Browsing by Author "Alessa, Sarah"

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NONPARAMETRIC TESTS FOR THE SIMPLE TREE ALTERNATIVE FOR LOCATION AND SCALE TESTING
(Saudi Digital Library, 2026) Alessa, Sarah; Magel, Rhonda
Testing differences in location and scale are critical across various fields. This research focuses on comparing, developing and modifying nonparametric tests to determine whether one or more treatment effects differ from the control. This study is divided into three parts. In the first part, we compared the Moses and Levene tests for differences in variances between two populations without assuming equal location parameters. Each test is evaluated using different versions: mean, median, and trimmed mean. Their performance is assessed using simulation studies in terms of maintaining significance levels and estimated powers under equal and unequal sample sizes and various subsample sizes (in Moses' test cases). The second part focuses on the simple tree alternative, comparing a control group with various levels of treatment based on scale parameter changes only. Four tests (Moses, Conover Squared Ranks, Hollander, and Mood) are compared, with three versions (mean, median, and trimmed mean) considered for all tests except Mood. The analysis examines how well these tests maintain significance levels, with power estimated under various distributions and different variance values. Notably, the Moses test is the only one unaffected by differences in location. The Levene test is excluded as it is designed for two-sided alternatives, whereas this part focuses on detecting whether at least one of the levels of the treatment has a larger variance than the control. Lastly, we developed tests for testing at least one treatment level having higher variance and/or mean than control, based on the simple tree alternative hypothesis. We proposed four new tests by combining the Mann-Whitney location test with each scale tests (Moses, Conover Squared Ranks, Hollander, and Mood). For the Moses, Conover Squared Ranks, and Hollander tests, we evaluated two versions using the mean and the median as measures of central tendency. iv We compared these four newly proposed nonparametric tests: Mann-Whitney and Moses; Mann-Whitney and Conover Squared Ranks; Mann-Whitney and Hollander; Mann-Whitney and Mood, with two previously tests: Alsubie and Magel test; Shukr and Magel tests. Their performances are compared by examining how well they maintain their significance levels and their estimated power under various conditions.
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