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A New Test Operator, VJ, Based on Class Frequencies

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Technical rept. 1 Feb 1971-30 Apr 1972

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The test statistic chi square of the Chi-square test may, if applied to a proper sample, be used for selecting distribution functions. When examining its use for this purpose its decision power was found to be very small due to a kind of pooling, an inherent property of its definition. In order to eliminate this pooling, a new test statistic, denoted by VJ, was introduced. It is defined by the number v sub i of sample elements which fall within each of r properly defined classes into which the space of the variable x has been divided. In fact chi square may be regarded as a statistic obtained from VJ by a pooling procedure. For this reason VJ was expected to have a much larger decision power than chi square as was verified by the example that the decision power for a specified case being 6.6 for chi square was raised to 69.1 for VJ. The properties of VJ have been thoroughly examined. In particular the class limits yielding the largest decision power have been determined with the result that, in some cases, the decision power was found to be somewhat larger than anyone sofar attained. The statistic VJ can also be used for stating whether a hypothetical distribution is acceptable or not and also for selecting the most probable one within a set of such distributions. Necessary tables for the practical use have been prepared.

Subject Categories:

  • Statistics and Probability

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