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Parametric ANCOVA and the Rank Transform ANCOVA When the Data are Conditionally Non-Normal and Heteroscedastic

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  • Stephen F. Olejnik
  • James Algina

Abstract

Parametric analysis of covariance was compared to analysis of covariance with data transformed using ranks. Using a computer simulation approach, the two strategies were compared in terms of the proportion of Type I errors made and statistical power when the conditional distribution of errors was normal and homoscedastic, normal and heteroscedastic, non-normal and homoscedastic, and non-normal and heteroscedastic. The results indicated that parametric ANCOVA was robust to violations of either normality or homoscedasticity. However, when both assumptions were violated, the observed α levels underestimated the nominal α level when sample sizes were small and α = .05. Rank ANCOVA led to a slightly liberal test of the hypothesis when the covariate was non-normal, the sample size was small, and the errors were heteroscedastic. Practical significant power differences favoring the rank ANCOVA procedures were observed with moderate sample sizes and a variety of conditional distributions.

Suggested Citation

  • Stephen F. Olejnik & James Algina, 1984. "Parametric ANCOVA and the Rank Transform ANCOVA When the Data are Conditionally Non-Normal and Heteroscedastic," Journal of Educational and Behavioral Statistics, , vol. 9(2), pages 129-149, June.
    • Handle: RePEc:sae:jedbes:v:9:y:1984:i:2:p:129-149
    DOI: 10.3102/10769986009002129
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    1. Lin, Yeqiang & Kerstetter, Deborah & Nawijn, Jeroen & Mitas, Ondrej, 2014. "Changes in emotions and their interactions with personality in a vacation context," Tourism Management, Elsevier, vol. 40(C), pages 416-424.

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