Determining Differences with Inferential Statistics

Abstract

Abstract This chapter provides information about inferential tests that could be used to analyze differences between groups. Quantitative researchers typically rely on inferential statistical procedures for testing hypotheses pertaining to differences between sets of scores. Although researchers nearly always find mathematical differences in scores from different groups, determining whether these differences are statistically significant requires inferential tests. Before deciding on a particular test, you must consider whether your data are nominal-, ordinal-, interval-, or ratio-level since different tests are suitable for each level. Also, you need to consider whether your data come from independent or dependent samples. Independent samples generally are gathered from groups that consist of different individuals. Dependent samples are gathered from the same group of individuals on multiple occasions. Specific details are provided for a variety of statistical procedures. For determining differences with interval- or ratio-level outcome data researchers typically use independent samples t-test, dependent samples t-test, one-way analysis of variance, repeated-measures analysis of variance, and post-hoc analyses. For ordinal data researchers may use the Mann-Whitney U test, the Wilcoxon test for paired samples, the Kruskal-Wallis test, and Friedman’s test. For nominal-level data the Chi square test of independence and McNemar’s test can be used.