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

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

ANOVA_robust: A SAS Macro for Parametric Tests of Mean Differences in One-Factor ANOVA Models

Testing the equality of several independent group means is a common statistical practice in the social sciences. The traditional analysis of variance (ANOVA) is one of the most popular methods. However, the ANOVA F test is sensitive to violations of the homogeneity of variance assumption. Many alternative tests have been developed in response to this problem of the F test. These tests include some modifications of the ANOVA F test and others based on the structured means modeling technique. This paper provides a SAS macro for testing the equality of group means using thirteen methods including the regular ANOVA F test. In addition, this paper summarizes the results of a simulation study that compares the performance of these tests in terms of their Type I error rate under different conditions, especially under violations of the homogeneity of variance assumption

A Comprehensive System For The Evaluation Of Innovative Online Instruction At A Research University: Foundations, Components, And Effectiveness

The delivery of post-secondary coursework via the Internet continues to gain momentum.  As a result, investigations into effective and appropriate methods of evaluating the effectiveness of these courses are required.  In an effort to meet this challenge, this study describes the development and implementation of an evaluation system applied to new online programs at a major research university. A systematic approach to evaluation provided formative feedback on the processes and products of course development using diverse data sources including course documents, interviews and web-based surveys.  Results of both quantitative and qualitative analyses support the integrity of the evaluation system and provide preliminary indications of course effectiveness based on student satisfaction

Parametric Tests for Two Population Means under Normal and Non-Normal Distributions

A simulation study was conducted to explore the performance of the independent means t-test, Satterthwaite’s approximate t-test, and the conditional t-test under various conditions. This study analyzed Type I error control and statistical power of these testing approaches and provided guidance on the proper selection among them

JMASM 47: ANOVA_HOV: A SAS Macro for Testing Homogeneity of Variance in One-Factor ANOVA Models (SAS)

Variance homogeneity (HOV) is a critical assumption for ANOVA whose violation may lead to perturbations in Type I error rates. Minimal consensus exists on selecting an appropriate test. This SAS macro implements 14 different HOV approaches in one-way ANOVA. Examples are given and practical issues discussed