row score and then you sum them up and you divide by the total of scores
We have the average of the deviation scores squared which is called variance.
NOTE: If take the square root of variance. We have another concept called the standard deviation.
Testing hypothesis concerning frequency data.
Sometimes a researcher handles data that are in a form of frequency counts or data already in form of percentages or proportions but can be converted to frequencies or occurring in different categories to test hypothesis connected with such data we compare the observed frequencies (frequency observed) with the expected frequency in relation to the problem being handled the statistical approach to this testing of the hypothesis is called the Chi square test.
The general formula is;
= observed frequency of a given category.
= expected frequency of a given category.
= summation out all categories (do it fro all category and get the overall).
obt = obtained.
=
= number of rows
= number of columns in the problem being handled.
NOTE:
If any or if either turns out to be zero ignore the one giving you a zero and use the other to get you degrees of freedom .
e.g
=
= (2)
.
Types of Chic-square tests
There are two types of these;
(a) Goodness of fit test (i.e. only one variable is being handled in the study).
(b) Test of independence (i.e. two variables being handled).
Goodness of fit-one variable for Chic-square test.
This is used when we have 2 or more categories or levels of one variable the interest whether the frequencies that we obtain for each category in our sample fit into or merge or correspond with the expected frequency in the target population in question as specified by the null hypothesis (i.e. the expected frequencies in the target population will be equally distributed in each of the categories taking into account the total frequencies we have collected from the field:
Categories
A B C Total
Observed : 10 15 20 45
Expected 15 15 15
Example
A researcher asked 120 students to indicate which teaching method at University they thought is the best 55 of them preferred the seminar method 35 preferred the lecturer method and 30 preferred the tutorial method.
Question: Test the hypothesis that there is no significant difference in preference for the 3 teaching method
Use P = .05.
Solution
Teaching methods
Seminar Lecturer Tutorial Total
Observed 55 35 30 120
Expected 40 40 40 120
= Seminar Lecturer Tutorial
+ +
= + +
= + +
X = + 0.625 + 2.50
corresponding expected figure.
=
.
NOTE: Once a Chi-square has been computed this value has been computed with the value (critical) which is given the table. With the appropriate degrees level of freedom and appropriate level of significance.
From Table 4:
Levels of significance
One tail
0.025
Two – tail
0.05
1 3.84
2 5.99
If the value of Chi-square observed is equal to a greater than the critical value of Chi-square then the results are not due to chance they are genuine results thus statistically significant in the example, the observed value is greater than the critical value.
Therefore we reject the null hypothesis and conclude that there a significant difference in the preference of students teaching methods given at the university. Hence more students prefer the seminar method.
Chi-square test of independence (Two variables)
The CST for impendent is used to measure the relationship between two variables to the question being asked is whether 2 variables are independent (unrelated to) of one another. The same formula is used for computing the Chi-square.
expected frequencies for each category are computed in the following ways;
(for a particular category) = row total x column total (for that category
Grand total
Example
An undergraduate sample of 70 males and 70 females were asked whether or not they prefer a line up system in their hall of residence. The following responses were collected.
Preference for line up system
Yes No
Gender Male 40 30
Females 60 10
Test the hypothesis at .05 level of significance and preference for the line up system is independent of gender.
Gender Yes No marginal totals
Male 40 500A 30 200B 7070
Female 60 500C 10 200D 70
Marginal total 100 40 140
Category :
=
=
=
.
=
= 1x1
= 1 .
.
Reject Ho (i.e. reject the hypothesis that preference for line up system is independent on gender that is preference for line up system is dependent on gender (for a researcher hypothesis we use is a one tail which is in preference).
To pinpoint where the preference is dependent on gender we examine those categories which contributed most to the overall value to the Chi-square.
More males do not want a line up system compared to females.
Explanation; can be that in Uganda culture is that man want to be served by woman.
TESTING HYPOTHESES ABOUT THE DIFFERENCE BETWEEN TWO SAMPLE MEANS
The common problem in research is to determine whether 2 groups do or don’t differ on the independent variable of interest the relevant statistical test for such a situation is the t-test. The t-test has 2 forms namely;
(i) The t-test for dependent (same group/ matching group correlation) group.
(ii) The t-test for independent (i.e. entirely separate) groups.
In both form the t-test value is computed and then with significance level of chosen and the appropriate degrees of freedom the critical value of it is obtained from the t-table.
If the computed t-value ( is greater than or equal to the t critical value then the results are declared statistically significant i.e. the difference between the means of the groups are not due to chance factors but the difference is a result of the independent variable handled in the study.
The t-test for dependent (same group/matching/correlated) groups
If the same individuals receive 2 different treatments (IVs) in a study (i.e one treatment after the other repeated design)
Or when the research design involves too much groups on one or more relevant variables then testing the difference between 2 means involves the t-test for the dependent or matched groups.
The formula is
d = difference between each pair of scores
n = number of pairs of scores.
Examples
Scores on digit memorisation before and taking alcohol are as follows;
Before After
Participant Cons. Alcohol Cons. Alcohol
1 6 3
2 14 8
3 8 4
4 4 6
5 16 9
6 7 2
7 19 12
Test the null hypothesis that there is no difference between digit memorisating under the 2 conditions.
Use .05 level of significance
Before After
Cons Alcohol Cons. Alcohol D D2
6 3 3 9
14 8 6 36
8 4 4 16
4 6 -2 4
16 9 7 49
7 2 5 25
=
=
=
=
Prefect the null hypotheses
The difference between the 2 means for the two difference conditions in the study are statistically significant.
