Hypothesis testing: Definition, Types and Characteristics (notes)
a) The difference should be attributed to random error but if you find there is difference you reject the null hypothesis.
b) Whether the difference is large enough for us to conclude that the population values are different. If there is large difference you accept the null hypothesis
Accept or Reject the Ho
The frequency polygon for the distribution is bell-shaped asymmetric curve called Normal curve
Majority of scores are at center.
Skewness
The times when the distribution is concentrated in either side is called Skewness. If the scores are concentrated at the UPPER end, so the tail is of the curve skews to the left, we call the curve is NEGATIVELY SKEWED
We can compare two frequency distributions with appropriately equal values of N as seen in the figure. It is easy to compare the spread and the concentration and the ability of girls is superior in that test than boys.
Characteristics of Hypothesis
i. It should be clear and precise otherwise your hypothesis will not be taken as reliable.
ii. It should be capable of tested for confirmation or disproved by observation.
iii. It should state relationship between variables (i.e. DVs and IVs), if its relational hypothesis. E.g. Academic performance and birth order.
iv. It should be specific and limited in scope. Narrower hypothesis are more testable
v. It should be tested in most simple terms to be understood by all concerned.
vi. It should be consistent with facts or theories
vii. It should be agreeable or pleasant to testing within a reasonable time because one can not spend life-time collecting data to test it.
viii. Hypothesis must explain the facts that give time to the need for explanation i.e. it should have empirical reference
Types of hypothesis
Alternative hypothesis is positive statement and is the one which we wish to prove true, e.g. There is relationship between academic performance and birth order of secondary school students.
Null hypothesis is a negative statement and is the one which we wish to disprove (reject). E.g. There is no relationship between academic performance and birth order of secondary school students.
Level of Significance
Level of significance is the power the researcher has to make decisions on whether or not his or her hypothesis (or observed evidence) is true.
Researchers normally take the probability of 5% (0.05) risk of making error and 95% being correct; or 1% (0.01) error and 99%;
As such we say that a researcher is willing to take 0.05 or less risk of reject Ho when it is true.
Thus 0.05 is the maximum value of the probability of rejecting Ho when it is true, and normally you determine it before testing the hypothesis.
In case you run statistics and get significant level of 0.06, will you accept or reject the Ho?
In case you run statistics and get significant level of 0.02, will you accept or reject the Ho?
Decision Rule or Testing Hypothesis
Type I and Type II Errors
In the process of testing hypothesis, there are same errors we can make
If we reject Ho when Ho is true we have committed type 1 error known as alpha error=α
But if we accept Ho when in fact Ho is not true we have committed type II error known as beta error=β error
Researchers always try their best to minimize both errors. However, as you try to reduce Type I you are most likely to commit Type II error.
You can not control both types simultaneously.
Hence you trade off between the two types of errors depending on which one is more costly in your results and conclusions
E.g. There is no relationship between malaria and chloroquine
If Type 1 involves the time and funds to conduct the experiment of manufacturing the medicine
While Type II error means taking risk of distributing the medicine to patients with uncertainty of treating malaria.
Then what would you prefer?
When testing hypothesis, you must make all possible efforts to strike a balance between committing Type 1 and Type 11 errors.
How?
By setting a very high level for Type 1 error when testing technique of a certain hypothesis
Interpretation of findings
What is interpretation?
r observed 0.02 < r critical 0.632 at 0.05 significant level
Hence, we accept the null hypothesis that, “There is no relationship between Math's and Civics performance among Makole standard 5 pupils”
We can say that interpretation is:
i. Drawing inference from the collected data after an analysis
ii. It is a search for a broader meaning of the research findings
Interpretation involves the following aspects:
To establish continuity in research through linking your results to those of others.
To establish relationship (of DVs and IVs within the collected data
To extend beyond the data of the study to include theories and hypotheses.
In short interpretation is an exercise through which the facts from the study could be explained and understood better.
