Robust ANCOVA: Some Small-sample Results when there are Multiple Groups and Multiple Covariates

Numerous methods have been proposed for dealing with the serious practical problems associated with the conventional analysis of covariance method, with an emphasis on comparing two groups when there is a single covariate. Recently, Wilcox (2005a: section 11.8.2) outlined a method for handling multiple covariates that allows nonlinearity and heteroscedasticity. The method is readily extended to multiple groups, but nothing is known about its small-sample properties. This paper compares three variations of the method, each method based on one of three measures of location: means, medians and 20% trimmed means. The methods based on a 20% trimmed mean or median are found to avoid Type I error probabilities well above the nominal level, but the method based on medians can be too conservative in various situations; using a 20% trimmed mean gave the best results in terms of Type I errors. The methods are based in part on a running interval smoother approximation of the regression surface. Included are comments on required sample sizes that are relevant to the so-called curse of dimensionality.     

Comparing J independent groups with a method based on trimmed means

The ANOVA-F test is the most popular and commonly used procedure for comparing J independent groups. However, it is well known that this method is very sensitive to non-normality, which has led to the derivation of alternative techniques based on robust estimators. In this work, ANOVA-F-test, trimmed mean Welch test, bootstrap-t trimmed mean Welch test, Schrader and Hettmansperger method with trimmed means, a percentile bootstrap method with trimmed means and a newly proposed method were compared in terms of both the Type I error probability and power. The proposed method compares well with ANOVA-F and other alternatives under various situations.     

Effectiveness of addiction science presentations to treatment professionals,using a modified Solomon study design

OBJECTIVES: Knowledge of addiction research findings is critical for healthcare professionals who treat addicted patients. However, there is little information available about the instructional effectiveness of lecture-slide presentations in changing knowledge vs. beliefs of such professionals. DESIGN: A modified Solomon four-group experimental design was used to assess the instructional effectiveness (knowledge gain vs. belief changes) of three-hour addiction science workshops presented to health-care professionals by neurobiologically-trained academic researchers. Effectiveness of the workshops was assessed by a 28-item questionnaire on participant versus control group knowledge/beliefs on addiction. Six-month follow-up questionnaires measured "retention" of knowledge and belief changes. RESULTS: The workshop participants showed significant knowledge gain and belief changes, whereas the two control groups showed no change in knowledge or beliefs. After six months, knowledge gains decreased, but were still higher than pre-test scores. In contrast, belief changes on three subscales persisted over six months in 40 to 52 percent of the subjects. CONCLUSIONS: These results illustrate a successful continuing education model by which academic researchers who are skilled teachers present a three-hour lecture-slide workshop with extensive question-and-answer sessions on addictions. We conclude that motivated health-care professionals can experience important knowledge gains and belief changes by participating in such workshops. In contrast to the transient retention of knowledge, belief changes persisted surprisingly well for at least six months in about half the subjects. These results suggest that long-term changes in the professional orientation of these health-care workers are possible.     

Demographic transition: A forcing model

Transition Theory provides the theoretical underpinning for many explanations for past population changes and, more importantly, for many population projections. Our paper proves, through the use of symbolic logic, that Transition Theory does not contain principles strong enough to support population projections. Such projections, consequently, must be based upon their author's intuition rather than a reasoned application of Transition Theory. We follow our proofs with a brief discussion of various ways in which the Theory may be modified. Our emphasis is upon and only upon the logical characters of these modifications.     

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

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 of a Type I error.     

A step-down heteroscedastic multiple comparison procedure

All-pairs power in a one-way ANOVA is the probability of detecting all true differences between pairs of means. Ramsey (1978) found that for normal distributions having equal variances, step-down multiple comparison procedures can have substantially more all-pairs power than single-step procedures, such as Tukey’s HSD, when equal sample sizes are randomly sampled from each group. This paper suggests a step-down procedure for the case of unequal variances and compares it to Dunnett's T3 technique. The new procedure is similar in spirit to one of the heteroscedastic procedures described by Hochberg and Tamhane (1987), but it has certain advantages that are discussed in the paper. Included are results on unequal sample sizes.