Use of Alternative Tests in Equality of Group Means in Cases of Non-homogeneous Variances: A Practice in Agriculture

Abstract

In this study, it was aimed to apply Welch and Brown-Forsythe tests as the analysis of variance was not used in the case of non-homogeneous variances.

F test was designed to test the variation of strawberry yield per decare across 7 different geographical regions in Turkey. In order to this test, the Levene test was used which is one of the necessary assumptions used in the homogeneity of variances to carry out this test. In conclusion of Levene's test, it was found that the variances were not homogeneous, and the square root transform was applied to the data, and the homogeneity of the variances was tested again, however, the homogeneity assumption of the variances could not be achieved. As a result of the Levene test that was performed on the data to which logarithmic transformation was also applied, the condition of homogeneity of variances could not be met. For this reason, Welch and Brown-Forsythe tests were applied. At the end of the application, the difference between strawberry yields according to the regions proved statistically significant (p<0.01). According to Tamhane, Dunnett T3 and Games-Howell multiple comparison tests, yield differences across regions were found between Mediterranean and Black Sea Regions. As a result, when the variances are not homogeneous and other assumptions are not met, Welch and Brown-Forsythe tests are alternative methods used in place of the F test. In cases where the variances were not homogeneous, it was found more appropriate to use the Tamhane, Dunnett T3 and Games-Howell tests out of the multiple comparison tests.