Also interpretation provide a theoretical conception which can serve as a guide to further research.
Why do we interpret our findings?
i. Because it is a way the researcher can make his or her abstract findings be understood by society and they can link the study with those of others
ii. Because it is a way to open new avenues of intellectuals and stimulates the quest for more knowledge
iii. Because is the way the researcher can appreciate his or her work, make others understand the significance of the study.
iv. Because it serves as a transition from explanatory to experimental research. Explanatory study does not have hypothesis to begin with, but later the interpretation of results lead to experimental research to test the worthiness
Techniques of Interpretation
i. Give reasonable explanation of the relations found in the study-know how generalization is done and concepts being formulated
ii. Extra information if collected must be considered during final interpretation of results, as this may be key factor in understanding the problem under study.
iii. Make consultations with genuine expert who will omit errors which does not bring logical argumentation. This person will help make correct interpretation and enhance the utility of the findings
iv. You must be in no hurry while interpreting results, because the conclusions which appear to be alright at the beginning may not at all be accurate.
Precautions in Interpretation
NB: Even when you try hard to minimize errors in sampling the respondents, collecting data and analyzing, making a mistake interpretation would lead to inaccurate conclusions
Some hints to consider
a) Satisfy yourself that
You have appropriate and adequate data for drawing inference
Data reflect good homogeneity
Proper analysis has been done using proper statistical methods
b) Must be cautious about errors e.g. Error due to false generalization or wrong interpretation e.g. Application of results beyond the range of observation, identify cause and effect etc.
Don’t affirm relationship with either Ha or Ho if its not there
Be competent with correct statistical measures for drawing inferences in your study
c) You can not separate analysis and interpretation so:
Take much care of reliability of data
Computational checks from time to time
Validation of results and
Comparison of results
d) Remember your task is:
Both to make sensitive observations of relevant occurrences and identify and disengage the factors that are initially not seen by our eyes.
Avoid generalization because your sample is restricted to particular time, particular are, and particular conditions
Hence frame your results within their limits
e) Remember there is constant interaction between initial hypothesis to be tested, theoretical conceptions and empirical observations in the field.
This is the opportunity to show creativity and originality of your work. So pay much attention to this interaction while engaged in interpretation
Report writing
No matter how brilliant your hypotheses are or how well designed and conducted your research is, the most important part of it is to communicate the results to others.
This is the purpose of research, to search knowledge and share with others.
Research report is the last step in research study which requires different skills to accomplish.
Steps in Report writing
i. Logical analysis of the subject matter
a) Either logically from simple to complex structure or
b) Chronologically i.e. on the bases of sequence in time or occurrence
ii. Preparation of final outline-this outline is a guide or aid to the logical or chronological organization of the report.
The guide is a remind of the important points to be included in the full report.
iii. Preparation of the rough draft- put down what you have done in your research study
Here you rewrite the first 3 chapter by changing the action verbs to past tense.
In chapter one you will put all various limitations faced in the field the techniques adopted for analysis, the presentation of findings, generalization of results, various suggestions and conclusions.
iv. Rewriting and polishing of the Rough Draft.
This is the most difficult part of the report writing because it requires more time than the rough draft in careful revision, looking at the weakness in logical development or presentation e.g. Whether or not the material has unity and consistency (pulling together the information)
The report stand upright, firm and exhibit a definite pattern
Whether or not it resemble an old wall of molding e.g. cement and loose brick
Check also whether in your rough draft you was consistent or not.
Also check the mechanics of writing e.g. grammar, spelling and usage of correct word phrases
v. Preparation of the final Bibliography
Bibliography which is normally appended to the research report is:
A list of pertinent books to the research. It must contain all the works you consulted in the course preparation of proposal and analysis.
