Book review

W.G.Cochran: Sampling Techniques, 3rd. Ed. John Wiley & Sons, New York-Santa Barbara-London-Sydney-Toronto 1977. 428 S., £ 12.50; $21.50.

H.Toutenburg: Vorhersage in linearen Modellen. Akademie-Verlag, Berlin 1975, VIII, 176b S., 3 Tab., 28,– M.

O.Kallenberg: Random Measure. Akademie-Verlag, Berlin 1975; Academic Press, London 1976. 104 pp., 28,– M.     

The robustness of the systemwise breusch-godfrey autocorrelation test for non-normal distributed error terms

Using Monte Carlo methods, the properties of systemwise generalisations of the Breusch-Godfrey test for autocorrelated errors are studied in situations when the error terms follow either normal or non-normal distributions, and when these errors follow either AR(1) or MA(1) processes. Edgerton and Shukur (1999) studied the properties of the test using normally distributed error terms and when these errors follow an AR(1) process. When the errors follow a non-normal distribution, the performances of the tests deteriorate especially when the tails are very heavy. The performances of the tests become better (as in the case when the errors are generated by the normal distribution) when the errors are less heavy tailed.     

Inferences on the lognormal mean for complete samples

In many engineering problems it is necessary to draw statistical inferences on the mean of a lognormal distribution based on a complete sample of observations. Statistical demonstration of mean time to repair (MTTR) is one example. Although optimum confidence intervals and hypothesis tests for the lognormal mean have been developed, they are difficult to use, requiring extensive tables and/or a computer. In this paper, simplified conservative methods for calculating confidence intervals or hypothesis tests for the lognormal mean are presented. In this paper, “conservative” refers to confidence intervals (hypothesis tests) whose infimum coverage probability (supremum probability of rejecting the null hypothesis taken over parameter values under the null hypothesis) equals the nominal level. The term “conservative” has obvious implications to confidence intervals (they are “wider” in some sense than their optimum or exact counterparts). Applying the term “conservative” to hypothesis tests should not be confusing if it is remembered that this implies that their equivalent confidence intervals are conservative. No implication of optimality is intended for these conservative procedures. It is emphasized that these are direct statistical inference methods for the lognormal mean, as opposed to the already well-known methods for the parameters of the underlying normal distribution. The method currently employed in MIL-STD-471A for statistical demonstration of MTTR is analyzed and compared to the new method in terms of asymptotic relative efficiency. The new methods are also compared to the optimum methods derived by Land (1971, 1973).     

On asymptotic non-normality of null distributions of mrpp statistics

Severe departures from normality occur frequently for null distributions of statistics associated with applications of mulLi-response permutation procedures (MRPP) for either small or large finite populations. This paper describes the commonly encountered situation associated with asymptotic non-normality for null distributions of MRPP statistics which does not depend on the underlying multivariate distribution. In addition, this paper establishes the existence of a non-degenerate underlying distribution for which the null distributions of MRPP statistics are asymptotically non-normal for essentially all size structure configurations. It is known that MRPP statistics are symmetric versions of a broader class of statistics, most of which are asymmetric. Because of the non-normality associated with null distributions of MRPP statistics, this paper includes necessary results for inferences based on the exact first three moments of anv statistic in this broader class (analogous to existing results for MRPP statistics).     

Smooth goodness of fit tests for the weibull distribution with singly censored data

The smooth goodness of fit tests are generalized to singly censored data and applied to the problem of testing Weibull (or extreme value) fit. Smooth tests, Pearson-type tests, and the spacings tests proposed by Mann, Schemer, and Fertig (1973) are compared on the basis of local asymptotic relative efficiency with respect to the asymptotic best test against generalized gamma alternatives, The smooth test of order one Is found to be most efficient for the generalized gamma alternatives.     

Computation of finite population parameters and approximate probability values for multi-response randomized block permutation procedures (mrbp)

An algorithm is presented for computing the finite population parameters and the approximate probability values associated with a recently-developed class of statistical inference techniques termed multi-response randomized block permutation procedures (MRBP).     

The Effect of a Variable Data Point on Hypothesis Tests for Means

The effect of a single variable data point, x, on the usual test statistics for traditional hypothesis tests for means is analyzed. It is shown that an outlier may have a profound and unexpected effect on the test statistic. Although it might appear that an outlier would tend to lend support to the alternate hypothesis, it may in fact detract from the significance of the test. In one-population tests and analysis of variance (ANOVA), the value of x that maximizes the significance of the test statistic is given. This value does not have to be unusually large or small. In fact, it often falls within the range of the other sample points. In the general one-population case, the limiting value for the test statistic is shown to be +1. In the case involving more than one population, it is shown that the limiting value of the test statistic is a function only of the number of members in the samples and not their relative values. Special cases are identified in which the test statistic is shown to have unique characteristics depending on the characteristics of the data.     

Modification of Tukey's additivity test

In this paper we discuss testing for an interaction in the two-way ANOVA with just one observation per cell. The known results are reviewed and a simulation study is performed to evaluate type I and type II risks of the tests. It is shown that the Tukey and Mandel additivity tests have very low power in case of more general interaction scheme. A modification of Tukey's test is developed to resolve this issue. All tests mentioned in the paper have been implemented in R package Additivity Tests.     

Accent on Teaching Materials

A linear combination test for combining several tests of the correlation coefficient in the bivariate normal distribution is proposed. The linear combination test is compared with the well-known Fisher method of combining tests. It is shown by a Monte Carlo study that the linear combination test has a larger power.     

An alternative method for global and partial comparison of two diagnostic systems based on ROC curves

In this paper, an alternative method for the comparison of two diagnostic systems based on receiver operating characteristic (ROC) curves is presented. ROC curve analysis is often used as a statistical tool for the evaluation of diagnostic systems. However, in general, the comparison of ROC curves is not straightforward, in particular, when they cross each other. A similar difficulty is also observed in the multi-objective optimization field where sets of solutions defining fronts must be compared with a multi-dimensional space. Thus, the proposed methodology is based on a procedure used to compare the performance of distinct multi-objective optimization algorithms. In general, methods based on the area under the ROC curves are not sensitive to the existence of crossing points between the curves. The new approach can deal with this situation and also allows the comparison of partial portions of ROC curves according to particular values of sensitivity and specificity of practical interest. Simulations results are presented. For illustration purposes, considering real data from newborns with very low birthweight, the new method was applied in order to discriminate the better index for evaluating the risk of death.