The twenty closest interpoint distances associated with each point set can be sorted from smallest to largest. The smallest two values are guaranteed to be identical. So we drop one. The values in the sorted order are called order statistics. For our test statistic we use a linear combination of the order statistics where the weights of the linear combination are given as they are defined by Fisher Linear Discriminant Analysis. To determine the Fisher weights, the first 5,000 of the 10,000 point data sets generated under the Null hypothesis and first 5,000 generated under the Alternative hypothesis are used. To determine the misdetect rate, the remaining 5,000 of the point data sets generated under the Null hypothesis and generated under the Alternative hypothesis are used. We find that the misdetect rate at the 1% significance level is .014, somewhat better than the .0245 misdetect rate using the geometric mean. We next look at the receiver operating curve for linear combination of these order statistics as given by the Fisher Linear Discriminant Analysis and compare it with the receiver operating curve for the other test statistics.

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