scholarly journals Comparing Means under Heteroscedasticity and Nonnormality: Further Exploring Robust Means Modeling

2020 ◽  
Vol 18 (1) ◽  
Author(s):  
Alyssa Counsell ◽  
Robert Philip Chalmers ◽  
Robert A. Cribbie
Keyword(s):  
Monte Carlo ◽  
Error Control ◽  
Type I Error ◽  
Monte Carlo Study ◽  
Type I ◽  
Variance Heterogeneity ◽  
Variance Homogeneity

Comparing the means of independent groups is a concern when the assumptions of normality and variance homogeneity are violated. Robust means modeling (RMM) was proposed as an alternative to ANOVA-type procedures when the assumptions of normality and variance homogeneity are violated. The purpose of this study is to compare the Type I error and power rates of RMM to the trimmed Welch procedure. A Monte Carlo study was used to investigate RMM and the trimmed Welch procedure under several conditions of nonnormality and variance heterogeneity. The results suggest that the trimmed Welch provides a better balance of Type I error control and power than RMM.

scholarly journals Comparing Means under Heteroscedasticity and Nonnormality: Further Exploring Robust Means Modeling

2020 ◽  
Author(s):  
Alyssa Counsell ◽  
R. Philip Chalmers ◽  
Rob Cribbie
Keyword(s):  
Monte Carlo ◽  
Error Control ◽  
Type I Error ◽  
Monte Carlo Study ◽  
Type I ◽  
Variance Heterogeneity ◽  
Variance Homogeneity

Researchers are commonly interested in comparing the means of independent groups when distributions are nonnormal and variances are unequal. Robust means modeling (RMM) has been proposed as an alternative to ANOVA-type procedures when the assumptions of normality and variance homogeneity are violated. This paper extends work comparing the Type I error and power rates of RMM to those for the trimmed Welch procedure. A Monte Carlo study was used to investigate RMM and the trimmed Welch procedure under several conditions of nonnormality and variance heterogeneity. Our results suggest that the trimmed Welch provides a better balance of Type I error control and power than RMM.

Silverstein's Nonparametric Many-One Test for a One-Way Design: A Monte Carlo Study

1981 ◽  
Vol 48 (1) ◽  
pp. 19-22 ◽  
Author(s):  
James D. Church ◽  
Edward L. Wike
Keyword(s):  
Monte Carlo ◽  
Type I Error ◽  
Monte Carlo Study ◽  
Error Rates ◽  
Wilcoxon Test ◽  
Type I ◽  
Type I Error Rates ◽  
Wilcoxon Rank Sum Test

A Monte Carlo study was done to find the Type I error rates for three nonparametric procedures for making k − 1 many-one comparisons in a one-way design. The tests ( t) were the Silverstein and Steel many-one ranks tests and the two-sample Wilcoxon rank-sum test, k = 3, 5, 7, and 10 treatments were crossed with n = 7, 10, and 15 replicates with 1000 simulations per k, n combination. Analyses of four Type I error rates showed that: (1) The Wilcoxon test had the best comparisonwise error rates; (2) none of the tests functioned well as protected tests; and (3) the Silverstein test had the best experimentwise error rates and was the recommended procedure for many-one tests for a one-way layout.

scholarly journals A Monte Carlo Study of an Iterative Wald Test Procedure for DIF Analysis

2016 ◽  
Vol 77 (1) ◽  
pp. 104-118 ◽  
Author(s):  
Mengyang Cao ◽  
Louis Tay ◽  
Yaowu Liu
Keyword(s):  
Monte Carlo ◽  
Type I Error ◽  
Test Procedure ◽  
Monte Carlo Study ◽  
Error Rates ◽  
Type I ◽  
Iterative Approach ◽  
Response Options ◽  
Type I Error Rates ◽  
Dichotomous Data

This study examined the performance of a proposed iterative Wald approach for detecting differential item functioning (DIF) between two groups when preknowledge of anchor items is absent. The iterative approach utilizes the Wald-2 approach to identify anchor items and then iteratively tests for DIF items with the Wald-1 approach. Monte Carlo simulation was conducted across several conditions including the number of response options, test length, sample size, percentage of DIF items, DIF effect size, and type of cumulative DIF. Results indicated that the iterative approach performed well for polytomous data in all conditions, with well-controlled Type I error rates and high power. For dichotomous data, the iterative approach also exhibited better control over Type I error rates than the Wald-2 approach without sacrificing the power in detecting DIF. However, inflated Type I error rates were found for the iterative approach in conditions with dichotomous data, noncompensatory DIF, large percentage of DIF items, and medium to large DIF effect sizes. Nevertheless, the Type I error rates were substantially less inflated in those conditions compared with the Wald-2 approach.

