SA Glantz and BK Slinker, Primer of Applied Regression and Analysis of Variance, McGraw-Hill, second edition, 2000.Ģ. This approach does not assume that the variance is the same for all comparisons. These comparisons have only n-1 degrees of freedom, so the confidence intervals are wider and the adjusted P values are higher. Some programs compute separate error term for each comparison. This extra power comes by an extra assumption that for every comparison you make, in the overall population from which the data were sampled the variation is the same for all those comparisons. Another way to look at this is n is the number of subcolumns, a is the number of rows, and b is the number of data set columns. If both factors are repeated measures, the number of degrees of freedom equals (n-1)(a-1)(b-1) where n is the number of subjects, a is the number of levels one factor, and b is the number of levels of the other factor. If only one factor is repeated measures, the number of degrees of freedom equals (n-1)(a-1) where n is the number of subjects and a is the number of levels of the repeated measures factor. Prism always computes the multiple comparison tests using a pooled error term (see page 583 of Maxwell and Delaney, 2). Multiple comparisons after two-way repeated measures ANOVA can be computed in two ways. Since Prism offers nearly the same multiple comparisons tests for one-way ANOVA and two-way ANOVA, we have consolidated the information on multiple comparisons. Multiple comparisons testing is one of the most confusing topics in statistics. The results will be the same whether or not you chose to assume sphericity and the value of epsilon will be 1.00000. If your repeated measures factor has only two levels, then the concept of sphericity doesn't apply. If you do not assume sphericity, Prism uses the the Greenhouse-Geisser correction and calculates epsilon. If you have data with repeated measures in both factors, Prism uses methods from Chapter 12 of Maxwell and Delaney (2) Prism computes repeated-measures two-way ANOVA calculations using the standard method explained especially well in Glantz and Slinker (1). How the repeated measures ANOVA is calculated If the P value is high, then you may question the decision to use repeated measures ANOVA in future experiments like this one. If the P value is small, this shows you have justification for choosing repeated measures ANOVA. The corresponding P value tests the null hypothesis that the subjects are all the same. This row quantifies how much of all the variation among the values is due to differences between subjects. Repeated measures ANOVA has one additional row in the ANOVA table, "Subjects (matching)". Also read the general page on the assumption of sphericity, and assessing violations of that assumption with epsilon. So read the general page on interpreting two-way ANOVA results first. When interpreting the results of two-way ANOVA, most of the considerations are the same whether or not you have repeated measures. Interpreting P values from repeated measures two-way ANOVA If one of the factors in ANOVA is dose (say 0, 10, 20 and 50 mg) or time (say 0, 10, 20, 30, 60 minutes), ANOVA treats these doses or time points just like it teats different species or different drugs, totally ignoring the fact that doses or time points are ordered. If one of the factors is a quantitative factor like time or dose, consider alternatives to ANOVA. Are you sure that ANOVA is the best analysis?īefore interpreting the ANOVA results, first do a reality check. Note there is a separate page for interpreting the fit of a mixed model.
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