It should be arranged alphabetically
vi. Writing the Final Draft
Your final draft should be written in:
a) Concise and objective style
b) In simple language i.e. avoid vague phrases e.g.. “It seems ” “there may be”
c) Avoid also abstract terminologies and technical slang (jargon)
d) Illustrations and examples on common experiences must be incorporated for effective communication of the findings to others
e) It should enthuse people (not dull) and maintain interests and must show originality
NB: Each research is intended to solve some intellectual or societal problem, so:
i. It must contribute to the solution of a problem
ii. Must add to knowledge of both the researcher and readers.
Layout of the research Report
Layout is what the report should contain. Unless for an academic research report (dissertation and thesis) others must contain 3 main parts
a) Preliminaries
b) Main text
c) End matter
Preliminaries-these include:
Title and date
Acknowledgement or preface or foreword
Table of contents
List of tables, figures, charts, maps etc.
Abbreviations
Preliminaries for a Dissertation you have more items like:
Certification where your supervisors certify that they have read and agree the document it is ready for submission. Their names signature and data appear
Declaration and copyright
Dedication
i. Acknowledgement
ii. Abstract or Executive summary and the list continue table of contents and the following.
Main text provides the main detail of the report
Each main section of the report begin on a new page
The main text should have the following subsections:
a) Chapter I one: Introduction
b) Chapter II: Literature review and conceptual theoretical framework
c) Chapter III: Methodology
d) Chapter IV: Presentation of the results and discussion
e) Chapter V: Conclusion, suggestion and the summary
iii. End matter are the appendices attached at the end of research report. These are:
a) Bibliographies
b) Technical data e.g. questionnaires, sample information, mathematical derivations
Types of Reports
i. Technical report emphasizes on:
a) The methods used in the study
b) The assumptions or hypothesis tested in the course of study
c) Detailed presentation of results including supporting data.
ii. Popular report-this emphasize on simplicity and attractiveness of reporting the results through
a) Clear writing
b) Minimization of technical e.g. mathematical
c) Details and liberal use of charts and diagrams
d) Attractiveness layout with large print, many subheadings, charts even cartoons are characteristics of popular report.
e) Much emphasis also is given on the practical aspects and policy implications.
Oral presentation
Sometimes you will be required to present your results orally.
This is effective particularly when policy recommendations are demanded by project results
Pros provides opportunity of give-and take decisions, better understanding of results and their implications
Cons
It lack permanent record concerning the research details
Its possible the findings may fade away from peoples memory even before the action is taken
Hence, in order to overcome this a written report may be circulated before the oral presentation and allow participants to refer to during the discussion
Oral presentation is effective when supplemented by various devices eg. Slides, wall charts, tables, use of black board or white board as it reduce boredom
Precautions for writing Research Report
Research report is a channel of communication between the researcher and the reader, thus this task must be done efficiently and effectively. To note of these
It should be long enough to cover the subject but short enough to maintain interest
It shouldn't be dull, but sustain readers interest
Avoid abstract terminologies and technical language. The report should convey the results as simple as possible. Readers are often interested to acquire a quick knowledge of the main results
Report should be appropriate and accordance to the objective of the study
Report should be free from grammatical errors
Present the report with logical analysis
Show originality of the results and attempt to solve a problem and must add new knowledge
At the end show policy implications related to the problem. Also forecast on the probable future research on the same field.
Appendices must be enlisted appropriately
Bibliographies must be of good quality (not more than 10 years)
Report must be attractive in appearance, neat, clean, whether typed or printed.
Calculated confidence limits must be mentioned in advance, and various constraints, challenges or limitations experienced in conducting the study should also be listed
Lastly, forget not to clearly state the objectives of the study, nature of the problem, methods employed and data analysis techniques.
Ethical Issues
Since the subject matter of the social scientist is human behavior, it is inevitable that scientific interests will conflict at times with values placed on the right of individuals to privacy and self determination
American psychological Association's Committee on Ethical standards stress the “informed consent” i.e. Participants volunteer to participate in the study.
In universities, there are institutional Review Board expected to review proposals for ethical consideration
At national level, there is national Board
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