Analysis of Variance

Abstract

While the “Student” t-test provides a powerful method for comparing sample means for testing differences between population means, when more than two groups are to be compared, the probability of finding at least one comparison significant by chance sampling error becomes greater than the alpha level (rate of Type I error) set by the investigator. Another method, the method of Analysis of Variance, provides a means of testing differences among more than two groups yet retain the overall probability level of alpha selected by the researcher. Your OpenStat4 package contains a variety of analysis of variance procedures to handle various research designs encountered in evaluation research. These various research designs require different assumptions by the researcher in order for the statistical tests to be justified. Fundamental to nearly all research designs is the assumption that random sampling errors produce normally distributed score distributions and that experimental effects result in changes to the mean, not the variance or shape of score distributions. A second common assumption to most designs using ANOVA is that the sub-populations sampled have equal score variances – this is the assumption of homogeneity of variance. A third common assumption is that the populations sampled have been randomly sampled and are very large (infinite) in size. A fourth assumption of some research designs where individual subjects or units of observation are repeatedly measured is that the correlation among these repeated measures is the same for populations sampled – this is called the assumption of homogeneity of covariance.