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The statistical validity of using ratio variables in human kinetics research

University of British Columbia

There were two main purposes of this investigation. The first was to examine the validity and reliability of commonly used ratio variables in human kinetics research, and to evaluate four ratio score models used to deflate the effect of the denominator. The second was to use computer simulation procedures to investigate the effect of using ratio variables on the circularity assumption of the covariance matrix and type I error rates in RM ANOVA tests. It is shown that a suitable common deflation model for all ratio variables may not exist, and different models should be used to derive an appropriate deflation model in empirical research. The results indicate that high reliability of the component variables does not necessarily result in high reliability of the transformed ratio variable. Thus, when a ratio variable is used the reliability should be examined based on the ratio variable data. It is recommended that five criteria be used to evaluate and compare the validity of deflation models: (a) zero correlation between a derived ratio variable and the denominator variable, (b) no curvilinear relationship between the derived ratio and the denominator in the scatterplots, (c) equality of the estimated expected value of the model and calculated mean of the derived ratio data, (d) high R², and (e) high reliability of the derived ratio data. Simulation results show that the characteristics (ε[sub x1], ε[sub x2], V[sub x1]/ V[sub x2], and pxiX2) of the two component variables strongly affect ε[sub x1/x2] and the type I error rate. In the condition ε[sub x1]= ε[sub x2], the magnitude of ε[sub x1/X2] is virtually the same as that of ε[sub x1] and ε[sub x2], regardless the level of ρ[sub x1x2] and V[sub x1]/ V[sub x2]. When ε[sub x1]<1.0 and ε[sub x2]=1.0, exi/X2 tends to have smaller magnitudes when ρ[sub x1x2] and V[sub x1]/ V[sub x2] are high, and greater magnitudes when ρ[sub x1x2] and V[sub x1]/ V[sub x2] are low. ^ε[sub x1/X2] exhibited the greatest bias and the largest standard deviation, resulting in a serious inflation of type I error rate in the condition V[sub x1]/ V[sub x2]=0.5, regardless of the conditions ε[sub x1], ε[sub x2], and ρ[sub x1x2] . If homogeneity of the denominator variable (small V[sub x2]) and large sample size are present, it may reduce the likelihood of bias in ^ε[sub x1/X2] and protect the type I error rate.

Thesis/Dissertation

application/pdf

2009-07-02

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http://hdl.handle.net/2429/10005

Human Kinetics

University of British Columbia

UBCV

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