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Full-Text Articles in Social and Behavioral Sciences
P-Values Versus Significance Levels, Phillip I. Good
P-Values Versus Significance Levels, Phillip I. Good
Journal of Modern Applied Statistical Methods
In this article Phillip Good responds to Richard Anderson's article Conceptual Distinction between the Critical p Value and the Type I Error Rate in Permutation Testing.
Conceptual Distinction Between The Critical P Value And The Type I Error Rate In Permutation Testing: Author Response To Peer Comments, Richard B. Anderson
Conceptual Distinction Between The Critical P Value And The Type I Error Rate In Permutation Testing: Author Response To Peer Comments, Richard B. Anderson
Journal of Modern Applied Statistical Methods
Richard Anderson responds to comments regarding his target article Conceptual Distinction between the Critical p Value and the Type I Error Rate in Permutation Testing.
A Response To Anderson's (2013) Conceptual Distinction Between The Critical P Value And Type I Error Rate In Permutation Testing, Fortunato Pesarin, Stefano Bonnini
A Response To Anderson's (2013) Conceptual Distinction Between The Critical P Value And Type I Error Rate In Permutation Testing, Fortunato Pesarin, Stefano Bonnini
Journal of Modern Applied Statistical Methods
Pesarin and Bonnini respond to Anderson's (2013) Conceptual Distinction between the Critical p value and Type I Error Rate in Permutation Testing
Conceptual Distinction Between The Critical P Value And The Type I Error Rate In Permutation Testing, Richard B. Anderson
Conceptual Distinction Between The Critical P Value And The Type I Error Rate In Permutation Testing, Richard B. Anderson
Journal of Modern Applied Statistical Methods
To counter past assertions that permutation testing is not distribution-free, this article clarifies that the critical p value (alpha) in permutation testing is not a Type I error rate and that a test's validity is independent of the concept of Type I error.
Empirical Sampling From Permutation Space With Unique Patterns, Justice I. Odiase
Empirical Sampling From Permutation Space With Unique Patterns, Justice I. Odiase
Journal of Modern Applied Statistical Methods
The exact distribution of a test statistic ultimately guarantees that the probability of a Type I error is exactly α. Several methods for estimating the exact distribution of a test statistic have evolved over the years with inherent computational problems and varying degrees of accuracy. The unique pattern of permutations resulting from using experimental data to sample within the permutation space without the risk of repeating permutations is identified. The method presented circumvents the theoretical requirements of asymptotic procedures and the computational difficulties associated with an exhaustive enumeration of permutations. Results show that time and space complexities are drastically reduced …
A Permutation Test For Compound Symmetry With Application To Gene Expression Data, Tracy L. Morris, Mark E. Payton, Stephanie A. Santorico
A Permutation Test For Compound Symmetry With Application To Gene Expression Data, Tracy L. Morris, Mark E. Payton, Stephanie A. Santorico
Journal of Modern Applied Statistical Methods
The development and application of a permutation test for compound symmetry is described. In a simulation study the permutation test appears to be a level-α test and is robust to non-normality. However, it exhibits poor power, particularly for small samples.
A Socratic Dialogue, Vance W. Berger
A Socratic Dialogue, Vance W. Berger
Journal of Modern Applied Statistical Methods
Socrates has found some aspects of medical biostatistics a bit confusing, and wishes to discuss some of these issues with Simplicio, a prominent medical researcher. This Socratic dialogue will shed some light on the errant use of parametric analyses in clinical trials.
Multiple Comparison Of Medians Using Permutation Tests, Scott J. Richter, Melinda H. Mccann
Multiple Comparison Of Medians Using Permutation Tests, Scott J. Richter, Melinda H. Mccann
Journal of Modern Applied Statistical Methods
A robust method is proposed for simultaneous pairwise comparison using permutation tests and median differences. The new procedure provides strong control of familywise error rate and has better power properties than the median procedure of Nemenyi/Levy. It can be more powerful than the Tukey-Kramer procedure using mean differences, especially for nonnormal distributions and unequal sample sizes.
The Effect Of Different Degrees Of Freedom Of The Chi-Square Distribution On The Statistical Power Of The T, Permutation T, And Wilcoxon Tests, Michèle Weber
Journal of Modern Applied Statistical Methods
The Chi-square distribution is used quite often in Monte Carlo studies to examine statistical power of competing statistics. The power spectrum of the t-test, Wilcoxon test, and permutation t test are compared under various degrees of freedom for this distribution. The two t tests have similar power, which is generally less than the Wilcoxon.