A Monte-Carlo Study of Type I Error Rates and Power for Tukey's Pocket Test

1996 ◽  
Vol 123 (4) ◽  
pp. 333-339 ◽  
Author(s):  
William P. Dunlap ◽  
Tammy Greer ◽  
Gregory O. Beatty
Keyword(s):  
Monte Carlo ◽  
Type I Error ◽  
Monte Carlo Study ◽  
Error Rates ◽  
Type I ◽  
Type I Error Rates

scholarly journals Empirical Comparison of Tests for One-Factor ANOVA Under Heterogeneity and Non-Normality: A Monte Carlo Study

2020 ◽  
Vol 18 (2) ◽  
pp. 2-30
Author(s):  
Diep Nguyen ◽  
Eunsook Kim ◽  
Yan Wang ◽  
Thanh Vinh Pham ◽  
Yi-Hsin Chen ◽  
...  
Keyword(s):  
Statistical Power ◽  
Error Control ◽  
Type I Error ◽  
Monte Carlo Study ◽  
Type I ◽  
Omnibus Test ◽  
Homogeneity Of Variance ◽  
Mean Equality ◽  
Comparison Of Tests ◽  
Structured Means

Although the Analysis of Variance (ANOVA) F test is one of the most popular statistical tools to compare group means, it is sensitive to violations of the homogeneity of variance (HOV) assumption. This simulation study examines the performance of thirteen tests in one-factor ANOVA models in terms of their Type I error rate and statistical power under numerous (82,080) conditions. The results show that when HOV was satisfied, the ANOVA F or the Brown-Forsythe test outperformed the other methods in terms of both Type I error control and statistical power even under non-normality. When HOV was violated, the Structured Means Modeling (SMM) with Bartlett or SMM with Maximum Likelihood was strongly recommended for the omnibus test of group mean equality.

Pairwise Multiple Comparison Procedures with Unequal N’s and/or Variances: A Monte Carlo Study

1976 ◽  
Vol 1 (2) ◽  
pp. 113-125 ◽  
Author(s):  
Paul A. Games ◽  
John F. Howell
Keyword(s):  
Monte Carlo ◽  
Sample Size ◽  
Error Rate ◽  
Type I Error ◽  
Monte Carlo Study ◽  
Multiple Comparison ◽  
Type I ◽  
Type I Errors ◽  
Type I Error Rate ◽  
Multiple Comparison Procedures

Three different methods for testing all pairs of yȳk, - yȳk’ were contrasted under varying sample size (n) and variance conditions. With unequal n’s of six and up, only the Behrens-Fisher statistic provided satisfactory control of both the familywise rate of Type I errors and Type I error rate on each contrast. Satisfactory control with unequal n’s of three and up is dubious even with this statistic.

Silverstein's Nonparametric Many-One Test for a Two-Way Design: A Monte Carlo Study

1981 ◽  
Vol 49 (3) ◽  
pp. 931-934
Author(s):  
James D. Church ◽  
Edward L. Wike
Keyword(s):  
Monte Carlo ◽  
Type I Error ◽  
Monte Carlo Study ◽  
Error Rates ◽  
Sign Test ◽  
Type I ◽  
Type I Error Rates ◽  
Step Down

A Monte Carlo study was done to find the Type I error rates for three nonparametric procedures for making k – 1 many-one comparisons in a two-way design. The tests were the Silverstein and Steel many-one tests and the two-sample step-down sign test. k = 3, 5, 7, and 10 treatments were crossed with n = 8, 11, and 15 blocks with 1000 simulations per k, n combination. The Silverstein test had the best experimentwise error rates and is recommended for many-one comparisons in a two-way design.

Comparison of Means: An F Test Followed by a Modified Multiple Range Procedure

1979 ◽  
Vol 4 (1) ◽  
pp. 14-23 ◽  
Author(s):  
Juliet Popper Shaffer
Keyword(s):  
Error Control ◽  
Type I Error ◽  
Critical Value ◽  
The Other ◽  
Type I ◽  
F Test ◽  
Range Test

If used only when a preliminary F test yields significance, the usual multiple range procedures can be modified to increase the probability of detecting differences without changing the control of Type I error. The modification consists of a reduction in the critical value when comparing the largest and smallest means. Equivalence of modified and unmodified procedures in error control is demonstrated. The modified procedure is also compared with the alternative of using the unmodified range test without a preliminary F test, and it is shown that each has advantages over the other under some circumstances.

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