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• W79884058 abstract "While violation of the homogeneity of variance assumption has received considerable attention, violation of the assumption of normally distributed data has not received as much attention. As a result, researchers may have the mistaken impression that as long as the assumptions of independence of observations and homogeneity of variance are satisfied, violations of the distributional assumption gave inconsequential effects. This paper reviews some of the relevant literature and reports the results of a new Monte Carlo study indicating that this is not the case. The simulation investigated the effects of varying skewness and kurtosis levels, while maintaining equal population variances, on the two-sample test and Welch's robust test. Sample sizes were either small or moderate, and equal or unequal. Results indicate that, with skewed distributions, the validity of both the test and the Welch test clearly depends on the two distributions being skewed in the same direction. When the two parent distributions are skewed in the same direction, both tests have quite acceptable Type I error rates, even with relatively small samples. However, when the two parent distributions are skewed in opposite directions, then the true Type I error rates can deviate markedly from the nominal level even though population variances are equal. The actual Type I error rate of the test performed at a 0.05 nominal level with homogeneous variances can be higher than 0.08 with a two-tailed test, and can be higher than 0.11 with a one-tailed test. (Contains 16 figures and 23 references.) (SLD) Reproductions supplied by EDRS are the best that can be made from the original document. Nonnormality Effects on t 1 THE EFFECT OF NONNORMALITY ON STUDENT'S TWO-SAMPLE T TEST PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL HAS BEEN GRANTED BY TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) Harold D. Delaney Department of Psychology, UNM, USA Andras Vargha Institute of Psychology, ELTE, Hungary Please address all correspondence concerning this manuscript to: Harold Delaney Department of Psychology University of New Mexico Albuquerque, NM 87131 E-mail: hdelaney@unm.edu Author Note U.S. DEPARTMENT OF EDUCATION Office of Educational Research and Improvement EDU ATIONAL RESOURCES INFORMATION CENTER (ERIC) This document has been reproduced as received from the person or organization originating it. Minor changes have been made to improve reproduction quality. Points of view or opinions stated in this document do not necessarily represent official OERI position or policy. Much of the work reported herein resulted from the collaborative efforts of Drs. Vargha and Delaney while Vargha was a Szechenyi Professor Scholar and supported by Hungarian OTKA, grant Nos.: TO18353 and T032157. Vargha's work was also supported by the Hungarian FKFP grant No. 0194/2000 and the Research Support Scheme of the Open Society Support Foundation, grant No.: 584/1998." @default.
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• W79884058 title "The Effect of Nonnormality on Student's Two-Sample T Test." @default.
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