That is alcohol has a weakening effect on digit memorization
or
Before Consuming alcohol After consuming alcohol
6.29
SD: SD = SD =
NOTE: Strengthen of effect
Statistical significance is not the whole study when testing a hypothesis once a researcher has established that there is statistical significance he should proceed to compute or establish the strength of the effect of the independent variable on the dependent variable. For testing, the difference between means the strength of the effect involves computing Omega squared which is (w2).
For the t-test for dependent or matched groups omega squared is given in the following formula.
.
T. test for independent groups
Two groups are independent when each receives one and only one treatment (IV).
Example
We may have an experimental group and a control group in a study in such a case we wish to test if the difference between the group. Means is big enough to conclude at the two kinds of treatments (ivs) had different effects on the dependent variable the formula is given as;
Where = mean for 1st group
= mean for 2nd group.
X =
NOTE: 1. If ³ then the difference between the two means is statistically significant.
2. Once a significance has been established between the 2 groups means the researcher should proceed to compute the strength of the difference (i.e. compute .
Example
Performance of males and females at a statistics test was as follows;
Group 1 (Females) Group 2 (Males)
3 6
2 5
6 9
5 8
4 7
Is there a significant difference in performance between the 2 groups use .05 level of significance
3 -1 1 6 1 1
2 -2 4 5 -2 4
6 2 4 9 2 4
5 1 1 8 1 1
0 0
= 10-2
= 80.
=
= 3.0.
= 2.306
(There is no difference).
TESTING HYPOTHESIS ABOUT THREE OR MORE SAMPLE MEANS
Many times researchers handle more than 2 groups in their studies in that case a t-test can’t be used because it will give misleading information instead the researcher can use the Fisher’s test (F-test).
Which allows one overall comparison of the group means. In order to carry out the f-test the researcher has to perform an analysis of variance 9ANOVA). Analysis of variance (ANOVA is a statistical technique employed to analyse the variance (variability) in multi-group studies. Variance is a measure of variability or spread among data or scores and it is defined by the following formula.
Variance (Var) =
N.B. in ANOVA.
i.e. variance is the mean or average of the squared deviation scores (from the mean).
NOTE: = deviation score
= deviation score squared
= sum of deviation scores squared.
= Sum of squares, SS (sum of squares) in ANOVA.
or = mean square (MS) in ANOVA.
In order to handle ANOVA therefore we need to compute various variability in the data the main ones include the following;
(i) Total variance (variability)
This means how different each score is from the total (grand) mean
i.e
NOTE:
(ii) Variance between groups.
How different the means of the various groups are from the total (grand mean).
i.e Group1 Group2 Group2
X11 X24 X31
X121 X22 x32
1 1 1
1 1 1
1 1 1
. . .
. . .
=
(iii) Variance within groups
How different each score in a given group is from the groups mean
Then the F-ratio is obtained is given by between groups variance deviation by within.
= between groups variance
within groups variance
NOTE:
The between groups variance is most commonly referred to as the mean square between groups. and within groups variance is more commonly referred to as the mean square within groups.
Thus = ( )
The significance of is found in the f-table which indicates the critical values if f observed.
³ With appropriate degree of freedom and significance level then the researcher can reject the null hypothesis and conclude that the group means significantly differ from each other.
NOTE: Once various computation in ANOVA have been completed the results are usually presented in a table and table takes the following format.
Source of variation (SV) SS Df Ms F
Between groups
With groups
Total
n = total number of observations (scores)
k = number of groups
Example
A study was conducted on the effectiveness of teacher training programmes in Uganda the following results were obtained on rakings of classroom teacher performance.
TYPES OF TEACHER TRAINING PROGRAMMES
Grade V Grade III Grade II
4 3 2
6 5 3
8 4 1
Test the hypothesis that there is no difference in classroom performance between the teachers who received different types of training us .05 level of significance.
TYPES OF TEACHER TRAINING PROGRAMMES:
Grade V Grade III Grade II
4 3 2
6 5 3
8 4 1
1.
= Group V Group III Group II
(4-4)2 (3-4)2 (2-4)2
+ (6-4)2 + (5-4)2 + (3-4)2
+ (8-4)2 (4-4)2 (1-4)2
= 02 -12 -22
22 + 12 + -12
22 02 -32
0 1 4
4 + 1 + 1
10 0 9
20 + 2 + 4 = 36.
2.
Grade V Grade III Grade II
3(6-4)2 + 3(4-4)2 + 3 (2-4)2
= 3(2)2 + 3(0)2 + 3(-2)2
= 3(4) + 3(0) + 3(4)
= 12 + 0 + 12
= 24
3.
Grade V Grade III Grade II
(4-6)2 (3-4)2 (2-2)2
+ (6-6)2 + (5-4)2 + (3-2)2
+ (8-6)2 (4-4)2 (1-2)2
= -22 -12 02
02 + 12 + 12
22 02 -12
4 1 0
0 + 1 + 1
4 0 1
8 + 2 + 42 = 12
NOTE:
e.g.
= 36-24
= 12.
Summary ANOVA of Teacher training programmes
SV SS Df M F
Bet groups 24 2 12 6 5.14
Within groups 12 6 2
Total 36 8
Interpretation
reject HO (null hypothesis)
There is no difference between the different types of the teacher training programmes.
NOTE: Once a researcher has established the significance between the means he/she can establish where the significance exactly arise from by performing. Pair wise comparisons of means using Fishers least significance difference (LSD) test if n is the same for each group or Fisher protected t-test (if n is different for each group).
1. LSD
Where = two tailed critical value for df = n-k(dfw)
Using P for ANOVA
= value obtained in ANOVA.
2. Fisher’s protected t-test.
