Repeated measures ANOVA and adjusted -tests when sphericity is violated: which procedure is best?

Introduction: One-way repeated measures ANOVA requires sphericity. Research indicates that violation of this assumption has an important impact on Type I error. Although more advanced alternative procedures exist, most classical texts recommend the use of adjusted -tests, which are frequently employed because they are intuitive, easy to apply, and available in most statistical software.

Non-normal Data in Repeated Measures ANOVA: Impact on Type I Error and Power.

Background: Repeated measures designs are commonly used in health and social sciences research. Although there are other, more advanced, statistical analyses, the F-statistic of repeated measures analysis of variance (RM-ANOVA) remains the most widely used procedure for analyzing differences in means. The impact of the violation of normality has been extensively studied for between-subjects ANOVA, but this is not the case for RM-ANOVA.

Report Quality of Generalized Linear Mixed Models in Psychology: A Systematic Review.

Generalized linear mixed models (GLMMs) estimate fixed and random effects and are especially useful when the dependent variable is binary, ordinal, count or quantitative but not normally distributed. They are also useful when the dependent variable involves repeated measures, since GLMMs can model autocorrelation. This study aimed to determine how and how often GLMMs are used in psychology and to summarize how the information about them is presented in published articles.

Current Practices in Data Analysis Procedures in Psychology: What Has Changed?

This paper analyzes current practices in psychology in the use of research methods and data analysis procedures (DAP) and aims to determine whether researchers are now using more sophisticated and advanced DAP than were employed previously. We reviewed empirical research published recently in prominent journals from the USA and Europe corresponding to the main psychological categories of Journal Citation Reports and examined research methods, number of studies, number and type of DAP, and statistical package. The 288 papers reviewed used 663 different DAP.

Manipulating the Alpha Level Cannot Cure Significance Testing.

We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from = 0.05 to = 0.005, is deleterious for the finding of new discoveries and the progress of science.

Non-normal data: Is ANOVA still a valid option?

Background: The robustness of F-test to non-normality has been studied from the 1930s through to the present day. However, this extensive body of research has yielded contradictory results, there being evidence both for and against its robustness. This study provides a systematic examination of F-test robustness to violations of normality in terms of Type I error, considering a wide variety of distributions commonly found in the health and social sciences.

Non-normal Distributions Commonly Used in Health, Education, and Social Sciences: A Systematic Review.

Statistical analysis is crucial for research and the choice of analytical technique should take into account the specific distribution of data. Although the data obtained from health, educational, and social sciences research are often not normally distributed, there are very few studies detailing which distributions are most likely to represent data in these disciplines. The aim of this systematic review was to determine the frequency of appearance of the most common non-normal distributions in the health, educational, and social sciences.

Effect of variance ratio on ANOVA robustness: Might 1.5 be the limit?

Inconsistencies in the research findings on F-test robustness to variance heterogeneity could be related to the lack of a standard criterion to assess robustness or to the different measures used to quantify heterogeneity. In the present paper we use Monte Carlo simulation to systematically examine the Type I error rate of F-test under heterogeneity. One-way, balanced, and unbalanced designs with monotonic patterns of variance were considered.

Sphericity estimation bias for repeated measures designs in simulation studies.

In this study, we explored the accuracy of sphericity estimation and analyzed how the sphericity of covariance matrices may be affected when the latter are derived from simulated data. We analyzed the consequences that normal and nonnormal data generated from an unstructured population covariance matrix-with low (ε = .57) and high (ε = .

The effect of skewness and kurtosis on the Kenward-Roger approximation when group distributions differ.

Background: This study examined the independent effect of skewness and kurtosis on the robustness of the linear mixed model (LMM), with the Kenward-Roger (KR) procedure, when group distributions are different, sample sizes are small, and sphericity cannot be assumed.

Methods: A Monte Carlo simulation study considering a split-plot design involving three groups and four repeated measures was performed.

Results: The results showed that when group distributions are different, the effect of skewness on KR robustness is greater than that of kurtosis for the corresponding values.

Should we rely on the Kenward-Roger approximation when using linear mixed models if the groups have different distributions?

