A Monte Carlo computer study of the power properties of six distribution-free and/or nonparametric statistical tests under various methods of resolving tied ranks when applied to normal and nonnormal data distributions
A study of the power properties of six nonparametric/distribution-free statistics was conducted via computer simulations using Monte Carlo techniques. These statistics utilized rank based procedures and shared an underlying assumption of population continuity such that samples were assumed to have no equal data values (zero difference scores, tied ranks). This assumption is almost never met in practice, however, especially with data in the social and behavioral sciences. The properties of such tests, in particular their power to detect real effects when they exist, is altered under such conditions compared to their theoretical performance when underlying assumptions are met. The nature and extent of these departures are often mathematically intractable, depending on complex interactions of particular combinations and degrees of violation. These tests have not been as extensively studied under violation of their assumptions as they need to be. Both theoretical and empirical data distributions were used for sampling, including the normal distribution for reference. Four of the distributions described by Micerri (1986, 1989) as being typical of the data found in social and behavioral science were used as the source of discrete, nonnormal data. Pure location shift effects were introduced, with integral amounts of shift for the Micceri (1986, 1989) distributions in order to get equal data values between groups. A number of methods for dealing with this situation have been suggested in the literature, but there are few empirical studies. This study looked at various methods for dealing with equal data values (tied ranks). The best overall results, across all tests and combinations of simulation parameters, were obtained by randomly resolving ties. The method of dropping ties and reducing the sample size performed very poorly and should be avoided. The pattern and occurrence of ties was also investigated, along with sampling adequacy. Critical values and associated probabilities were also generated for four of the tests.
|Year of publication:||
|Authors:||Fay, Bruce Robert|
Wayne State University
|Type of publication:||Other|
ETD Collection for Wayne State University
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