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Abstract

In many simple designs, observed frequencies in subclasses defined by a qualitative variable are compared to the frequencies expected on the basis of population proportions, design parameters or models. Often there is a quantitative variable which may be affected in the same way as the frequencies. Its differences among the groups may also be analyzed. A simple test is described that combines the effects on the frequencies and on the quantitative variable based on comparing the sums of the values for the quantitative value within each group to the random expectation. The sampling variance of the difference is derived and is shown to combine the qualitative and quantitative aspects in a logical way. A version of the test based on enumeration of the possible values of the sum is described, an example is analyzed, factors affecting the test's power are discussed and extensions are suggested.

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