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Multiple Comparison Tests
Many research projects involve testing multiple research hypotheses. These research hypotheses could be evaluated using comparisons of means, bivariate correlations, regressions, and so forth, and in fact most studies consist of a mixture of different types of test statistics. An important consideration when conducting multiple tests of significance is how to deal with the increased likelihood (relative to conducting a single test of significance) of falsely declaring one (or more) hypotheses statistically significant, titled the multiple comparisons problem. This multiple comparisons problem is especially relevant to the topic of research design because the issues associated with the multiple comparisons problem relate directly to designing studies (i.e., number and nature of variables to include) and deriving a data analysis strategy for the study. This entry introduces the multiple comparisons problem and discusses some of the strategies that have been proposed for dealing with it.
The Multiple Comparisons Problem
To help clarify the multiple comparisons problem, imagine a soldier who needed to cross fields containing land mines in order to obtain supplies. It is clear that the more fields the individual crosses, the greater the probability that he or she will activate a land mine; likewise, researchers conducting many tests of significance have an increased chance of erroneously finding tests significant. It is important to note that although the issue of multiple hypothesis tests has been labeled the multiple comparisons problem, most likely because a lot of the research on multiple comparisons has come within the framework of mean comparisons, it applies to any situation in which multiple tests of significance are being performed.
Imagine that a researcher is interested in determining whether overall course ratings differ for lecture, seminar, or computer-mediated instruction formats. In this type of experiment, researchers are often interested in whether significant differences exist between any pair of formats, for example, do the ratings of students in lecture-format classes differ from the ratings of students in seminar-format classes. The multiple comparisons problem in this situation is that in order to compare each format in a pairwise manner, three tests of significance need to be conducted (i.e., comparing the means of lecture vs. seminar, lecture vs. computer-mediated, and seminar vs. computer-mediated instruction formats). There are numerous ways of addressing the multiple comparisons problem and dealing with the increased likelihood of falsely declaring tests significant.
Common Multiple Testing Situations
There are many different settings in which researchers conduct null hypothesis testing, and the following are just a few of the more common settings in which multiplicity issues arise: (a) conducting pairwise and/or complex contrasts in a linear model with categorical variables; (b) conducting multiple main effect and interaction tests in a factorial analysis of variance (ANOVA) or multiple regression setting; (c) analyzing multiple simple effect, interaction contrast, or simple slope tests when analyzing interactions in linear models; (d) analyzing multiple univariate ANOVAs after a significant multivariate ANOVA (MANOVA); (e) analyzing multiple correlation coefficients; (f) assessing the significance of multiple factor loadings or factor correlations in factor analysis; (g) analyzing multiple dependent variables separately in linear models; (h) evaluating multiple parameters simultaneously in a structural equation model; and (i) analyzing multiple brain voxels for stimulation in functional magnetic resonance imaging research. Further, as stated previously, most studies involve a mixture of many different types of test statistics.
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