JSM 2004 - Toronto

Abstract #302061

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Activity Number: 345
Type: Contributed
Date/Time: Wednesday, August 11, 2004 : 12:00 PM to 1:50 PM
Sponsor: Section on Statistical Education
Abstract - #302061
Title: Classroom Simulation: Are Variance-stabilizing Transformations Really Useful?
Author(s): Rebecca E. Brafman*+ and Bruce E. Trumbo and Eric A. Suess
Companies: California State University, Hayward and California State University, Hayward and California State University, Hayward
Address: , , ,
Keywords: variance-stabilizing transformation ; non-normal data ; simulation ; Minitab/S-Plus/R ; teaching ; log/arcsine/square root
Abstract:

When population variances of observations in an ANOVA are a known function of their population means, many textbooks recommend variance-stabilizing transformations. Examples are square root transformation for Poisson data, arcsine of square root for binomial proportions, and log for exponential data. To investigate the usefulness of transformations in one-factor ANOVAs with nonnormal data, we use simulations to approximate the true significance level and power of F-tests--with and without various variance-stabilizing transformations. In our examples, logarithmic transformations of exponential data prove especially valuable. Simulation code for S-Plus and R is provided (Minitab and SAS for some). Classroom use of these simulations in a second statistics course reinforces concepts of significance level and power, illustrates appropriate use and interpretation of transformations, encourages exploration, and teaches computer skills important in the job market.

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