Comment on "Protecting the overall rate of Type I errors for pairwise comparisons with an omnibus test statistic": or Fisher's two-stage strategy still does not work.

1980 ◽  
Vol 88 (2) ◽  
pp. 354-355 ◽  
Author(s):  
T. A. Ryan
Keyword(s):  
Pairwise Comparisons ◽  
Type I ◽  
Test Statistic ◽  
Omnibus Test ◽  
Type I Errors ◽  
Two Stage

Protecting the overall rate of Type I errors for pairwise comparisons with an omnibus test statistic.

1979 ◽  
Vol 86 (4) ◽  
pp. 884-888 ◽  
Author(s):  
Harvey J. Keselman ◽  
Paul A. Games ◽  
Joanne C. Rogan
Keyword(s):  
Pairwise Comparisons ◽  
Type I ◽  
Test Statistic ◽  
Omnibus Test ◽  
Type I Errors

Heteroscedastic Methods for Performing All Pairwise Comparisons of Regression Lines Associated With J Independent Groups

Methodology ◽  
2015 ◽  
Vol 11 (3) ◽  
pp. 110-115 ◽  
Author(s):  
Rand R. Wilcox ◽  
Jinxia Ma
Keyword(s):  
Least Squares ◽  
Pairwise Comparisons ◽  
Simple Extension ◽  
Type I ◽  
Type I Errors ◽  
Well Elderly ◽  
Using Data

Abstract. The paper compares methods that allow both within group and between group heteroscedasticity when performing all pairwise comparisons of the least squares lines associated with J independent groups. The methods are based on simple extension of results derived by Johansen (1980) and Welch (1938) in conjunction with the HC3 and HC4 estimators. The probability of one or more Type I errors is controlled using the improvement on the Bonferroni method derived by Hochberg (1988) . Results are illustrated using data from the Well Elderly 2 study, which motivated this paper.

scholarly journals Identifying Which of J Independent Binomial Distributions Has the Largest Probability of Success

2020 ◽  
Vol 18 (2) ◽  
pp. 2-9
Author(s):  
Rand Wilcox
Keyword(s):  
Binomial Distribution ◽  
Random Variables ◽  
Independent Random Variables ◽  
Pairwise Comparisons ◽  
Type I ◽  
Type I Errors ◽  
Binomial Distributions ◽  
Probability Of Success

Let p1,…, pJ denote the probability of a success for J independent random variables having a binomial distribution and let p(1) ≤ … ≤ p(J) denote these probabilities written in ascending order. The goal is to make a decision about which group has the largest probability of a success, p(J). Let p̂1,…, p̂J denote estimates of p1,…,pJ, respectively. The strategy is to test J − 1 hypotheses comparing the group with the largest estimate to each of the J − 1 remaining groups. For each of these J − 1 hypotheses that are rejected, decide that the group corresponding to the largest estimate has the larger probability of success. This approach has a power advantage over simply performing all pairwise comparisons. However, the more obvious methods for controlling the probability of one more Type I errors perform poorly for the situation at hand. A method for dealing with this is described and illustrated.

scholarly journals An Empirical Likelihood Ratio-Based Omnibus Test for Normality with an Adjustment for Symmetric Alternatives

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Chioneso Show Marange ◽  
Yongsong Qin
Keyword(s):  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Integral Transformation ◽  
Good Control ◽  
Real Data ◽  
Type I ◽  
Test Statistic ◽  
Omnibus Test ◽  
Empirical Likelihood Ratio ◽  
Test For Normality

An omnibus test for normality with an adjustment for symmetric alternatives is developed using the empirical likelihood ratio technique. We first transform the raw data via a jackknife transformation technique by deleting one observation at a time. The probability integral transformation was then applied on the transformed data, and under the null hypothesis, the transformed data have a limiting uniform distribution, reducing testing for normality to testing for uniformity. Employing the empirical likelihood technique, we show that the test statistic has a chi-square limiting distribution. We also demonstrated that, under the established symmetric settings, the CUSUM-type and Shiryaev–Roberts test statistics gave comparable properties and power. The proposed test has good control of type I error. Monte Carlo simulations revealed that the proposed test outperformed studied classical existing tests under symmetric short-tailed alternatives. Findings from a real data study further revealed the robustness and applicability of the proposed test in practice.

