The effects of different outlier accommodation methods on various hypothesis test results

Many researches are made every day to increase the level of students', teacher, custadian and such success or attitude in the field of education. In these studies, data sets containing outliers can be encountered. It is stated in the literature that the presence of outliers in the data sets is a situation that affects the statistical analysis. Outliers accommodation methods are used to decrease the effects of outliers. In this study, it is aimed to determine whether the findings of independent samples t-test, one-way variance analysis, two-way variance analysis, and simple regression analysis differ when trimmed mean, winsorized mean, and truncation methods are used to deal with outliers. The research is important because it provides information about under which conditions which method is more effective in removing the effects of outliers. According to the purpose of the research, raw datasets which consist of three independent and one dependent variables for small (158), medium (308) and large (608) samples were produced in the R program. Two-category, four-category variables and score2 variable are assumed to be independent and the score is assumed to be dependent variables. Score variables of size 150, 300, and 600 were produced and 8 outliers were added to each one later. After the score variable was produced, independent variables with 2 and 4 categories and the score2 variable were defined. The variables which were obtained were matched randomly for each sample size and turned into a data set containing 2 categories, 4 categories, score, and score2 variables. Z score, box chart, and normal Q-Q chart methods of determining outliers are used and the values which are determined as outliers in least two of these methods are accepted as the outlier. According to the results of the t-test, it was observed that t values increased in small and medium samples which outlier accommodation methods are used in, whereas t values decreased in large samples. P values generally decreased for all three samples. According to the results of one way ANOVA test, it was observed that in small, medium, and large samples F values generally increased and p values decreased. According to the results of two way ANOVA test, it was observed that F values generally increased in small and large samples whereas it decreased in medium samples. However, it was observed that P values decreased. according to the result of simple regression analysis, for all three sample sizes r, the square of R, α, β values decreased, and p-value increased. The trimmed mean method is suggested to use for independent samples t-test and two-way variance analysis in all three samples size. However, in one-way variance analysis, trimmed mean in small and medium sample sizes, winsorized mean or trimmed mean method is suggested to use in large samples. In simple regression analysis, the truncation method is suggested to use for small and medium-size samples, and the trimmed mean method should be used for large samples.