Issn Print: 0195-9131
Publication Date: 2001/05/01
TYPE I ERROR RATES IN REPEATED MEASURES ANOVA WHEN USING RATIO VARIABLES
Y Liu; R W. Schutz
+ Author Information
Author Information: Western Michigan University, Kalamazoo, MI, USA; The University of British Columbia, Vancouver, BC, Canada
Excerpt
A ratio variable Y = X1/X2, a composite variable that consists of two component variables (a numerator variable X1, and á denominator variable X2), has been widely used as a dependent variable in human movement and health related research (e.g., moment of force, Vo2max, and waist-to-hip ratio). The purpose of this study was to investigate how the variation and the correlation of the component variables affect type I error rates in RM ANOVA while using ratio variables. Monte Carlo simulation procedures showed that the characteristics (covariance structure, relative variance, and correlation) of the two component variables strongly effect both the covariance structure of the type I error rate in RM ANOVA. In the condition of equal covariance structure of the component populations, the convariance structure of the ratios was virtually the same as that of the components (population epsilon = 1.0), regardless of the level of the correlation and the relative variation of the component variables. If only the numerator violated the assumption of circularity, the population epsilon of the ratio data tended to have smaller magnitudes when the correlation and the relative coefficient of variation (Cv1/Cv2) between the numerator and denominator were high. Under the same condition, the population epsilon tended to have greater magnitudes when the correlation and Cv1/Cv2 were low. The estimate of the population epsilon exhibited the greatest bias and the largest standard deviation, resulting in a serious inflation of type I error rate, in the condition of low Cv1/Cv2 (0.5), regardless of the conditions of the epsilon and correlation of the component variables. The results suggest that researchers should make an effort to reduce the variation of the denominator variable in data collection process. If homogeneity of the denominator variable and large sample size are present (e.g., Cv2 is smaller than Cv1, n > 30), it may reduce the likelihood of blassing epsilon and protect the type I error rate when ratios are used in RM ANOVA.
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