A Note on Non-Parametric Tests for the Interaction in Two-Way Layouts

A suggestion is given of how to prove main and interaction effects in two-way layouts independent of each other even if the data are just ordinally scaled. Starting from HILDEBRAND'S (1980a, b) non-parametric approach which presupposes interval-scaled data, transformations of ranks are settled before analysis per analogy to the H-test takes place. That is, the same formula of an asymptotically X²-distributed test-statistic results but mean ranks are used instead of mean scores in order to partialize, for instance, main effects while testing interaction effect. Finally an allusion is given of how to handle ties as well as unequal sample sizes.     

A Note on Combining Dependent Tests of Significance

In combining several tests of significance the individual test statistics are allowed to be stochastically dependent. By choosing the weighted inverse normal method for the combination, the dependency of the original test statistics is then characterized by a correlation of the transformed statistics. For this correlation a confidence region, an unbiased estimator and an unbiased estimate of its variance are derived. The combined test statistic is extended to include the case of possibly dependent original test statistics. Simulation studies show the performance of the actual significance level.     

Robust Umbrella Tests for a Generalized Behrens-Fisher Problem

This paper is concerned with testing for umbrella alternatives in a k-sample location problem when the underlying populations have possibly different shapes. Following CHEN and WOLFE (1990b), rank-based modifications of the HETTMANSPERGER-NORTON (1987) tests are considered for both the settings where the peak of the umbrella is known and where it is unknown. The proposed procedures are exactly distribution-free when the continuous populations are identical with any shape. Moreover, the modified test for peak-known umbrella alternatives remains asymptotically distribution-free when the continuous populations are assumed to be symmetric, even if they differ in shapes. Comparative results of a Monte Carlo study are presented.     

A Note on Plots of P-Values to Evaluate Many Tests Simultaneously

Schweder and Spjøtvoll (1982) proposed an informal graphical procedure for simultaneous evaluation of possibly related tests, based on a plot of cumulative p-values using the observed significance probabilities. We formalize this notion by application of Holm's (1979) sequentially rejective Bonferroni procedure: this maintains an overall experimentwise significance level, and yields an immediate estimate of the number of true hypotheses.     

A Note on Optimality of Certain Rank Tests for Ordered Alternatives in Randomized Blocks

Nonparametric tests for ordered alternatives in randomised block designs based on within block rankings have been proposed by many authors. This note is concerned with the optimality of the choice of so-called regression constants usually considered in such rank tests. Some examples are discussed.     

Non-Parametric Methods for the 2-Period-Cross-Over Design Under Weak Model Assumptions

A nonparametric analysis for the two period cross-over design has first been suggested by Koch (1972) and has been discussed by Hills and Armitage (1979). As known rank tests on sums or differences of the data are applied in this procedure, the results on the one hand are not invariant under monotonous transformations and on the other hand the procedure is only correct for models with additive effects. Therefore, in the present article generalized effects will first be defined in the 2-period cross-over design without the assumption of a linear model and then rank test will be presented which test tese effects without the need of sums or differences of the data. In the appendix the equivalence of the hypothesis for the generalized effects to the known hypotheses for the effects in the linear model will be shown. The application of the procedures will be demonstrated by means of an example in literature.     

Comment on Baylor: A Note About Dreams of Scientific Problem Solving

Creative problem-solving dreams virtually always occur only after the dreamer has done extensive work on the issue awake. Most typically, a person is stuck at one particular step of a multiple phase process and the dream solves that step. The dream of Dmitri Mendeleev about The Periodic Table of the Elements is no exception. All accounts of this event agree that he'd worked for years on the Table, produced other drafts, but that he attributed the version he was most satisfied with to a dream. It is less clear whether Kedrov is correct in his reconstruction that it was the reversal of columns vs. rows which the dream provided. Accounts of dreams from contemporary scientists and inventors are a richer source for the detail required to generalize about the role of dreams in problem solving.     

A Note on the Use of Objective Tests in Physiology

The use of objective tests in the examination of pharmacy undergraduates in physiology is described, and examples are given. These tests have produced examinations of high reliability and discriminating power, and are at least as acceptable to the examinees as traditional essay-type questions.     

