Page 261 - DMGT404 RESEARCH_METHODOLOGY

Unit 12: Hypothesis Testing

The phrase “test of significance” was coined by Ronald Fisher: “Critical tests of this kind may be Notes
called tests of significance, and when such tests are available we may discover whether a second
sample is or is not significantly different from the first.”
Hypothesis testing is sometimes called confirmatory data analysis, in contrast to exploratory
data analysis. In frequency probability, these decisions are almost always made using null-
hypothesis tests; that is, ones that answer the question. Assuming that the null hypothesis is
true, what is the probability of observing a value for the test statistic that is at least as extreme
as the value that was actually observed? One use of hypothesis testing is deciding whether
experimental results contain enough information to cast doubt on conventional wisdom.

12.1 Steps Involved in Hypothesis Testing

1. Formulate the null hypothesis, with H and H , the alternate hypothesis. According to the
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given problem, H represents the value of some parameter of population.
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2. Select on appropriate test assuming H to be true.
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3. Calculate the value.
4. Select the level of significance other at 1% or 5%.
5. Find the critical region.

6. If the calculated value lies within the critical region, then reject H .
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7. State the conclusion in writing.

12.1.1 Formulate the Hypothesis

The normal approach is to set two hypotheses instead of one, in such a way, that if one hypothesis
is true, the other is false. Alternatively, if one hypothesis is false or rejected, then the other is true
or accepted. These two hypotheses are:
1. Null hypothesis
2. Alternate hypothesis

Let us assume that the mean of the population is m and the mean of the sample is x. Since we
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have assumed that the population has a mean of m , this is our null hypothesis. We write this as
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H m = m , where H is the null hypothesis. Alternate hypothesis is H = m. The rejection of null
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hypothesis will show that the mean of the population is not m . This implies that alternate
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hypothesis is accepted.
12.1.2 Significance Level

Having formulated the hypothesis, the next step is its validity at a certain level of significance.
The confidence with which a null hypothesis is accepted or rejected depends upon the
significance level. A significance level of say 5% means that the risk of making a wrong
decision is 5%. The researcher is likely to be wrong in accepting false hypothesis or rejecting
a true hypothesis by 5 out of 100 occasions. A significance level of say 1% means, that the
researcher is running the risk of being wrong in accepting or rejecting the hypothesis is one of
every 100 occasions. Therefore, a 1% significance level provides greater confidence to the
decision than 5% significance level.

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