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H J Keselman

Publications and source records attributed to H J Keselman.

12 recordsLinked to original sources
PubMed2003

Repeated measures one-way ANOVA based on a modified one-step M-estimator.

Wilcox, Keselman, Muska and Cribbie (2000) found a method for comparing the trimmed means of dependent groups that performed well in simulations, in terms of Type I errors, with a sample size as small as 21. Theory and simulations indicate that little power is lost under normality when using trimmed means rather than untrimmed means, and trimmed means can result in substantially higher power when sampling from a heavy-tailed distribution. However, trimmed means suffer from two practical concerns described in this paper. Replacing trimmed means with a robust M-estimator addresses these concerns, but control over the probability of a Type I error can be unsatisfactory when the sample size is small. Methods based on a simple modification of a one-step M-estimator that address the problems with trimmed means are examined. Several omnibus tests are compared, one of which performed well in simulations, even with a sample size of 11.

Analysis of Variance↗
PubMed2003

Pairwise multiple comparisons: a model comparison approach versus stepwise procedures.

Researchers in the behavioural sciences have been presented with a host of pairwise multiple comparison procedures that attempt to obtain an optimal combination of Type I error control, power, and ease of application. However, these procedures share one important limitation: intransitive decisions. Moreover, they can be characterized as a piecemeal approach to the problem rather than a holistic approach. Dayton has recently proposed a new approach to pairwise multiple comparisons testing that eliminates intransitivity through a model selection procedure. The present study compared the model selection approach (and a protected version) with three powerful and easy-to-use stepwise multiple comparison procedures in terms of the proportion of times that the procedure identified the true pattern of differences among a set of means across several one-way layouts. The protected version of the model selection approach selected the true model a significantly greater proportion of times than the stepwise procedures and, in most cases, was not affected by variance heterogeneity and non-normality.

Humans↗
PubMed2002

Controlling the rate of Type I error over a large set of statistical tests.

When many tests of significance are examined in a research investigation with procedures that limit the probability of making at least one Type I error--the so-called familywise techniques of control--the likelihood of detecting effects can be very low. That is, when familywise error controlling methods are adopted to assess statistical significance, the size of the critical value that must be exceeded in order to obtain statistical significance can be extremely large when the number of tests to be examined is also very large. In our investigation we examined three methods for increasing the sensitivity to detect effects when family size is large: the false discovery rate of error control presented by Benjamini and Hochberg (1995), a modified false discovery rate presented by Benjamini and Hochberg (2000) which estimates the number of true null hypotheses prior to adopting false discovery rate control, and a familywise method modified to control the probability of committing two or more Type I errors in the family of tests examined--not one, as is the case with the usual familywise techniques. Our results indicated that the level of significance for the two or more familywise method of Type I error control varied with the testing scenario and needed to be set on occasion at values in excess of 0.15 in order to control the two or more rate at a reasonable value of 0.01. In addition, the false discovery rate methods typically resulted in substantially greater power to detect non-null effects even though their levels of significance were set at the standard 0.05 value. Accordingly, we recommend the Benjamini and Hochberg (1995, 2000) methods of Type I error control when the number of tests in the family is large.

Achievement↗
PubMed2001

Mixed-model pairwise multiple comparisons of repeated measures means.

One approach to the analysis of repeated measures data allows researchers to model the covariance structure of the data rather than presume a certain structure, as is the case with conventional univariate and multivariate test statistics. This mixed-model approach was evaluated for testing all possible pairwise differences among repeated measures marginal means in a Between-Subjects x Within-Subjects design. Specifically, the authors investigated Type I error and power rates for a number of simultaneous and stepwise multiple comparison procedures using SAS (1999) PROC MIXED in unbalanced designs when normality and covariance homogeneity assumptions did not hold. J. P. Shaffer's (1986) sequentially rejective step-down and Y. Hochberg's (1988) sequentially acceptive step-up Bonferroni procedures, based on an unstructured covariance structure, had superior Type I error control and power to detect true pairwise differences across the investigated conditions.

Humans↗
PubMed2001

The analysis of repeated measures designs: a review.

Repeated measures ANOVA can refer to many different types of analysis. Specifically, this vague term can refer to conventional tests of significance, one of three univariate solutions with adjusted degrees of freedom, two different types of multivariate statistic, or approaches that combine univariate and multivariate tests. Accordingly, it is argued that, by only reporting probability values and referring to statistical analyses as repeated measures ANOVA, authors convey neither the type of analysis that was used nor the validity of the reported probability value, since each of these approaches has its own strengths and weaknesses. The various approaches are presented with a discussion of their strengths and weaknesses, and recommendations are made regarding the 'best' choice of analysis. Additional topics discussed include analyses for missing data and tests of linear contrasts.

Analysis of Variance↗
PubMed2000

An examination of the robustness of the empirical Bayes and other approaches for testing main and interaction effects in repeated measures designs.

