CHAPTER 11 - Significance Tests for Means, Variances, Frequency Distributions, and Sequential Arrangements

Abstract

This chapter discusses the significance tests for means, variances, frequency distributions, and sequential arrangements. It presents the methods of comparing samples will be systematized, generalized, and put on a firmer basis. In the parlance of the statistician, a test is a procedure for accepting or rejecting a statistical hypothesis. In general, a statistical hypothesis is any statement relating one or several samples to some universe or some universes. There is no possibility whatsoever of determining confidence levels that is reliable in all situations. F-test permits testing the null hypothesis that the variances of the parent populations of two samples are identical. The test rests on the assumption that the universes from which the samples were drawn are normal distributions or distributed approximately normal. The parent populations of the samples are different if, however, the variances do not differ significantly; the samples were either drawn from the same population or from different universes with the same variance. The Student t-test and the variance ratio test may be applied mechanically. One should be more careful, however, when using the Chi-square test.