Classroom Simulation: Are Variance-stabilizing Transformations Really Useful
نویسندگان
چکیده
When population variances of observations in an ANOVA are a known function of their population means, many textbooks recommend using variancestabilizing transformations. Examples are: square root transformation for Poisson data, arcsine of square root for binomial proportions, and log for exponential data. We investigate the usefulness of transformations in onefactor, 3-level ANOVAs with nonnormal data. Simulations approximate the true significance level and power of F-tests—with and without various variance-stabilizing transformations. Findings: logarithmic and rank transformations of exponential data can be useful when the number of replications is small and the separation in means is large. Simulation code for Minitab and S-Plus/ R is provided. Classroom use of such simulations in a second statistics course reinforces concepts of significance level and power, encourages exploration, and teaches computer skills important in the job market.
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