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The power of a chi-square test, and thus the required sample size, are a function of the noncentrality parameter that can be obtained as the limiting expectation of the test statistic under an alternative hypothesis specification. Herein, we apply this principle to derive simple expressions for two tests that are commonly applied to discrete ordinal data. The Wilcoxon rank sum test for the equality of distributions in two groups is algebraically equivalent to the Mann-Whitney test. The Kruskal-Wallis test applies to multiple groups. These tests are equivalent to a Cochran-Mantel-Haenszel mean score test using rank scores for a set of C-discrete categories. Although various authors have assessed the power function of the Wilcoxon and Mann-Whitney tests, herein it is shown that the power of these tests with discrete observations, that is, with tied ranks, is readily provided by the power function of the corresponding Cochran-Mantel-Haenszel mean scores test for two and R > 2 groups. These expressions yield results virtually identical to those derived previously for rank scores and also apply to other score functions. The Cochran-Armitage test for trend assesses whether there is an monotonically increasing or decreasing trend in the proportions with a positive outcome or response over the C-ordered categories of an ordinal independent variable, for example, dose. Herein, it is shown that the power of the test is a function of the slope of the response probabilities over the ordinal scores assigned to the groups that yields simple expressions for the power of the test. Copyright © 2011 John Wiley & Sons, Ltd.
The Biostatistics Center, Departments of Epidemiology and Biostatistics and Statistics, The George Washington University, 6110 Executive Boulevard, Suite 750, Rockville, MD, 20852, USA. firstname.lastname@example.org.
This article was published in the following journal.
Name: Statistics in medicine
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The number of units (persons, animals, patients, specified circumstances, etc.) in a population to be studied. The sample size should be big enough to have a high likelihood of detecting a true difference between two groups. (From Wassertheil-Smoller, Biostatistics and Epidemiology, 1990, p95)
The analysis of a chemical substance by inserting a sample into a carrier stream of reagent using a sample injection valve that propels the sample downstream where mixing occurs in a coiled tube, then passes into a flow-through detector and a recorder or other data handling device.
A type of scanning probe microscopy in which a very sharp conducting needle is swept just a few angstroms above the surface of a sample. The tiny tunneling current that flows between the sample and the needle tip is measured, and from this are produced three-dimensional topographs. Due to the poor electron conductivity of most biological samples, thin metal coatings are deposited on the sample.
The process of discovering or asserting an objective or intrinsic relation between two objects or concepts; a faculty or power that enables a person to make judgments; the process of bringing to light and asserting the implicit meaning of a concept; a critical evaluation of a person or situation.
Studies determining the effectiveness or value of processes, personnel, and equipment, or the material on conducting such studies. For drugs and devices, CLINICAL TRIALS AS TOPIC; DRUG EVALUATION; and DRUG EVALUATION, PRECLINICAL are available.