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

K811 acetylation regulates ZEB1 dimerization, protein stability, and NuRD complex interactions to promote lung adenocarcinoma progression and metastasis

View full abstracthttps://openworks.mdanderson.org/leading-edge/1010/thumbnail.jp

Trimming, Transforming Statistics, And Bootstrapping: Circumventing the Biasing Effects Of Heterescedasticity And Nonnormality

Researchers can adopt different measures of central tendency and test statistics to examine the effect of a treatment variable across groups (e.g., means, trimmed means, M-estimators, & medians. Recently developed statistics are compared with respect to their ability to control Type I errors when data were nonnormal, heterogeneous, and the design was unbalanced: (1) a preliminary test for symmetry which determines whether data should be trimmed symmetrically or asymmetrically, (2) two different transformations to eliminate skewness, (3) the accuracy of assessing statistical significance with a bootstrap methodology was examined, and (4) statistics that use a robust measure of the typical score that empirically determined whether data should be trimmed, and, if so, in which direction, and by what amount were examined. The 56 procedures considered were remarkably robust to extreme forms of heterogeneity and nonnormality. However, we recommend a number of Welch-James heteroscedastic statistics which are preceded by the Babu, Padmanaban, and Puri (1999) test for symmetry that either symmetrically trimmed 10% of the data per group, or asymmetrically trimmed 20% of the data per group, after which either Johnson\u27s (1978) or Hall\u27s (1992) transformation was applied to the statistic and where significance was assessed through bootstrapping. Close competitors to the best methods were found that did not involve a transformation

Trimming, Transforming Statistics, And Bootstrapping: Circumventing the Biasing Effects Of Heterescedasticity And Nonnormality.

Researchers can adopt different measures of central tendency and test statistics to examine the effect of a treatment variable across groups

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

A Test Of Symmetry

When data are nonnormal in form classical procedures for assessing treatment group equality are prone to distortions in rates of Type I error and power to detect effects. Replacing the usual means with trimmed means reduces rates of Type I error and increases sensitivity to detect effects. If data are skewed, say to the right, then it has been postulated that asymmetric trimming, to the right, should be better at controlling rates of Type I error and power to detect effects than symmetric trimming from both tails of the data distribution. Keselman, Wilcox, Othman and Fradette (2002) found that Babu, Padmanabhan and Puri\u27s (1999) test for symmetry when combined with a heteroscedastic statistic which compared either symmetrically or asymmetrically determined means provided excellent Type I error control even when data were extremely heterogeneous and very nonnormal in form. In this paper, we present a detailed discussion of the Babu et al. procedure as well as a numerical example demonstrating its use

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

A Test of Symmetry.

When data are nonnormal in form classical procedures for assessing treatment group equality are prone to distortions in rates of Type I error and power to detect effects