For the comparison of more than two independent samples the Kruskal-Wallis H test is a preferred procedure in many situations. However, the exact null and alternative hypotheses, as well as the assumptions of this test, do not seem to be very clear among behavioral scientists. This article attempts to bring some order to the inconsistent, sometimes controversial treatments of the Kruskal-Wallis test. First we clarify that the H test cannot detect with consistently increasing power any alternative hypothesis other than exceptions to stochastic homogeneity. It is then shown by a mathematical derivation that stochastic homogeneity is equivalent to the equality of the expected values of the rank sample means. This finding implies that the null hypothesis of stochastic homogeneity can be tested by an ANOVA performed on the rank transforms, which is essentially equivalent to doing a Kruskal-Wallis H test. If the variance homogeneity condition does not hold then it is suggested that robust ANOVA alternatives performed on ranks be used for testing stochastic homogeneity. Generalizations are also made with respect to Friedman’s G test.
Abstract:ROPstat is a wide scope statistical program package which offers specialties in three domains: 1) robust techniques, 2) ordinal analyses, and 3) pattern and person oriented methods. Many of them are not available in other common statistical softwares. In the present paper, first the general features and the main structure of ROPstat are briefly outlined, followed by a more detailed summary of pattern-oriented methods (detecting and imputing missing values, residual case identification, different types of classifications, post-analyses after classifications, etc.). In the last section we present some selected person-oriented scientific questions and show with real-life research data how they can be analyzed using ROPstat.
Studying the effect of psychedelic substances on expression of creativity is a challenging problem. Our primary objective was to study the psychometric measures of creativity after a series of ayahuasca ceremonies at a time when the acute effects have subsided. The secondary objective was to investigate how entoptic phenomena emerge during expression of creativity. Forty individuals who were self-motivated participants of ayahuasca rituals in Brazil completed the visual components of the Torrance Tests of Creative Thinking before and the second day after the end of a two-week long ceremony series. Twenty-one comparison subjects who did not participate in recent psychedelic use also took the Torrance tests twice, two weeks apart. Repeated ingestion of ayahuasca in the ritual setting significantly increased the number of highly original solutions and phosphenic responses. However, participants in the ayahuasca ceremonies exhibited more phosphenic solutions already at the baseline, probably due to the fact that they had more psychedelic experiences within six months prior to the study than the comparison subjects did. This naturalistic study supports the notion that some measures of visual creativity may increase after ritual use of ayahuasca, when the acute psychoactive effects are receded. It also demonstrates an increased entoptic activity after repeated ayahuasca ingestion.
The paper focuses on the internal validity of clustering solutions. The "goodness" of a cluster structure can be judged by means of different cluster quality coefficient (QC) measures, such as the percentage of explained variance, the point-biserial correlation, the Silhouette coefficient, etc. The paper presents the most commonly used QCs occurring in well-known statistical program packages, and we have strived to make the presentation as non technical as possible to make it accessible to the applied researcher. The focus is on QCs useful in person-oriented research. Based on simulated data with independent variables, the paper shows that QCs can be strongly influenced by the number of clusters and the number of input variables, and that the value of a QC can be fairly high even in the absence of any real cluster structure. When evaluating the internal validity, it is helpful to relate the QCs of a clustering solution to those obtained in parallel analyses of random data. We also introduce a new type of QC, measuring the relative improvement (MORI) of a QC obtained for a certain clustering solution relative to the corresponding QC based on a relevant type of random data.
In a comparison of 2 treatments, if outcome scores are denoted by X in 1 condition and by Y in the other, stochastic equality is defined as P(X < Y) = P(X > Y). Tests of stochastic equality can be affected by characteristics of the distributions being compared, such as heterogeneity of variance. Thus, various robust tests of stochastic equality have been proposed and are evaluated here using a Monte Carlo study with sample sizes ranging from 10 to 30. Three robust tests are identified that perform well in Type I error rates and power except when extremely skewed data co-occur with very small n. When tests of stochastic equality might be preferred to tests of means is also considered.
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