The document discusses the concept and characteristics of research hypotheses, emphasizing their development and testing methodologies. It outlines the procedure for hypothesis testing, including setting up hypotheses, determining significance levels, and making decisions based on statistical analysis. Additionally, it covers types of errors in hypothesis testing and introduces concepts such as standard error and its utility.

1. Research Hypothesis
Dr. Ravindra
Associate Professor
Department of Commerce
Indira Gandhi University, Meerpur, Rewari
Email: ravindra.commerce@igu.ac.in
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2. Meaning and Definition of Research
Hypothesis
• Meaning
Research hypothesis is tentative assumption made in order to draw
out and test its logical or empirical consequences. As such the
manner in which research hypothesis are developed is particularly
important since they provide the focal point for research.
• Definition
“Hypothesis is a tentative generalization, the validity of which
remains to be tested, in its most eliminatory stage it’s may be very
hunchy, gussy and imaginative data which became the basis of
action and investigation.”
“A hypothesis in statistics is simply a quantitative statement about
the population.”
By: Prof. Morris Hamburg
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3. Characteristics
• Hypothesis should be clear and specific.
• Delimiting the research area.
• Explain about, what type of data is required.
• Guide about the statistical tool required.
• Keep the researcher on right track.
• It’s sharpening the thinking of researcher.
• Hypothesis should be capable of being tested.
• Hypothesis should be stated as far as possible in most simple terms.
• Hypothesis should be amenable to testing within reasonable time.
• Hypothesis must explain the facts that gave rise to the need for
explanation.
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4. How does one go about developing working
hypothesis?
• Discuss with colleagues and experts.
• Examine the related data and concerned records if available.
• Review of similar studies in the area of research.
• Exploratory personal investigation.
• Some time dreams/sixth sense of the researcher also play major
role in developing the hypothesis.
Thus, working hypothesis arise as result of a priori thinking about
the subject, examination of the available data and the material
including in related studies and the counsel of experts and
interested parties.
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5. Testing of Hypothesis
The theory of hypothesis testing was introduced by Jerzey
Neywman (1894-1981) and Egon Pearson (1895-1980) in letter
half of 19 centaury. In inferential analysis, generalizations have to
be drawn about the population parameters based upon the evidence
obtained from the study of the sample. Hypothesis testing is a
statistical tool that helps us in decision making in such a scenario.
Statistical inference treats two different classes of problems:
1. Hypothesis testing i.e. to test some hypothesis about parent
population from which sample is drawn.
2. Estimation i.e. to use the ‘statistics’ obtained from the sample as
estimate of the unknown ‘parameter’ of the population from which
the sample is drawn.
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6. Procedure of Testing the Hypothesis
The procedure of testing hypotheses follows five
sequential steps, which are as:
1. Set up the Hypothesis
2. Set up the significance level
3. Setting a test criterion
4. Doing calculations
5. Making decisions
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7. Procedure of Testing the Hypothesis
1. Set up the Hypothesis: In the context of statistical
analysis, we often talk about null hypothesis and
alternative hypothesis. The null hypothesis is a very
useful tool in testing the significance of difference. In its
simplest form the hypothesis asserts that there is no real
difference in the sample and the population in the
particular matter under consideration, hence, the word
‘null’ which means ‘invalid’, ‘void’ or ‘amounting to
nothing’, and that the difference found is accidental and
unimportant arising out of fluctuations of sampling.
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8. Procedure of Testing the Hypothesis
As against the null hypothesis, the alternative hypothesis
specifies those values that the researcher believes to hold
true, and, of course, he hopes that the sample data leads to
acceptance of this hypothesis as true. The null and
alternative hypotheses are distinguished by the use of two
different symbols i.e.
Ho = Null Hypothesis
Ha = Alternative Hypothesis
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9. Procedure of Testing the Hypothesis
2. Set up a Suitable Significance Level: The next step is
to test the validity of Ho against that of Ha as at certain
level of significance. The confidence with which an
experimenter rejects or retains a null hypothesis depends
upon the significance level adopted. The significance level
generally express in a percentage i.e. 5% level of
significance or 1% level of significance. At 5% level of
significance the value of SE is 1.96, whereas, at 1% level
the value of SE is 2.58. .95 ÷ 2 = .4750 or .99 ÷ 2 = .4950
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10. Procedure of Testing the Hypothesis
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11. Procedure of Testing the Hypothesis
3. Setting a Test Criterion: This involves selecting an appropriate
probability distribution for the particular test. Some probability
distributions that are commonly used in testing procedures are t-
test, F-test, Chi-square test etc.
