Yazd University Journal of Statistical Modelling: Theory and Applications 2676-7392 6 2 2025 07 01 Tests for one-way analysis of covariance with heteroscedasticity 153 171 4232 10.22034/jsmta.2026.23408.1185 EN Ali Akbar Jafari Department of Statistics, Yazd University, Yazd, Iran 0000-0002-2980-338X Soltan Mohammad Sadooghi-Alvandi Department of Statistics, Shiraz University, Shiraz, Iran Journal Article 2025 07 23 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. https://jsm.yazd.ac.ir/article_4232_17dc71e491881152ed1e25ea46281bef.pdf