Tests for one-way analysis of covariance with heteroscedasticity

Document Type : Original Scientific Paper

Authors

1 Department of Statistics, Yazd University, Yazd, Iran

2 Department of Statistics, Shiraz University, Shiraz, Iran

Abstract

The one-way analysis of covariance model is used to evaluate the equality between multiple treatments in the presence of a covariate‎. ‎Presenting a test that controls the size is a major consideration for this model especially when the variances are unequal‎, ‎since the actual size of the test depends on the values of the variances‎. ‎The traditional F test in the analysis of covariance problem can produce unreliable outcomes‎, ‎and there is no simple manipulation test that satisfactorily controls the size‎. ‎The calculations for the generalized F test and parametric bootstrap test are complicated and must be performed using Monte Carlo techniques‎. ‎In this study‎, ‎we first suggest a generalized test for the analysis of covariance problem and then construct three approximate tests that do not have the problems of earlier tests‎. ‎The performance of the generalized test and the three simple tests is shown using extensive simulations‎. ‎When the variances are very unequal‎, ‎the actual sizes of these tests can be close to the nominal size and rarely exceed the nominal level‎. ‎Three data sets illustrate the application of the methods.

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References

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Journal of Statistical Modelling: Theory and Applications
Volume 6, Issue 2
July 2025
Pages 153-171

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History

  • Receive Date: 23 July 2025
  • Revise Date: 09 February 2026
  • Accept Date: 28 August 2026

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