On an Approach to Testing Hypotheses About the Identity of Distributions in Two Samples with Small Sizes

Abstract

This article proposes a group of new criteria for testing hypothesis about the identity of distributions in two small size samples. Their special feature is the dependence on the sample generating distribution even under the null hypothesis. The result of this paper is a certain comprehensive methodology for answering the question about identity of distributions of two given samples, containing one to three tens of observations. The main components of this methodology are: (a) visual sample comparison by a “regression” graph of dependence of their quantiles of the same order, (b) choosing the suitable test from the given group of regression goodness-of-fit tests, using the fact that under the null hypothesis the quantile graph must be close to the line y = x, (c) a modernized method of modeling bootstrap samples for determining different quality characteristics of the chosen goodness-of-fit test. The article does not contain theoretical results that might be formulated as a mathematical theorem. Its conclusions are based on statistical analysis of a large number of sample pairs of different size and origin. Description of such analysis methodology is based on three demonstrative examples from biology.