Benjamin S. Duran

Small-sample behavior of some multisample nonparametric tests for scale

Abstract Several nonparametric and parametric statistics for testing the equality of scale parameters are compared with respect to their power and stability of error rates. When the populations have mass confined to the positive axis, the c-sample analog of the sum of squared ranks test and the Kruskal-Wallis test are found to be very robust and powerful. When the populations are symmetrical, the c-sample analogs of the two-sample Mood and two-sample Ansari-Bradley tests are robust for small samples, and are more powerful than Boxs test. Tables of exac probabilities and corresponding critical values of the nonparametric statistics are given for testing the equality of scales for small samples.

A Note on the Analysis of the Manova Model and its Application to Growth Curves

Maximum likelihood estimators fot the Parameter matrix X in the generalized miltivariata analysis of variance (MANOV) mode; E(Y) = AXB, are used in developing tast Procedures for testins the general Linear hypothesis HO DXE = ?. Applications of these results are applied to the data from a recent environmental study.

An example of cluster analysis applied to a large geologic data set: Aerial radiometric data from Copper Mountain, Wyoming

One objective of the aerial radiometric surveys flown as part of the U.S. Department of Energys National Uranium Resource Evaluation (NURE) program was to ascertain the spatial distribution of near-surface radioelement abundances on a regional scale. Some method for identifying groups of observations with similar γ-ray spectral signatures and radioelement concentration values was therefore required. It is shown in this paper that cluster analysis can identify such groups with or without a priori knowledge of the geology of an area. An approach that combines principal components analysis with convergentk-means cluster analysis is used to classify 6991 observations (each observation comprising three radiometric variables) from the Precambrian rocks of the Copper Mountain, Wyoming area. This method is compared with a convergentk-means analysis that utilizes available geologic knowledge. Both methods identify four clusters. Three of the clusters represent background values for the Precambrian rocks of the area, and the fourth represents outliers (anomalously high214Bi). A segmentation of the data corresponding to “geologic reality” as interpreted by other methods has been achieved by perceptive quantitative analysis of aerial radiometric data. The techniques employed are composites of classical clustering methods designed to handle the special problems presented by large data sets.

The rank transform in the two-sample location problem

In the two-sample location problem, if the t-statistic is computed as a function of the ranks of the observations rather than the observations themselves, the resulting statistic, Tr, is a function of the Wilcoxon statistic. It is shown here that Tr, has approximately a t-distribution. The ARE of the T-test is identical to that of the Wilcoxon test. A Monte Carlo study reveals that the T-test is more robust, with regard to the significance level, than the t-test.

Estimating the probability of misclassification and variate selection

Abstract This paper considers the problem of estimating the probability of misclassifying normal variates using the usual discriminant function when the parameters are unknown. The probability of misclassification is estimated, by Monte Carlo simulation, as a function of n 1 and n 2 (sample sizes), p (number of variates) and α (measure of separation between the two populations). The probability of misclassification is used to determine, for a given situation, the best number and subset of variates for various sample sizes. An example using real data is given.

A Robust Test in the Multivariate Two-Sample Location Problem

SYNOPTIC ABSTRACTA frequently employed test for the equality of two mean vectors is Hotellings two-sample T2, which assumes multinormality of the populations. When the multinormality assumption is violated, modified versions of T2 and/or nonparametric statistics are utilized. In this paper, it is shown that if Hotellings T2 statistic is computed as a function of the ranks (instead of the original observations), the resulting statistic is a monotone function of a nonparametric statistic. Just as T2 reduces to the square of a t-statistic in univariate distributions, the rank T2 reduces to a rank transform statistic TR proposed by Conover and Iman (1981). For several bivariate distributions, Monte Carlo results are presented, which suggest robustness of rank T2.

A comparison of some nonparametric tests for scale

This paper presents simulated power functions for the sum of squared ranks, Wilcoxon Savages T and locally most powerful tests for the two-sample scale problem using small samples drawn from gamma distributions. Also, pitman efficiencies of each of these tests relative to the best test test are compared for gamma distributionsd. In addition, the sum of squared ranks is shown to be prferable to a composite test due to Woinsky in some situations.

Comparison of Some Classification Techniques

The so-called table look-up classification procedure and a modification of it are discussed. These and several other classification techniques are evaluated and simulation results comparing some of the techniques are displayed. Indications are that the table look-up technique is quite useful in classifying large sets of data, such as in remote sensing data analysis.

On the table look-up in discriminate analysis

The discriminate analysis problem is discussed briefly. An analytical formulation of the so-called Eppler (Table Look-up) algorithm is given along with a modification which equates the algorithm with the classical Bayes procedure. Simulation results comparing several discriminate analysis techniques are given.

A monte carlo comparison of some t-tests

A class of statistical tests for testing the hypothesis H 0Δ=0, where Δ is a location parameter, is proposed. The test statistic is defined in terms of the signed ranks of the sample data. Il is shown, by the method of moment matching, that under the null hypothesis test statistics in the proposed class have approximately a t-distribution. A Monte Carlo simulation study is presented inorder to compare the significance levels and power of these tests with numerous other tests.