D. J. Best

Welch's approximate solution for the Behrens-Fisher problem

The Wald, likelihood ratio, and score statistics have been calculated for the Behrens–Fisher problem. These statistics provide asymptotically equivalent and weakly optimal tests. The test based on the Wald statistic was found to be very similar to the V test discussed by Welch (1937); hence the V test was compared with the likelihood ratio and score tests in a power study. Since the powers were very similar and the V test was more convenient to use from several points of view, we recommend this test. Sizes of the V test, as well as a power comparison with the usual pooled t test, were also obtained.

The BIAS of the maximum likelihood estimators of the von mises-fisher concentration parameters

It is shown that the bias of the maximum likelihood estimators of the concentration parameters of the von Mises and Fisher distributions is considerable. New estimators which are either nearly unbiased or nearly median unbiased are proposed.

Interpreting the skewness coefficient

We examine and extend the argument of Horswell and Looney (1993), who claimed that the test for normality based on the sample skewness coefficient does not reliably discriminate between skewed and symmetric distributions. Theoretical and simulation evidence is given.

Smooth extensions of Pearsons's product moment correlation and Spearman's rho

A smooth model for doubly ordered two-way contingency tables with no fixed marginals is given and the score test of the hypothesis of independence derived. For the saturated model the score statistic is the familiar Pearons Xp2, and the first component is simply related to Pearsons product moment correlation. The higher-order components provide the promised extensions. They provide powerful direction tests and are easy to use and interpret, assessing if the bivariate moments of the data are consistent with what might be expected under the independence model. If ranks are used the score statistic is still Xp2, and the first component is simply related to Spearmans rho. The higher-order components again provide the promised extensions. In both cases the components permit an informative and close scrutiny of the data.

Nonparametric Analysis for Doubly Ordered Two-Way Contingency Tables

Tsujitani (1992, Biometrics 48, 267-269) and Kateri (1993, Biometrics 49, 950-951) considered analyses for two-way contingency tables. In this reader reaction a nonparametric analysis using mnidrank scores is given. This analysis can be interpreted in terms of bivariate moments, does not make model assumptions, takes into account the ordinal nature of the data, and allows Monte Carlo P values to be given.

Nonparametric comparison of two histograms.

Scholz and Stephens (1987, Journal of the American Statistical Association 82, 918-924) proposed a nonparametric k-sample Anderson-Darling statistic for grouped data. This note demonstrates that a partition-of-chi 2 method may give a more powerful nonparametric test, particularly when alternatives other than location shift are important. A taste-test example provides motivation.

Effects of polyethylene bags, ethylene absorbent and 1-methylcyclopropene on the storage of Japanese pears

Summary Storage of the ‘Nijisseiki’ cultivar of Japanese pears was studied over three seasons for periods up to 36 weeks at 0°C. Storage in 50 μm thick low-density polyethylene (LDPE) bags at 0°C considerably delayed yellowing in all experiments, even after fruit was removed to 20°C for 1 week at the end of storage. The addition of an ethylene absorbent made from potassium permanganate on aluminium oxide (Purafil II) further delayed yellowing. Carbon dioxide levels in both treatments varied, but were generally in the range 2–3%. Oxygen levels remained high, generally 16–19%. In bags without Purafil, ethylene levels rose slightly during storage and were generally about 0.15 μl l–1. When Purafil was included in the bags, the ethylene level was reduced 10-fold or more. A sensory test indicated that the use of LDPE bags and ethylene absorbent resulted in fruit with better eating quality than fruit stored in air. Disorders over the 3-year investigation were low even after long-term storage. The use of polyethylene bags reduced the severity of flesh browning, and flesh spot decay was virtually absent. The use of bags increased the severity of core browning. Inclusion of an ethylene absorbent in bags reduced the severity of disorders, particularly core browning. Treatment of the fruit with 1-methylcyclopropene (1-MCP), before or during storage, resulted in higher ethylene levels in the polyethylene bags. At the concentrations used, 1-MCP did not improve the storage of ‘Nijisseiki’ compared to the use of polyethylene bags with Purafil II.

Tests for Symmetry Based on the One-Sample Wilcoxon Signed Rank Statistic

ABSTRACT The one-sample Wilcoxon signed rank test was originally designed to test for a specified median, under the assumption that the distribution is symmetric, but it can also serve as a test for symmetry if the median is known. In this article we derive the Wilcoxon statistic as the first component of Pearsons X 2 statistic for independence in a particularly constructed contingency table. The second and third components are new test statistics for symmetry. In the second part of the article, the Wilcoxon test is extended so that symmetry around the median and symmetry in the tails can be examined seperately. A trimming proportion is used to split the observations in the tails from those around the median. We further extend the method so that no arbitrary choice for the trimming proportion has to be made. Finally, the new tests are compared to other tests for symmetry in a simulation study. It is concluded that our tests often have substantially greater powers than most other tests.

Tests of Fit for the Geometric Distribution

Abstract This article gives power comparisons of some tests of fit for the Geometric distribution. These tests include a Chernoff–Lehmann X 2 test, some smooth tests, a Kolmogorov–Smirnov test, and an Anderson–Darling test. This article suggests that a good test of fit analysis is provided by a data dependent Chernoff–Lehmann X 2 test with class expectations greater than unity, and its components. These data dependent statistics involve arithmetically simple parameter estimation, convenient approximate distributions, and provide a fairly complete assessment of how well the data agrees with a Geometric distribution. The power comparisons indicate also that the best performed single statistic is the Anderson–Darling statistic.

Goodness of fit for the Poisson distribution

Two problems with the usual X2 test of fit for the Poisson distribution are how to pool the data and how much power is lost by this pooling. Smooth tests of fit as outlined in Rayner and Best (1989) avoid the pooling problems and provide weakly optimal and therefore powerful tests. Power comparisons between X2, smooth tests and a modified Kolmogorov-Smirnov statistic are given.