ERIC Number: ED069666
Record Type: RIE
Publication Date: 1972-Mar
Reference Count: 0
An Empirical Investigation of Specified Violations of the Assumptions Underlying Statistical Techniques. Final Report.
Havlicek, Larry L.
The purpose of this study was to empirically determine the effects of quantified violations of the underlying assumptions of parametric statistical tests commonly used in educational research, namely the correlation coefficient (r) and the t test. The effects of heterogeneity of variance, nonnormality, and nonlinear transformations of scales were studied separetely and in all combinations. Monte Carlo procedures were followed to generate random digits which had the following shapes: normal, positively skewed, negatively skewed, and leptokurtic. Interval, ordinal, and percentile rank transformations were used for all of the computations which were based on 5,000 sets of randomly generated numbers, each set containing either 5, 15, or 30 such numbers. A total of 1,332 combinations of differences in shape of distribution, variance, size of sample, and type of scale were studied. The results indicate that the distribution or r do not deviate significantly from the theoretical distributions even under the most severe combinations of violations. However, there were many significant discrepancies for the t test. The results of this study lead to the conclusion that the t test is not as robust as generally thought and that researchers should consider all of the basic assumptions before applying this test to their data. (Author)
Publication Type: N/A
Education Level: N/A
Sponsor: Office of Education (DHEW), Washington, DC. Regional Research Program.
Authoring Institution: Kansas Univ., Lawrence. School of Education.