Probabilities and Critical Values for z, chi square, r, t, and F

Abstract

The requirements of psychological research often necessitate considerable familiarity with various probability functions, most notably the z., chi-square, r, t, and distributions. In most cases, experimenters employ numbers of groups, numbers of subjects, and a nominal alpha level such that the significance (or lack thereof) of a particular test statistic can be readily determined by reference to any available statistical table. However, this is not always the case. For instance, in using the test for homogeneity of variance, reference must be made to the distribution on n 1 ~ 1 and n2 1 degrees of freedom, where n refers to the number of subjects in the respective groups. When n becomes even moderately large, a substantial majority of statistical tables are of minimal value; at best, linear interpolation using the available information can be attempted. Alternately, experimenters may have statistics for frequently tabled degrees of freedom but may need a probability value other than the traditional .05, .01, or .001 levels of significance. For example, researchers who employ a Bonferroni approach (e.g., Harris, 1975) in conducting multiple comparisons or who wish to establish a familywise alpha level often end up with a specified level of significance not easily found in any statistical table. The purpose of this paper is to describe a computer program that will aid in the solution of both of these problems. Description. The program consists of a brief main routine and 10 subprogram functions. The main routine controls all input and output operations and calls the appropriate function(s), as needed. When the user wishes to obtain probability value(s) for a given test statistic, input consists of a short character string, indicating the probability distribution to be referenced (e.g., F for the distribution), degrees of freedom (as appropriate), and the test statistic. Output consists of the test statistic input to the program, degrees of freedom (when appropriate), and the two-tailed significance level associated with this statistic. In the case in which the user wishes to obtain a critical value for a predetermined probability value, input consists of a short character string indicating the distribution to be referenced (e.g., CT for a critical value for the t distribution), degrees of freedom (as appropriate), and a two-tailed significance level. Output consists of the alpha level input to the program, the associated critical