Reply to Quinn and Keough

Abstract

dependent observations. We chose a real data set, rather than a contrived one, that presented additional challenges (such as small sample size). Quinn and Keough have brought up several points concerning our paper. We respond to comments 1 and 3 and comment on their Table 1. Comment 1. Quinn and Keough state that we repeat the vague claims of the robustness of analysis of variance (ANOVA) procedures that are found in many textbooks. Robustness of ANOVA procedures is a controversial issue among statisticians. Some advocate the use of ANOVA when moderate deviations from the assumptions occur (e.g., Montgomery 1984, p. 87, 91). Zar (1984, p. 170) carefully provides primary references for the robustness of ANOVA, concluding that ... analysis of variance may typically be depended upon unless the data deviate severely from the underlying assumptions. The statement that we used in our paper is somewhat milder than these, more in agreement with Quinn and Keough's own statements in Comment 1. We agree with Quinn and Keough that exploratory data analysis is always advisable. But when the data set is very small, as in this case, normality checks will yield little useful information (Montgomery 1984, p. 86), and tests for homogeneity of variances are unreliable (Zar 1984, p. 183). Comment 3. Quinn and Keough correct a misstatement made concerning the assumptions needed for validity of the repeated measures procedure. We had intended to state that the standard ANOVA assumptions are necessary but not sufficient conditions for the repeated measures procedure. The additional sphericity assumptions mentioned by Quinn and Keough, one form of which is referred to as the Huynh-Feldt conditions (Huynh and Feldt 1970), should have been stated in our paper for informational purposes. However, from a practical point of view, we felt that a discussion of these conditions would contribute little to the point of the paper because they are difficult to test for, especially in a small data set of the type we analyzed, and because of their theoretical complexity. Also, Huynh and Feldt (1980) indicate that some departure from sphericity may not substantially change the nature of the traditional F tests in repeated measures designs (see Read et al. 1988, p. 605-606). Quinn and Keough suggest two possible alternative forms of analysis. One of these is use of multivariate analysis of variance (MANOVA). We avoided a discussion of this technique because it is our feeling that univariate techniques should be used if possible in order to avoid the additional complexities associated with multivariate procedures. The Greenhouse-Geisser (GG) correction that is used to adjust for violations of the sphericity assumption recommended as the second alternative has been shown in simulation studies to be ultraconservative (Ott 1988, p. 800). Concerning Table 1. There are a number of reasons why Quinn and Keough's numbers in Table 1 differ somewhat from ours: