Abstract

Variance is very important in test statistics as it measures the degree of reliability of estimates. It depends not only on the sample size but also on other factors such as population size, type of data and its distribution, and method of sampling or experiments. But here, we assume that these other fasctors are fixed, and that the test statistic depends only on the sample size.

When the sample size is larger, the variance will be smaller. Smaller variance makes test statistics larger or gives more significant results in testing a hypothesis. Whatever the hypothesis is, it does not matter. Thus, the test result is often misleading because much of it reflects the sample size. Therefore, we discuss the large sample problem in performing traditional tests and show how to fix this problem.

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