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. |