HYPOTHESES TESTING

Concept of Hypotheses A hypotheses is a proposition which the researcher wants to verify. It may be mentioned that while a hypotheses is useful, it is not always necessary.

Steps in Hypothesis Testing 1.Formulate a hypothesis 2.Set up a suitable significance level 3.Choose a test criterion 4.Compute 5.Make decisions

1. Formulate a Hypothesis The conventional approach to hypothesis testing is to set up two hypothesis 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. Theses two hypotheses are: i)Null hypothesis ii)Alternative hypothesis The term “null” means nothing or invalid. Let us assume that the mean of the population is u 0.

Formulate a Hypothesis Since we have assumed that the population has a mean µ 0, then our null hypothesis is Ho: µ = µ 0, where Ho is the null hypothesis. The alternative hypotheses is Ha: µ ≠µ 0. The rejection of the null hypothesis will show that the mean of the population is not µ 0. This implies that some other hypothesis is accepted. The other hypothesis is called the alternative hypothesis. It may be noted that there can be two or more alternative hypothesis though only one alternative hypothesis can be tested at one time against the null hypothesis.

2. Set Up a Suitable Significance Level Having formulated the hypothesis, the next step is to test its validity at a certain level of significance. The confidence with which a null hypothesis is rejected or accepted depends upon the significance level used for the purpose. A significance level of, say 5 percent, means that in the long run, the risk of making the wrong decision is about 5 percent. A significance level of, say 1 percent, implies that the researcher is running the risk of being wrong in accepting or rejecting the hypothesis in 1 out of every 100 occasions. Thus, a 1 percent, significance level provides greater confidence to the decision than a 5 percent significance level.

3. Select Test Criterion The next step in hypothesis testing is the selection of an appropriate statistical technique as a test criterion. There are many techniques from which one is to be chosen. For example, when the hypothesis pertains to a large sample (30 or more), the Z-test implying normal distribution is used. When a sample is small (less than 30), the use of the Z-test will be inappropriate. Instead, the t-test will be more suitable. The test criteria which are frequently used in hypothesis testing are Z, t, F, and Chi square test.

4. Compute After having selected the statistical technique to verify the hypothesis, the next step is the performance of various computations, necessary for the application of that particular test. These computations include the testing statistic as also its standard error.

5. Make Decisions The last step in hypothesis testing is to draw a statistical decision, involving the acceptance or rejection of the null hypothesis. This will depend on whether the computed value of the test criterion falls in the region of acceptance or in the region of rejection at a given level of significance. It may be noted that the statement rejecting the hypothesis is much stronger than the statement accepting the hypothesis. It is much easier to prove something false than to prove it true.