Robustness of analysis of covariance (ancova) under the distributions assumptions and variance homogeneity

Abstract

Aim: As in all parametric methods, the ANCOVA method assumes that normal distributions of errors, homogeneity of variances, and error terms are independent of each other. However, unusual distributions in practice are more common than normal distribution. In this study, it is aimed to examine ANCOVA method or type 1 error rates under different distribution conditions and homogeneity of variances. Materials and Methods: For this purpose, a simulation studies under different scenarios was conducted. Random numbers were generated from Gamma, Beta and Normal distributions considering different groups and different sample sizes. In the simulation studies, 10000 replications were run under the null hypothesis of no group differences and type-I error rates were calculated for each scenario. Results: According to the results, in the case of the normal distribution with homogeneous variance, the proportion of Type I error is high in the groups with the sample size of n=20 and n=40. In the case of normal distribution with the heterogeneous variance, the deviation has been observed in the groups with the sample size of n = 10 and n = 30, and n = 40. These results are the same as the results of Gamma distribution. In the Beta distribution, , there is a deviation in the groups with n=10 and n=20 where the sample sizes are small. Conclusion: The results showed that type-I error rate is affected by skewness of the distribution, sample size and homogeneity of variance. Further work can be extended by simulation studies under different distributions and parameter values.

Keywords

• analysis of covariance
• beta
• gamma
• normal
• robustness
• type-i error