scholarly journals Extensions to the Kruskal-Wallis test and a generalised median test with extensions

1997 ◽  
Vol 1 (1) ◽  
pp. 13-25 ◽  
Author(s):  
J. C. W. Rayner ◽  
D. J. Best
Keyword(s):  
Null Hypothesis ◽  
Treatment Effects ◽  
Contingency Tables ◽  
Higher Order ◽  
Fixed Number ◽  
Equal Treatment ◽  
Order Moment ◽  
Test Statistic ◽  
Median Test ◽  
Type Data

The data for the tests considered here may be presented in two-way contingency tables with all marginal totals fixed. We show that Pearson's test statistic XP2 (P for Pearson) may be partitioned into useful and informative components. The first detects location differences be tween the treatments, and the subsequent components detect dispersion and higher order moment differences. For Kruskal-Wallis-type data when there are no ties, the location component is the Kruskal-Wallis test. The subsequent components are the extensions. Our approach enables us to generalise to when there are ties, and to when there is a fixed number of categories and a large number of observations. We also propose a generalisation of the well-known median test. In this situation the location-detecting first component of XP2 reduces to the usual median test statistic when there are only two categories. Subsequent components detect higher moment departures from the null hypothesis of equal treatment effects

scholarly journals REMAXINT: a two-mode clustering-based method for statistical inference on two-way interaction

2021 ◽  
Author(s):  
Zaheer Ahmed ◽  
Alberto Cassese ◽  
Gerard van Breukelen ◽  
Jan Schepers
Keyword(s):  
Null Hypothesis ◽  
Type I Error ◽  
Type I ◽  
The Novel ◽  
Simulation Studies ◽  
Test Statistic ◽  
Clustering Model ◽  
Novel Method ◽  
Main Effects ◽  
Empirical Case Studies

AbstractWe present a novel method, REMAXINT, that captures the gist of two-way interaction in row by column (i.e., two-mode) data, with one observation per cell. REMAXINT is a probabilistic two-mode clustering model that yields two-mode partitions with maximal interaction between row and column clusters. For estimation of the parameters of REMAXINT, we maximize a conditional classification likelihood in which the random row (or column) main effects are conditioned out. For testing the null hypothesis of no interaction between row and column clusters, we propose a $$max-F$$ m a x - F test statistic and discuss its properties. We develop a Monte Carlo approach to obtain its sampling distribution under the null hypothesis. We evaluate the performance of the method through simulation studies. Specifically, for selected values of data size and (true) numbers of clusters, we obtain critical values of the $$max-F$$ m a x - F statistic, determine empirical Type I error rate of the proposed inferential procedure and study its power to reject the null hypothesis. Next, we show that the novel method is useful in a variety of applications by presenting two empirical case studies and end with some concluding remarks.

Permutation Tests for Common Locations Among Samples With Unequal Variances

1994 ◽  
Vol 19 (3) ◽  
pp. 217-236 ◽  
Author(s):  
Paul W. Mielke ◽  
Kenneth J. Berry
Keyword(s):  
Null Hypothesis ◽  
Treatment Effects ◽  
Alternative Hypothesis ◽  
Permutation Tests ◽  
Experimental Designs ◽  
Bivariate Distributions ◽  
Unequal Variances ◽  
Trace Test ◽  
Location Shift ◽  
Power Comparisons

In completely randomized experimental designs where population variances are equal under the null hypothesis, it is not uncommon to have multiplicative treatment effects that produce unequal variances under the alternative hypothesis. Permutation procedures are presented to test for (a) median location and scale shifts, (b) scale shifts only, and (c) mean location shifts only. Corresponding multivariate extensions are provided. Location-shift power comparisons between the parametric Bartlett-Nanda-Pillai trace test and three alternative multivariate permutation tests for five bivariate distributions are included.

Was This in Your Statistics Textbook? IV. Frequency Data

1989 ◽  
Vol 25 (1) ◽  
pp. 11-25
Author(s):  
D. J. Finney
Keyword(s):  
Statistical Analysis ◽  
Contingency Tables ◽  
The Other ◽  
Frequency Data ◽  
Significance Tests ◽  
Test Statistic ◽  
Jumping To Conclusions ◽  
Proper Role ◽  
Measure Of Association

SUMMARYObservations that are frequencies rather than measurements often call for special types of statistical analysis. This paper comments on circumstances in which methods for one type of data can sensibly be used for the other. A section on two-way contingency tables emphasizes the proper role of χ2 a test statistic but not a measure of association; it mentions the distinction between one-tail and two-tail significance tests and reminds the reader of dangers. Multiway tables bring new complications, and the problems of interactions when additional classificatory factors are explicit or hidden are discussed at some length. A brief outline attempts to show how probit, logit, and similar techniques are related to the analysis of contingency tables. Finally, three unusual examples are described as illustrations of the care that is needed to avoid jumping to conclusions on how frequency data should be analysed.

scholarly journals Test of Association in the Presence of Complex Environment

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Muhammad Aslam ◽  
Osama H. Arif
Keyword(s):  
Contingency Tables ◽  
Complex Environment ◽  
Test Statistic ◽  
Test Of Independence ◽  
The Real ◽  
Classical Statistics ◽  
Neutrosophic Statistics

A new test of independence under neutrosophic statistics for testing the association between two criteria of classification is presented in this paper. The necessary contingency tables for the neutrosophic population and the neutrosophic sample are presented. The test statistic of the proposed test is introduced under neutrosophic statistics. A real example from education is selected to explain the proposed test. From the real example, it is concluded that the proposed test of independence is more informative, flexible, and suitable to be applied under uncertainty as compared to the existing test under classical statistics.

scholarly journals Comparing Entropies in Portfolio Diversification with Fuzzy Value at Risk and Higher-Order Moment

2020 ◽  
pp. 1-16
Author(s):  
Mahdi Pourrafiee ◽  
AmirHossein Nafei ◽  
Shokoufe Banihashemi ◽  
S. Pourmohammad Azizi
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Higher Order ◽  
Portfolio Diversification ◽  
Order Moment
Sign in / Sign up

Export Citation Format

Share Document