The study explores the robustness to violations of normality and sphericity of linear mixed models when they are used with the Kenward-Roger procedure (KR) in split-plot designs in which the groups have different distributions and sample sizes are small. The focus is on examining the effect of skewness and kurtosis. To this end, a Monte Carlo simulation study was carried out, involving a split-plot design with three levels of the between-subjects grouping factor and four levels of the within-subjects factor.

The effect of skewness and kurtosis on the robustness of linear mixed models.

This study analyzes the robustness of the linear mixed model (LMM) with the Kenward-Roger (KR) procedure to violations of normality and sphericity when used in split-plot designs with small sample sizes. Specifically, it explores the independent effect of skewness and kurtosis on KR robustness for the values of skewness and kurtosis coefficients that are most frequently found in psychological and educational research data. To this end, a Monte Carlo simulation study was designed, considering a split-plot design with three levels of the between-subjects grouping factor and four levels of the within-subjects factor.

[Effect of the violation of normality and sphericity in the linear mixed model in split-plot designs].

This study aimed to evaluate the robustness of the linear mixed model, with the Kenward-Roger correction for degrees of freedom, when implemented in SAS PROC MIXED, using split-plot designs with small sample sizes. A Monte Carlo simulation design involving three groups and four repeated measures was used, assuming an unstructured covariance matrix to generate the data. The study variables were: sphericity, with epsilon values of 0.

Using the linear mixed model to analyze nonnormal data distributions in longitudinal designs.

Using a Monte Carlo simulation and the Kenward-Roger (KR) correction for degrees of freedom, in this article we analyzed the application of the linear mixed model (LMM) to a mixed repeated measures design. The LMM was first used to select the covariance structure with three types of data distribution: normal, exponential, and log-normal. This showed that, with homogeneous between-groups covariance and when the distribution was normal, the covariance structure with the best fit was the unstructured population matrix.

Drug awareness in adolescents attending a mental health service: analysis of longitudinal data.

One of the procedures used most recently with longitudinal data is linear mixed models. In the context of health research the increasing number of studies that now use these models bears witness to the growing interest in this type of analysis. This paper describes the application of linear mixed models to a longitudinal study of a sample of Spanish adolescents attending a mental health service, the aim being to investigate their knowledge about the consumption of alcohol and other drugs.

Regression-based techniques for statistical decision making in single-case designs.

The present study evaluates the performance of four methods for estimating regression coefficients used to make statistical decisions about intervention effectiveness in single-case designs. Ordinary least square estimation is compared to two correction techniques dealing with general trend and a procedure that eliminates autocorrelation whenever it is present. Type I error rates and statistical power are studied for experimental conditions defined by the presence or absence of treatment effect (change in level or in slope), general trend, and serial dependence.

General linear mixed model for analysing longitudinal data in developmental research.

Many areas of psychological, social, and health research are characterised by hierarchically structured data. Growth curves are usually represented by means of a two-level hierarchical structure in which observations are the first-level units nested within subjects, the second-level units. With data such as these, the best option for analysis is the general linear mixed model, which can be used even with longitudinal data series in which intervals are not constant or for which over the passage of time there is loss of data.

[Information and communication technologies in teaching applied and experimental designs].

In this work, an innovative teaching model applied to methodological contents in psychology is presented. The proposed didactic model includes Information and Communication Technologies (ICT), such as CD-ROMs, web sites and Internet. These resources complement class attendance.

Evaluating effects in short time series: alternative models of analysis.

In the applied context, short time-series designs are suitable to evaluate a treatment effect. These designs present serious problems given autocorrelation among data and the small number of observations involved. This paper describes analytic procedures that have been applied to data from short time series, and an alternative which is a new version of the generalized least squares method to simplify estimation of the error covariance matrix.

Autocorrelation problems in short time series.

The work of Huitema (1985) on autocorrelation in behavioral data suggests that the use of conventional statistical methods is justified. The present study restates the problem of autocorrelation by analyzing 100 baselines of small samples designs published in the Journal of Applied Behavior Analysis during 1992. The results show a negative bias in the autocorrelations, especially with very small samples.