Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A comparison of tests for homoscedasticity using simulation and empirical data

  • Anastasios Katsileros (Department of Crop Science, Agricultural University of Athens) ;
  • Nikolaos Antonetsis (Department of Crop Science, Agricultural University of Athens) ;
  • Paschalis Mouzaidis (Department of Forestry and Natural Resources, Democritus University of Thrace) ;
  • Eleni Tani (Department of Crop Science, Agricultural University of Athens) ;
  • Penelope J. Bebeli (Department of Crop Science, Agricultural University of Athens) ;
  • Alex Karagrigoriou (Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean)
  • Received : 2023.04.23
  • Accepted : 2023.10.14
  • Published : 2024.01.31
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Abstract

The assumption of homoscedasticity is one of the most crucial assumptions for many parametric tests used in the biological sciences. The aim of this paper is to compare the empirical probability of type I error and the power of ten parametric and two non-parametric tests for homoscedasticity with simulations under different types of distributions, number of groups, number of samples per group, variance ratio and significance levels, as well as through empirical data from an agricultural experiment. According to the findings of the simulation study, when there is no violation of the assumption of normality and the groups have equal variances and equal number of samples, the Bhandary-Dai, Cochran's C, Hartley's Fmax, Levene (trimmed mean) and Bartlett tests are considered robust. The Levene (absolute and square deviations) tests show a high probability of type I error in a small number of samples, which increases as the number of groups rises. When data groups display a nonnormal distribution, researchers should utilize the Levene (trimmed mean), O'Brien and Brown-Forsythe tests. On the other hand, if the assumption of normality is not violated but diagnostic plots indicate unequal variances between groups, researchers are advised to use the Bartlett, Z-variance, Bhandary-Dai and Levene (trimmed mean) tests. Assessing the tests being considered, the test that stands out as the most well-rounded choice is the Levene's test (trimmed mean), which provides satisfactory type I error control and relatively high power. According to the findings of the study and for the scenarios considered, the two non-parametric tests are not recommended. In conclusion, it is suggested to initially check for normality and consider the number of samples per group before choosing the most appropriate test for homoscedasticity.

Keywords

Acknowledgement

The authors extend their appreciation to the editor and referees for their valuable comments and suggestions, which has enhanced the quality of the current manuscript's presentation.

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