Rand R. Wilcox

Modern Robust Data Analysis Methods: Measures of Central Tendency

Various statistical methods, developed after 1970, offer the opportunity to substantially improve upon the power and accuracy of the conventional t test and analysis of variance methods for a wide range of commonly occurring situations. The authors briefly review some of the more fundamental problems with conventional methods based on means; provide some indication of why recent advances, based on robust measures of location (or central tendency), have practical value; and describe why modern investigations dealing with nonnormality find practical problems when comparing means, in contrast to earlier studies. Some suggestions are made about how to proceed when using modern methods.

Effectiveness of a lifestyle intervention in promoting the well-being of independently living older people: results of the Well Elderly 2 Randomised Controlled Trial

Background Older people are at risk for health decline and loss of independence. Lifestyle interventions offer potential for reducing such negative outcomes. The aim of this study was to determine the effectiveness and cost-effectiveness of a preventive lifestyle-based occupational therapy intervention, administered in a variety of community-based sites, in improving mental and physical well-being and cognitive functioning in ethnically diverse older people. Methods A randomised controlled trial was conducted comparing an occupational therapy intervention and a no-treatment control condition over a 6-month experimental phase. Participants included 460 men and women aged 60–95 years (mean age 74.9±7.7 years; 53% <

Robust Correlation Analyses: False Positive and Power Validation Using a New Open Source Matlab Toolbox

12 000 annual income) recruited from 21 sites in the greater Los Angeles metropolitan area. Results Intervention participants, relative to untreated controls, showed more favourable change scores on indices of bodily pain, vitality, social functioning, mental health, composite mental functioning, life satisfaction and depressive symptomatology (ps<0.05). The intervention group had a significantly greater increment in quality-adjusted life years (p<0.02), which was achieved cost-effectively (US

Statistics for the social sciences.

41 218/UK £24 868 per unit). No intervention effect was found for cognitive functioning outcome measures. Conclusions A lifestyle-oriented occupational therapy intervention has beneficial effects for ethnically diverse older people recruited from a wide array of community settings. Because the intervention is cost-effective and is applicable on a wide-scale basis, it has the potential to help reduce health decline and promote well-being in older people. Trial Registration clinicaltrials.gov identifier: NCT0078634.

New monte carlo results on the robustness of the anova f, w and f statistics

Pearson’s correlation measures the strength of the association between two variables. The technique is, however, restricted to linear associations and is overly sensitive to outliers. Indeed, a single outlier can result in a highly inaccurate summary of the data. Yet, it remains the most commonly used measure of association in psychology research. Here we describe a free Matlab(R) based toolbox (http://sourceforge.net/projects/robustcorrtool/) that computes robust measures of association between two or more random variables: the percentage-bend correlation and skipped-correlations. After illustrating how to use the toolbox, we show that robust methods, where outliers are down weighted or removed and accounted for in significance testing, provide better estimates of the true association with accurate false positive control and without loss of power. The different correlation methods were tested with normal data and normal data contaminated with marginal or bivariate outliers. We report estimates of effect size, false positive rate and power, and advise on which technique to use depending on the data at hand.

ANOVA: A Paradigm for Low Power and Misleading Measures of Effect Size?

Why learn statistics? describing data probability discrete random variables continuous random variables sampling distributions hypothesis testing and confidence intervals comparing two independent groups ANOVA - comparing two or more groups two-way designs comparing dependent groups multiple comparisons correlation and regression categorical data methods based on ranks.

A Table for Rinott's Selection Procedure

Because the usual F test for equal means is not robust to unequal variances, Brown and Forsythe (1974a) suggest replacing F with the statistics F or W which are based on the Satterthwaite and Welch adjusted degrees of freedom procedures. This paper reports practical situations where both F and W give * unsatisfactory results. In particular, both F and W may not provide adequate control over Type I errors. Moreover, for equal variances, but unequal sample sizes, W should be avoided in favor of F (or F ), but for equal sample sizes, and possibly unequal variances, W was the only satisfactory statistic. New results on power are included as well. The paper also considers the effect of using F or W only after a significant test for equal variances has been obtained, and new results on the robustness of the F test are described. It is found that even for equal sample sizes as large as 50 per treatment group, there are practical situations where the F test does not provide adequately control over the probability...

A generally robust approach for testing hypotheses and setting confidence intervals for effect sizes.

Over 30 years ago, Tukey made it evident that slight departures from normality can substantially lower power when means are compared, and that a popular measure of effect size can be highly misleading. At the time there were no methods for dealing with the problem raised in Tukey’s paper, and some of the more obvious and seemingly intuitive solutions have since been found to be highly unsatisfactory. Today there are practical methods for not only dealing with the problem raised by Tukey, but also achieving more accurate confidence intervals and control over the probability of a Type I error. More generally, there are many robust and exploratory ways of comparing groups that can reveal important differences that are missed by conventional methods based on means, and even modern methods based solely on robust measures of location. This article reviews these new techniques.

A generally robust approach to hypothesis testing in independent and correlated groups designs

Rinott proposed an exact two-stage solution to the ranking and selection problem of determining which of k normal distributions has the largest mean. This paper supplies the exact constants needed to apply Rinotts solution...

The New and Improved Two-Sample t Test

Standard least squares analysis of variance methods suffer from poor power under arbitrarily small departures from normality and fail to control the probability of a Type I error when standard assumptions are violated. This article describes a framework for robust estimation and testing that uses trimmed means with an approximate degrees of freedom heteroscedastic statistic for independent and correlated groups designs in order to achieve robustness to the biasing effects of nonnormality and variance heterogeneity. The authors describe a nonparametric bootstrap methodology that can provide improved Type I error control. In addition, the authors indicate how researchers can set robust confidence intervals around a robust effect size parameter estimate. In an online supplement, the authors use several examples to illustrate the application of an SAS program to implement these statistical methods.