Procedure of Testing Hypothesis

The procedure of testing hypothesis is briefly described below:

1.    Set up a hypothesis:

The first thing in hypothesis testing is to set up a hypothesis about a population parameter. Then we collect sample data, produce sample statistics, and use this information to decide how likely it is that our hypothesized population parameter is correct. The conventional approach to hypothesis testing is not to construct a single hypothesis about the population parameter but rather to set up two different hypotheses. These hypotheses must be so constructed that if one hypothesis is accepted, the other is rejected and vice versa.

The two hypotheses in a statistical test are normally referred to as:

(i)    Null hypothesis, and

(ii)    Alternative hypothesis.

The null hypothesis is a very useful tool in testing the significance of difference. In the simplest form the hypothesis asserts that there is no true 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.

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 lead to acceptance of this hypothesis as true. The alternative hypothesis may embrace the whole range of values rather than single point.

The null and alternative hypothesis are distinguished by the use of two different symbols, H0 representing the null hypothesis and Ha the alternative hypothesis. Thus a psychologist who wishes to test whether or not a certain class of people have a mean I.Q higher than 100 might establish the following null and alternative hypotheses:

        H0 = µ = 100 (null hypothesis)

        Ha = µ    = 100 (Alternative hypothesis)

Or, if he is interested in testing the difference between the mean I.Q of two groups, this psychologist may like to establish the null hypothesis that the two groups have equal means (µ1 - µ2 = 0) and the alternative hypothesis that their means are not equal (µ1 - µ2 ≠ 0)

        H0: µ1 - µ2 = 0 (null hypothesis)

        Ha µ1 - µ2 ≠ 0 (alternative hypothesis)

2.    Set up a suitable significance level.

Having set up the hypothesis, the next step is to test the validity of H0 against Ha at a certain level of significance. The confidence with which an experimenter – or retains – a null hypothesis depends upon the significance level adopted. The significance level is customarily expressed as a percentage, such as 5 percent, 1 percent and the like. A level of significance of, say, 5 percent, is the probability of rejecting the null hypothesis if it is true.

3.    Setting a test criterion.

The third step in hypotheses testing procedure is to construct a test criterion. This involves selecting an appropriate probability distribution for the particular test, that is, a probability distribution which can properly be applied. Some probability distributions that are commonly used in testing procedures are t, F and X₂.

4.    Doing computations.

Having taken the first three steps, we have completely designed a statistical test. We now proceed to the fourth step – 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 the testing statistic.

5.    Making decision.

Finally, as a fifth step, we may draw statistical conclusions and take decisions. A statistical decision will depend on whether the computed value of the test criterion falls in the region of rejection or the region of acceptance.

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