A Unified Approach to Some Standard Statistical Tests

Standard introductory texts on statistical methods in psychology deal with tests on means, variances, correlations, and proportions prior to treating the analysis of variance. Generally, excluding ANOVA, they cover a maximum of 12 testing situations, dealing with, for each of the above four parameters, a “1-Sample,” “2-Sample Independent,” and “Two-Sample Dependent” hypothesis test. Many books present only a subset of these twelve situations. For example, standard texts seldom present procedures for comparing correlations from two dependent samples. In this chapter, we shall develop a general theoretical approach which will handle (with some minor adjustments for individual cases) all of the standard testing situations for means, proportions, and correlations. (Variances will require a special treatment later.) The method will also allow us to generate test statistics for a variety of circumstances not always covered in psychological statistics texts. Later, as a convenient by-product, we will also develop a general procedure for constructing confidence intervals, using a slight modification of the material developed in this section. Our approach will be as follows. First, we shall develop general theory which applies to all of the relevant testing situations. Then we will apply the theory, adding modifications and/or improvements where applicable, to testing means, proportions, and correlations.