A Closed-form Jackknife Solution for the Behrens-Fisher Problem

A simple, closed-form jackknife estimate of the actual variance of the Mann-Whitney-Wilcoxon statistic, as opposed to the standard permutational variance under the test's null hypothesis has been derived which permits avoiding anticonservative performance in the presence of heterosce-dasticity. The formulation given allows modifications of the exponential scores test, of censored data tests by Gehan (1965), Peto & Peto (1977) and Prentice (1978), of tests for monotonic τ association by Kendall (1962) and for tests of ordered k-sample hypotheses. A Monte Carlo study supports recommendations for the jackknife procedures, but also shows their limited advantages in exponential scores and censored data versions. Thus, the paper extends results by Fligner & Policello (1981).     

Robustness of Statistical Tests in the Two-Sample Location Problem

A simulation study was performed to compare three statistical tests with respect to their performances in the two-sample location problem for contaminated normal distributions. The three tests were: the t-test, the rank-transformed t-test, and the Wilcoxon rank-sum test. The results showed the t-test to be inferior to the other two tests.     

A Note on The Computer Marking of Objective Tests

A considerable proportion of biology teachers in schools and technical colleges are at present using or contemplating using radioactive isotopes for certain experiments in their courses. These experiments (a general list appears at the end of the article) are easy to perform and usually biologically instructive.

For the teacher the experiment naturally does not stop with performing it; solutions have to be prepared, supervision and suggestions have to be given to students concerning data handling, half-life and self-absorption corrections, etc. An awareness of the pitfalls in both technique and result interpretation has to be gained and this is usually not possible even in an intensive one week course that most teachers have attended.

For this reason this article covers the minimum necessary nuclear fundamentals such as levels of activity, specific activity and the use of carrier materials. The way the isotope is assayed and the corrections that need to be made or taken into account to obtain a valid result is also described in detail. A minimum of statistics necessary for such a valid result is similarly covered. From experience gained in running short radio-isotope courses for teachers some common misconceptions that often arise due to lack of course time have also been included.     

A Note on Measures of Multivariate Kurtosis

We propose a measure of multivariate kurtosis suggested from Mardia's measure of multivariate skewness b₁,p, and examine its relationship both to Mardia's measure of multivariate kurtosis b₂,p, and to a smooth test of multivariate kurtosis ǔ₄².     

Survival Tests for r Groups

In this paper we give the generalization of the score tests covering the case of ties and we give examples where the expressions in matrix form are completely specified for the weighted tests and the score tests for the case of r groups. It is worth mentioning that although the score tests are not generally included in the commercial software, these tests should be used if it can be assumed that the censoring mechanism is equal in the r groups or if there is no censoring (Lawless , 1982). We establish the equivalence between “numerators” of these families of tests. As result of this equivalence we define four new tests that complete the classification of score and weighted tests. The Kruskal‐Wallis test (1952) appears as a particular case of the score tests for the case of non‐censoring. A simulation study has been done in order to compare the performance of the tests described in this paper. An example is included to make the understanding of the paper easier.     

What Do We Really Know About Mendeleev's Dream of the Periodic Table? A Note on Dreams of Scientific Problem Solving

As is well known, some dreams have been instrumental in important scientific discoveries. Kekulé's dream of the whirling snakes is probably the most famous instance though there was apparently no public written record of it until some 28 years later. Loewi, even in his own autobiographic material, appears never to have provided a written report of the dream that led him to carry out the experiment demonstrating the chemical transmission of nerve impulses to a frog's heart. Mendeleev's dream of the periodic table of elements in its completed form is apparently specious, despite repeated citations. Not only is there no dream report but evidence rests on a colleague's second-hand account. Kedrov's examination of archival material indicates (1) that Mendeleev had already discovered the periodic table before the alleged dream took place; and (2) that a dream quite plausibly occurred somewhat later that depicted an improved representation of the periodic table. Kedrov's reconstruction is consistent with other accounts of dreams and the process of scientific discovery.     

A Study of Distribution-free Tests for Umbrella Alternatives

In this paper we are concerned with test procedures for umbrella alternatives in the k-sample location problem. Distribution-free tests are considered for both cases where the peak of the umbrella is known or unknown. Comparative results of a Monte Carlo power study are presented.