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Full-Text Articles in Statistics and Probability
A Robust Nonparametric Measure Of Effect Size Based On An Analog Of Cohen's D, Plus Inferences About The Median Of The Typical Difference, Rand Wilcox
Journal of Modern Applied Statistical Methods
The paper describes a nonparametric analog of Cohen's d, Q. It is established that a confidence interval for Q can be computed via a method for computing a confidence interval for the median of D = X1 − X2, which in turn is related to making inferences about P(X1 < X2).
An Inferential Method For Determining Which Of Two Independent Variables Is Most Important When There Is Curvature, Rand Wilcox
An Inferential Method For Determining Which Of Two Independent Variables Is Most Important When There Is Curvature, Rand Wilcox
Journal of Modern Applied Statistical Methods
Consider three random variables Y, X1 and X2, where the typical value of Y, given X1 and X2, is given by some unknown function m(X1, X2). A goal is to determine which of the two independent variables is most important when both variables are included in the model. Let τ1 denote the strength of the association associated with Y and X1, when X2 is included in the model, and let τ2 be defined in an analogous manner. If it is assumed …
Within Groups Anova When Using A Robust Multivariate Measure Of Location, Rand Wilcox, Timothy Hayes
Within Groups Anova When Using A Robust Multivariate Measure Of Location, Rand Wilcox, Timothy Hayes
Journal of Modern Applied Statistical Methods
For robust measures of location associated with J dependent groups, various methods have been proposed that are aimed at testing the global hypothesis of a common measure of location applied to the marginal distributions. A criticism of these methods is that they do not deal with outliers in a manner that takes into account the overall structure of the data. Location estimators have been derived that deal with outliers in this manner, but evidently there are no simulation results regarding how well they perform when the goal is to test the some global hypothesis. The paper compares four bootstrap methods …
Comparing Two Independent Groups Via A Quantile Generalization Of The Wilcoxon-Mann-Whitney Test, Rand R. Wilcox
Comparing Two Independent Groups Via A Quantile Generalization Of The Wilcoxon-Mann-Whitney Test, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
The Wilcoxon-Mann-Whitney test, as well as modern improvements, are based in part on an estimate of p = P(D < 0), where D = X−Y and X and Y are independent random variables; a common goal is to test H0: p = 0.5. This corresponds to testing H0: ξ0.5, where ξ0.5 is the 0.5 quantile of the distribution of D. If the distributions associated with X and Y do not differ, then D has a symmetric distribution about zero. In particular, ξq + ξ1-q = 0 for any q ≤ 0.5, where ξq is the qth quantile. Methods aimed at testing H0: p = 0.5 are generalized by …
Comparing The Strength Of Association Of Two Predictors Via Smoothers Or Robust Regression Estimators, Rand R. Wilcox
Comparing The Strength Of Association Of Two Predictors Via Smoothers Or Robust Regression Estimators, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
Consider three random variables, Y , X1 and X2, having some unknown trivariate distribution and let n2j (j = 1, 2) be some measure of the strength of association between Y and Xj. When n2j is taken to be Pearson’s correlation numerous methods for testing Ho : n21 = n22 have been proposed. However, Pearson’s correlation is not robust and the methods for testing H0 are not level robust in general. This article examines methods for testing H0 based on a robust fit. The …
Quantile Regression: On Inferences About The Slopes Corresponding To One, Two Or Three Quantiles, Rand R. Wilcox, Kathleen Costa
Quantile Regression: On Inferences About The Slopes Corresponding To One, Two Or Three Quantiles, Rand R. Wilcox, Kathleen Costa
Journal of Modern Applied Statistical Methods
The problem of testing hypotheses about the slope of a quantile regression line when the sample size is small is considered. A modified bootstrap method is suggested that is found to have certain advantages over the inverse rank method recommended by Koenker (1994). A method is suggested that simultaneously controls the probability of at least one Type I error when performing two or three tests corresponding to two or three specific quantiles. Using data from actual studies, it is illustrated that the new method can yield substantially shorter confidence intervals than the rank inverse method and, even with a large …
An Omnibus Test When Using A Regression Estimator With Multiple Predictors, Rand R. Wilcox
An Omnibus Test When Using A Regression Estimator With Multiple Predictors, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
In quantile regression, the goal is to estimate theγ quantile of Y given values for p predictors. Methods for making inferences about the individual slope parameters have been proposed, some of which have been found to perform very well in simulations. But for an omnibus test that all slope parameters are zero, it appears that little is known about how best to proceed. For the special case γ =.5, a drop-in-dispersion test has been recommended, but it requires a large sample size to control the probability of a Type I error and it assumes that the usual error term is …
Ancova: A Robust Omnibus Test Based On Selected Design Points, Rand R. Wilcox
Ancova: A Robust Omnibus Test Based On Selected Design Points, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
Many robust analogs of the classic analysis of covariance method have been proposed. One approach, when comparing two independent groups, uses selected design points and then compares the groups at each design point using some robust method for comparing measures of location. So, if K design points are of interest, K tests are performed. There are rather obvious ways of performing, instead, an omnibus test that for all K points, no differences between the groups exist. One of the main results here is that several variations of these methods can perform very poorly in simulations. An alternative approach, based in …
Within By Within Anova Based On Medians, Rand R. Wilcox
Within By Within Anova Based On Medians, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
This article considers a J by K ANOVA design where all JK groups are dependent and where groups are to be compared based on medians. Two general approaches are considered. The first is based on an omnibus test for no main effects and no interactions and the other tests each member of a collection of relevant linear contrasts. Based on an earlier paper dealing with multiple comparisons, an obvious speculation is that a particular bootstrap method should be used. One of the main points here is that, in general, this is not the case for the problem at hand. The …