Abstract
In this article, we describe a new statistic. It has a number of qualities that recommend it for use as a one-sample test for goodness-of-fit. It is easy to describe and compute, and so is useful as a teaching tool. It is a distribution-free statistic. Its distribution is skewed and it has a comparatively large range of values. Therefore, it can supply more critical points that correspond to desired alpha levels. We can determine the .01, .05, .10, and .20 critical points for any large value of n by using a generalized formula. We can extend the definition of this statistic to a two-sample situation. It is a test that provides excellent power. My results show that the power is on a par with the Cramer-Von Mises one-sample test for goodness-of-fit. This article contains five sections, as follows: 1. Defining the new statistic, A. 2. Description of the tests of power. 3. Tables of the distribution for the A statistic. 4. Table summarizing the results of the power tests. 5. A brief bibliography.
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