A Heteroscedastic ANOVA Procedure With Specified Power

1987 ◽  
Vol 12 (3) ◽  
pp. 271-281 ◽  
Author(s):  
Rand R. Wilcox
Keyword(s):  
Treatment Group ◽  
Practical Problem ◽  
Approximate Solutions ◽  
Accurate Method ◽  
Single Stage ◽  
Type I ◽  
Type I Errors ◽  
Two Stage ◽  
Unequal Variances ◽  
Normal Distributions

When testing the equality of the means of J independent normal distributions, two-stage procedures have the advantage of providing exact control over both Type I errors and power even when the variances are unequal. Single-stage procedures have been proposed for handling unequal variances, but recent results (which are briefly reviewed in this paper) have shown that in certain practical situations these approximate solutions give unsatisfactory control over both Type I errors and power. A practical problem with two-stage procedures is the assumption that an equal number of observations is sampled from each treatment group in the first stage. Of course, for various reasons, a researcher might conduct a study resulting in unequal sample sizes. This paper describes a simple yet accurate method for dealing with this problem.

Consequences of Going-Concern Opinion Inaccuracy at the Audit Office Level

2020 ◽  
Vol 39 (3) ◽  
pp. 185-208
Author(s):  
Qiao Xu ◽  
Rachana Kalelkar
Keyword(s):  
Market Share ◽  
Audit Quality ◽  
Type I ◽  
Type I Errors ◽  
Negatively Associated ◽  
Going Concern ◽  
Big 4 ◽  
Office Market ◽  
Going Concern Opinion ◽  
Office Level

SUMMARY This paper examines whether inaccurate going-concern opinions negatively affect the audit office's reputation. Assuming that clients perceive the incidence of going-concern opinion errors as a systematic audit quality concern within the entire audit office, we expect these inaccuracies to impact the audit office market share and dismissal rate. We find that going-concern opinion inaccuracy is negatively associated with the audit office market share and is positively associated with the audit office dismissal rate. Furthermore, we find that the decline in market share and the increase in dismissal rate are primarily associated with Type I errors. Additional analyses reveal that the negative consequence of going-concern opinion inaccuracy is lower for Big 4 audit offices. Finally, we find that the decrease in the audit office market share is explained by the distressed clients' reactions to Type I errors and audit offices' lack of ability to attract new clients.

scholarly journals Testing for treatment effect in covariate-adaptive randomized trials with generalized linear models and omitted covariates

2021 ◽  
pp. 096228022110082
Author(s):  
Yang Li ◽  
Wei Ma ◽  
Yichen Qin ◽  
Feifang Hu
Keyword(s):  
Generalized Linear Models ◽  
Treatment Effect ◽  
Linear Models ◽  
Type I Error ◽  
Type I ◽  
Test Statistic ◽  
Asymptotic Results ◽  
Adaptive Randomization ◽  
Adjustment Method ◽  
Inflated Type

Concerns have been expressed over the validity of statistical inference under covariate-adaptive randomization despite the extensive use in clinical trials. In the literature, the inferential properties under covariate-adaptive randomization have been mainly studied for continuous responses; in particular, it is well known that the usual two-sample t-test for treatment effect is typically conservative. This phenomenon of invalid tests has also been found for generalized linear models without adjusting for the covariates and are sometimes more worrisome due to inflated Type I error. The purpose of this study is to examine the unadjusted test for treatment effect under generalized linear models and covariate-adaptive randomization. For a large class of covariate-adaptive randomization methods, we obtain the asymptotic distribution of the test statistic under the null hypothesis and derive the conditions under which the test is conservative, valid, or anti-conservative. Several commonly used generalized linear models, such as logistic regression and Poisson regression, are discussed in detail. An adjustment method is also proposed to achieve a valid size based on the asymptotic results. Numerical studies confirm the theoretical findings and demonstrate the effectiveness of the proposed adjustment method.

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.

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