Multiple Comparison Procedures, Trimmed Means And Transformed Statistics

A modification to testing pairwise comparisons that may provide better control of Type I errors in the presence of non-normality is to use a preliminary test for symmetry which determines whether data should be trimmed symmetrically or asymmetrically. Several pairwise MCPs were investigated, employing a test of symmetry with a number of heteroscedastic test statistics that used trimmed means and Winsorized variances. Results showed improved Type I error control than competing robust statistics

A Comparison Of Methods For Longitudinal Analysis With Missing Data

In a longitudinal two-group randomized trials design, also referred to as randomized parallel-groups design or split-plot repeated measures design, the important hypothesis of interest is whether there are differential rates of change over time, that is, whether there is a group by time interaction. Several analytic methods have been presented in the literature for testing this important hypothesis when data are incomplete. We studied these methods for the case in which the missing data pattern is non-monotone. In agreement with earlier work on monotone missing data patterns, our results on bias, sampling variability, Type I error and power support the use of a procedure due to Overall, Ahn, Shivakumar, and Kalburgi (1999) that can easily be implemented with SAS’s PROC MIXE

Assessing Treatment Effects in Randomized Longitudinal Two-Group Designs with Missing Observations

SAS’s PROC MIXED can be problematic when analyzing data from randomized longitudinal two-group designs when observations are missing over time. Overall (1996, 1999) and colleagues found a number of procedures that are effective in controlling the number of false positives (Type I errors) and are yet sensitive (powerful) to detect treatment effects. Two favorable methods incorporate time in study and baseline scores to model the missing data mechanism; one method was a single-stage PROC MIXED ANCOVA solution and the other was a two-stage endpoint analysis using the change scores as dependent scores. Because the twostage approach can lack sensitivity to detect effects for certain missing data mechanisms, in this article we examined variations of the single-stage approach under conditions not considered by Overall et al., in order to assess the generality of the procedure’s positive characteristics. The results indicate when and when not it is beneficial to include a baseline score as a covariate in the model. As well, we provide clarification regarding the merits of adopting an endpoint analysis as compared to the single-stage PROC MIXED procedure

Robust Confidence Intervals for Effect Size in the Two-Group Case

The probability coverage of intervals involving robust estimates of effect size based on seven procedures was compared for asymmetrically trimming data in an independent two-groups design, and a method that symmetrically trims the data. Four conditions were varied: (a) percentage of trimming, (b) type of nonnormal population distribution, (c) population effect size, and (d) sample size. Results indicated that coverage probabilities were generally well controlled under the conditions of nonnormality. The symmetric trimming method provided excellent probability coverage. Recommendations are provided

Analyzing Group by Time Effects in Longitudinal Two-Group Randomized Trial Designs With Missing Data

We investigated bias, sampling variability, Type I error and power of nine approaches for testing the group by time interaction in a repeated measures design under three types of missing data mechanisms. One procedure due to Overall, Ahn, Shivakumar, and Kalburgi (1999) performed reasonably well over a range of conditions

Confidence Intervals for the Squared Multiple Semipartial Correlation Coefficient

The squared multiple semipartial correlation coefficient is the increase in the squared multiple correlation coefficient that occurs when two or more predictors are added to a multiple regression model. Coverage probability was investigated for two variations of each of three methods for setting confidence intervals for the population squared multiple semipartial correlation coefficient. Results indicated that the procedure that provides coverage probability in the [.925, .975] interval for a 95% confidence interval depends primarily on the number of added predictors. Guidelines for selecting a procedure are presented

Confidence Intervals For An Effect Size When Variances Are Not Equal

Confidence intervals must be robust in having nominal and actual probability coverage in close agreement. This article examined two ways of computing an effect size in a two-group problem: (a) the classic approach which divides the mean difference by a single standard deviation and (b) a variant of a method which replaces least squares values with robust trimmed means and a Winsorized variance. Confidence intervals were determined with theoretical and bootstrap critical values. Only the method that used robust estimators and a bootstrap critical value provided generally accurate probability coverage under conditions of nonnormality and variance heterogeneity in balanced as well as unbalanced designs

Conventional And Robust Paired And Independent-Samples \u3cem\u3et\u3c/em\u3e Tests: Type I Error And Power Rates

Monte Carlo methods were used to examine Type I error and power rates of 2 versions (conventional and robust) of the paired and independent-samples t tests under nonnormality. The conventional (robust) versions employed least squares means and variances (trimmed means and Winsorized variances) to test for differences between groups

A Power Comparison of Robust Test Statistics Based On Adaptive Estimators

Seven test statistics known to be robust to the combined effects of nonnormality and variance heterogeneity were compared for their sensitivity to detect treatment effects in a one-way completely randomized design containing four groups. The six Welch-James-type heteroscedastic tests adopted either symmetric or asymmetric trimmed means, were transformed for skewness, and used a bootstrap method to assess statistical significance. The remaining test, due to Wilcox and Keselman (2003), used a modification of the well-known one-step M-estimator of central tendency rather than trimmed means. The Welch-James-type test is recommended because for nonnormal data likely to be encountered in applied research settings it should be more powerful than the test presented by Wilcox and Keselman. However, the reverse is true for data that are extremely nonnormal

Robust Modifications of the Levene and O’Brien Tests for Spread

Variants of Levene’s and O’Brien’s procedures not investigated by Keselman, Wilcox & Algina (2008) were examined. Simulations indicate that a new O’Brien variant provides very good Type I error control and is simpler for applied researchers to compute than the method recommended by Keselman, et al