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Type I Error Rates and Power Estimates of Selected Parametric and Nonparametric Tests of Scale

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  • Stephen F. Olejnik
  • James Algina

Abstract

Estimated Type I error rates and power are reported for the Brown-Forsythe, O’Brien, Klotz, and Siegel-Tukey procedures. The effect of aligning the data, by using deviations from group means or group medians, is investigated for the latter two tests. Normal and non-normal distributions, equal and unequal sample-size combinations, and equal and unequal means are investigated for a two-group design. No test is robust and most powerful for all distributions, however, using O’Brien’s procedure will avoid the possibility of a liberal test and provide power almost as large as what would be provided by choosing the most powerful test for each distribution type. Using the Brown-Forsythe procedure with heavy-tailed distributions and O’Brien’s procedure for other distributions will increase power modestly and maintain robustness. Using the mean-aligned Klotz test or the unaligned Klotz test with appropriate distributions can increase power, but only at the risk of increased Type I error rates if the tests are not accurately matched to the distribution type.

Suggested Citation

  • Stephen F. Olejnik & James Algina, 1987. "Type I Error Rates and Power Estimates of Selected Parametric and Nonparametric Tests of Scale," Journal of Educational and Behavioral Statistics, , vol. 12(1), pages 45-61, March.
    • Handle: RePEc:sae:jedbes:v:12:y:1987:i:1:p:45-61
    DOI: 10.3102/10769986012001045
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