In a previous paper, Boik presented an empirical Bayes (EB) approach to the analysis of repeated measurements. The EB approach is a blend of the conventional univariate and multivariate approaches. Specifically, in the EB approach, the underlying covariance matrix is estimated by a weighted sum of the univariate and multivariate estimators. In addition to demonstrating that his approach controls test size and frequently is more powerful than either the epsilon-adjusted univariate or multivariate approaches, Boik showed how conventional multivariate software can be used to conduct EB analyses. Our investigation examined the Type I error properties of the EB approach when its derivational assumptions were not satisfied as well as when other factors known to affect the conventional tests of significance were varied. For comparative purposes we also investigated procedures presented by Huynh and by Keselman, Carriere, and Lix, procedures designed for non-spherical data and covariance heterogeneity, as well as an adjusted univariate and multivariate test statistic. Our results indicate that when the response variable is normally distributed and group sizes are equal, the EB approach was robust to violations of its derivational assumptions and therefore is recommended due to the power findings reported by Boik. However, we also found that both the EB approach and the adjusted univariate and multivariate procedures were prone to depressed or elevated rates of Type I error when data were non-normally distributed and covariance matrices and group sizes were either positively or negatively paired with one another. On the other hand, the Huynh and Keselman et al. procedures were generally robust to these same pairings of covariance matrices and group sizes.

Bayes Theorem↗
PubMed2000

Repeated measures ANOVA: some new results on comparing trimmed means and means.

This paper considers the common problem of testing the equality of means in a repeated measures design. Recent results indicate that practical problems can arise when computing confidence intervals for all pairwise differences of the means in conjunction with the Bonferroni inequality. This suggests, and is confirmed here, that a problem might occur when performing an omnibus test of equal means. The problem is that the probability of rejecting is not minimized when the means are equal and the usual univariate F test is used with the Huynh-Feldt correction (epsilon) for the degrees of freedom. That is, power can actually decrease as the mean of one group is lowered, although eventually it increases. A similar problem is found when using a multivariate method (Hotelling's T2). Moreover, the probability of a Type I error can exceed the nominal level by a large amount. The paper considers methods for correcting this problem, and new results on comparing trimmed means are reported as well. In terms of both Type I errors and power, simulations reported here suggest that a percentile t bootstrap used with 20% trimmed means and an analogue of the epsilon-adjusted F gives the best results. This is consistent with extant theoretical results comparing methods based on means with trimmed means.

Analysis of Variance↗
PubMed2000

Testing treatment effects in repeated measures designs: trimmed means and bootstrapping.

Non-normality and covariance heterogeneity between groups affect the validity of the traditional repeated measures methods of analysis, particularly when group sizes are unequal. A non-pooled Welch-type statistic (WJ) and the Huynh Improved General Approximation (IGA) test generally have been found to be effective in controlling rates of Type I error in unbalanced non-spherical repeated measures designs even though data are non-normal in form and covariance matrices are heterogeneous. However, under some conditions of departure from multisample sphericity and multivariate normality their rates of Type I error have been found to be elevated. Westfall and Young's results suggest that Type I error control could be improved by combining bootstrap methods with methods based on trimmed means. Accordingly, in our investigation we examined four methods for testing for main and interaction effects in a between- by within-subjects repeated measures design: (a) the IGA and WJ tests with least squares estimators based on theoretically determined critical values; (b) the IGA and WJ tests with least squares estimators based on empirically determined critical values; (c) the IGA and WJ tests with robust estimators based on theoretically determined critical values; and (d) the IGA and WJ tests with robust estimators based on empirically determined critical values. We found that the IGA tests were always robust to assumption violations whether based on least squares or robust estimators or whether critical values were obtained through theoretical or empirical methods. The WJ procedure, however, occasionally resulted in liberal rates of error when based on least squares estimators but always proved robust when applied with robust estimators. Neither approach particularly benefited from adopting bootstrapped critical values. Recommendations are provided to researchers regarding when each approach is best.

Humans↗
PubMed1998

Testing treatment effects in repeated measures designs: an update for psychophysiological researchers.

In 1987, Jennings enumerated data analysis procedures that authors must follow for analyzing effects in repeated measures designs when submitting papers to Psychophysiology. These prescriptions were intended to counteract the effects of nonspherical data, a condition know to produce biased tests of significance. Since this editorial policy was established, additional refinements to the analysis of these designs have appeared in print in a number of sources that are not likely to be routinely read by psychophysiological researchers. Accordingly, this paper includes additional procedures not previously enumerated in the editorial policy that can be used to analyze repeated measurements. Furthermore, I indicate how numerical solutions can easily be obtained.

Bias↗
PubMedDate not supplied

The analysis of repeated measures designs in medical research.

Medical researchers can employ repeated measures designs to study the effects of a treatment over time or when each subject receives all treatments. Univariate F tests and multiple comparison procedures for comparing means constitute the methods to test for the presence of treatment effects. For validity, however, these tests must satisfy the sphericity assumption. To circumvent the biasing effects of non-sphericity, this paper shows the applicability of the Greenhouse and Geisser three stage approach for univariate omnibus hypothesis testing in repeated measures designs containing any number of repeated factors. In addition, we present a multiple comparison procedure which provides a valid or robust test and thus controls the overall probability of a Type I error.

Research Design↗