Jmasm20: Exact Permutation Critical Values For The Kruskal-Wallis One-Way Anova, Justice I. Odiase, Sunday M. Ogbonmwan
Jmasm20: Exact Permutation Critical Values For The Kruskal-Wallis One-Way Anova, Justice I. Odiase, Sunday M. Ogbonmwan
Journal of Modern Applied Statistical Methods
The exhaustive enumeration of all the permutations of the observations in an experiment is the only possible way of truly constructing exact tests of significance. The permutation paradigm requires no distributional assumptions and works well with values that are normal, almost normal and non-normally distributed. The Kruskal-Wallis test does not require the assumptions that the samples are from normal populations and that the samples have the same standard deviation. In this article, the exact permutation distribution of the Kruskal-Wallis test statistic is generated empirically by actually obtaining all the distinct permutations of an experiment. The tables of exact critical values …
Training Statisticians To Be Alert To The Dangers Of Misapplying Statistical Methods, Vance W. Berger
Training Statisticians To Be Alert To The Dangers Of Misapplying Statistical Methods, Vance W. Berger
Journal of Modern Applied Statistical Methods
Statisticians are faced with a variety of challenges. Their ability to cope successfully with these challenges depends, in large part, on the quality of their training. It is not the purpose of this article to present a comprehensive training plan that will overhaul the standard curriculum a statistician might follow under current training regimens (i.e., in a degree program). Rather, the objective is to point out important areas that appear to be under-represented in standard curricula and correspondingly overlooked too often in practice. The hope is that these areas might be better integrated into the training of the next generation …
An Algorithm For Generating Unconditional Exact Permutation Distribution For A Two-Sample Experiment, Justice I. Odiase, Sunday M. Ogbonmwan
An Algorithm For Generating Unconditional Exact Permutation Distribution For A Two-Sample Experiment, Justice I. Odiase, Sunday M. Ogbonmwan
Journal of Modern Applied Statistical Methods
An Algorithm that generates the unconditional exact permutation distribution of a 2 x n experiment is presented. The algorithm is able to handle ranks as well as actual observations. It makes it possible to obtain exact p-values for several statistics, especially when sample sizes are small and the application of large sample approximation is unreliable. An illustrative implementation is achieved and leads to the computation of exact p-values for the Mood test when the sample size is small.
Multivariate And Multistrata Nonparametric Tests: The Nonparametric Combination Method, Livio Corain, Luigi Salmaso
Multivariate And Multistrata Nonparametric Tests: The Nonparametric Combination Method, Livio Corain, Luigi Salmaso
Journal of Modern Applied Statistical Methods
Researchers and practitioners in many scientific disciplines and industrial fields are often faced with complex problems when dealing with comparisons between two or more groups using classical parametric methods. The data arising from real problems rarely are in agreement with stringent parametric assumptions. The NonParametric Combination (NPC) methodology frees the researcher from stringent assumptions of parametric methods and allows a more flexible analysis, both in terms of specification of multivariate hypotheses and in terms of the nature of the variables involved in the analysis. An outline of NPC methodology is given, along with case studies.
Depth Based Permutation Test For General Differences In Two Multivariate Populations, Yonghong Gao
Depth Based Permutation Test For General Differences In Two Multivariate Populations, Yonghong Gao
Journal of Modern Applied Statistical Methods
For two p-dimensional data sets, interest exists in testing if they come from the common population distribution. Proposed is a practical, effective and easy to implement procedure for the testing problem. The proposed procedure is a permutation test based on the concept of the depth of one observation relative to some population distribution. The proposed test is demonstrated to be consistent. A small Monte Carlo simulation was conducted to evaluate the power of the proposed test. The proposed test is applied to some numerical examples.
Fast Permutation Tests That Maximize Power Under Conventional Monte Carlo Sampling For Pairwise And Multiple Comparisons, J. D. Opdyke
Fast Permutation Tests That Maximize Power Under Conventional Monte Carlo Sampling For Pairwise And Multiple Comparisons, J. D. Opdyke
Journal of Modern Applied Statistical Methods
While the distribution-free nature of permutation tests makes them the most appropriate method for hypothesis testing under a wide range of conditions, their computational demands can be runtime prohibitive, especially if samples are not very small and/or many tests must be conducted (e.g. all pairwise comparisons). This paper presents statistical code that performs continuous-data permutation tests under such conditions very quickly often more than an order of magnitude faster than widely available commercial alternatives when many tests must be performed and some of the sample pairs contain a large sample. Also presented is an efficient method for obtaining a …
Extensions Of The Concept Of Exchangeability And Their Applications, Phillip I. Good
Extensions Of The Concept Of Exchangeability And Their Applications, Phillip I. Good
Journal of Modern Applied Statistical Methods
Permutation tests provide exact p-values in a wide variety of practical testing situations. But permutation tests rely on the assumption of exchangeability, that is, under the hypothesis, the joint distribution of the observations is invariant under permutations of the subscripts. Observations are exchangeable if they are independent, identically distributed (i.i.d.), or if they are jointly normal with identical covariances. The range of applications of these exact, powerful, distribution-free tests can be enlarged through exchangeability- preserving transforms, asymptotic exchangeability, partial exchangeability, and weak exchangeability. Original exact tests for comparing the slopes of two regression lines and for the analysis of …
Parametric Analyses In Randomized Clinical Trials, Vance W. Berger, Clifford E. Lunneborg, Michael D. Ernst, Jonathan G. Levine
Parametric Analyses In Randomized Clinical Trials, Vance W. Berger, Clifford E. Lunneborg, Michael D. Ernst, Jonathan G. Levine
Journal of Modern Applied Statistical Methods
One salient feature of randomized clinical trials is that patients are randomly allocated to treatment groups, but not randomly sampled from any target population. Without random sampling parametric analyses are inexact, yet they are still often used in clinical trials. Given the availability of an exact test, it would still be conceivable to argue convincingly that for technical reasons (upon which we elaborate) a parametric test might be preferable in some situations. Having acknowledged this possibility, we point out that such an argument cannot be convincing without supporting facts concerning the specifics of the problem at hand. Moreover, we have …