4. Doing Calculations: Having taken the first three steps, we have
completely designed a statistical test. We now proceed to the
fourth steps- performance of various computations- from a random
sample of size n, necessary for the test. These calculations include
the testing statistics and the standard error of testing statistics.
5. Making Decisions: Finally at fifth step, we may draw statistical
conclusions and take decisions. A statistical conclusion or decision
of rejection or acceptance the null hypothesis is as under:
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12. Procedure of Testing the Hypothesis
Decision Criterion
a. Test statistic approach
Calculated test Statistics > Table Value, Ho Rejected
Calculated test Statistics ≤ Table Value, Ho Accepted
b. P-value approach
If calculated P-value ≥ Critical Value i.e. 0.05, Ho is
Accepted.
If calculated P-value < Critical Value i.e. 0.05, Ho is
Rejected.
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13. Concepts Related to Testing the
Hypothesis
Type-I Error and Type-II Error
Type-I Error: In a statistical hypothesis testing
experiment, a Type-I error is committed by rejecting the
null hypothesis when it is true. Type-I error is denoted by
‘α’.
Type-II Error: The Type-II error is committed by not
rejecting the null hypothesis when it is false. The
probability of committing a Type-II is denoted by ‘β’.
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14. Concepts Related to Testing the
Hypothesis
Accept Ho Reject Ho
Ho is True Correct Decision Type-I Error
[Confidence Level (1-α)] [Critical Value – α]
Ho is False Type – II Error Correct Decision
[β ] [Power of the Test (1-β)]
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15. Two- tailed and One-tailed test of Hypothesis
• Two-tailed test: When rejection region/criterion is locating on both
side of the distribution then it is the case of two-tailed test i.e.
Ha: u ≠ uo
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16. Continue….
• One-tailed test: When the decision region/criterion locates on one
side of the distribution, then it is the case of one-tailed i.e. Ha: u >
uo or Ha: u < uo
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17. Standard Errors
Standard Error: Standard deviation of sampling distribution is
called the standard error.
Sampling Distribution: If we select number of samples of same
size from a given population, and calculate some statistics (like
mean, mode, SD etc.) from each sample, we shall get a series of
values of these statistics. These values obtained from different
samples can be put in the form of a frequency distribution. The
distribution so formed of all possible values of a statistics is called
‘sampling distribution’.
Universe Distribution: Such a distribution emerges when each and
every item of the universe is studied, and we have full knowledge
of its mean and standard deviation.
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18. Standard Errors
Sample Distribution: If instead of all the items of the universe
we study only a small part of it i.e. takes a sample, we arrived
at a distribution which technically called a sample
distribution.
Properties of Sampling Distribution
1. The arithmetic mean of the sampling distribution is the same
as the mean of the universe from which samples were taken.
2. The sampling distribution of mean has a standard deviation
equal to the population standard deviation by the square root
of the sample size.
3. The sampling distribution of means is normally distributed.
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19. Utility of Standard Deviation
Utilities of S.D.
1. It is used as an instrument in testing the hypothesis.
2. Standard error provides the idea about the unreliability of
a sample. The greater the SE, the greater is the departure
of actual frequency from the expected ones hence the
greater the unreliability of the sample. The reciprocal of
S.E., is a measure of reliability of the sample.
3. With the help of S.E. we can determine the limits within
which the parameter values are expected to lie i.e. Mean±
3 S.E. will gives you 99.73% values.
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20. (Appendix) Normal Distribution Table
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21. (Appendix) Appropriate Tools for Casual Association
Sr. No. Dependent Variable Independent Variable Tool for Analysis
1. Metric Metric Regression
2. Metric Metric and Non- metric Regression
3. Metric Non-metric variable with
Two Categories t-test
4. Metric Non-metric Variable with
More than two Categories ANOVA
5. Metric More than one Non-metric Factorial Design
Independent Variable (one-way ANOVA)
6. More than one One or more non-metric MANOVA
Metric Variable Independent Variable
7. Non-metric Metric Discriminant Analysis
8. Non-metric Non-metric Chi-Square Test
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22. Research Hypothesis
Thank You !
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