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Rand R. Wilcox - One of the best experts on this subject based on the ideXlab platform.
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Comparing J independent groups with a Method based on trimmed means
Communications in Statistics - Simulation and Computation, 2017Co-Authors: A. Firat Özdemir, Rand R. Wilcox, Engin YildiztepeAbstract:ABSTRACTThe 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.
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Comparing robust regression lines associated with two dependent groups when there is heteroscedasticity
Computational Statistics, 2014Co-Authors: Rand R. Wilcox, Florence ClarkAbstract:The paper deals with three approaches to comparing the regression lines corresponding to two dependent groups when using a robust estimator. The focus is on the Theil–Sen estimator with some comments about alternative estimators that might be used. The first approach is to test the global hypothesis that the two groups have equal intercepts and slopes in a manner that allows a heteroscedastic error term. The second approach is to test the hypothesis of equal intercepts, ignoring the slopes, and testing the hypothesis of equal slopes, ignoring the intercepts. The third approach is to test the hypothesis that the regression lines differ at a specified design point. This last goal corresponds to the classic Johnson and Neyman Method when dealing with independent groups and when using the ordinary least squares regression estimator. Based on extant studies, there are guesses about how to proceed in a manner that will provide reasonably accurate control over the Type I error probability: Use some type of Percentile Bootstrap Method. (Methods that assume the regression estimator is asymptotically normal were not considered for reasons reviewed in the paper.) But there are no simulation results providing some sense of how well they perform when dealing with a relatively small sample size. Data from the Well Elderly II study are used to illustrate that the choice between the ordinary least squares estimator and the Theil–Sen estimator can make a practical difference.
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Comparing two independent groups via the lower and upper quantiles
Journal of Statistical Computation and Simulation, 2013Co-Authors: Rand R. Wilcox, David M. Erceg-hurn, Florence Clark, Mike CarlsonAbstract:The most common strategy for comparing two independent groups is in terms of some measure of location intended to reflect the typical observation. However, it can be informative and important to compare the lower and upper quantiles as well, but when there are tied values, extant techniques suffer from practical concerns reviewed in the paper. For the special case where the goal is to compare the medians, a slight generalization of the Percentile Bootstrap Method performs well in terms of controlling Type I errors when there are tied values [Wilcox RR. Comparing medians. Comput. Statist. Data Anal. 2006;51:1934–1943]. But our results indicate that when the goal is to compare the quartiles, or quantiles close to zero or one, this approach is highly unsatisfactory when the quantiles are estimated using a single order statistic or a weighted average of two order statistics. The main result in this paper is that when using the Harrell–Davis estimator, which uses all of the order statistics to estimate a quant...
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Comparing Measures of Location: Some Small-Sample Results When Distributions Differ in Skewness and Kurtosis Under Heterogeneity of Variances
Communications in Statistics - Simulation and Computation, 2012Co-Authors: A. Firat Özdemir, Rand R. Wilcox, Engin YildiztepeAbstract:This article considers the problem of comparing two independent groups in terms of some measure of location. Nine Methods, including a new Method and a new robust estimator, were compared in terms of actual significance level and power. Simulations were performed using data generated from both theoretical distributions and data stemming from actual studies. For the theoretical distributions, the Bootstrap-t B 2 t Method (with 20% trimming) and Yuen's test (with 10% trimming) performed best. Otherwise, the Bootstrap-t B 2 t Method (with 25% trimming) and a Percentile Bootstrap Method with trimmed means (20% and 25% trimming) or one-step M-estimator performed best.
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Comparing two dependent groups via quantiles
Journal of Applied Statistics, 2012Co-Authors: Rand R. Wilcox, David M. Erceg-hurnAbstract:This paper considers two general ways dependent groups might be compared based on quantiles. The first compares the quantiles of the marginal distributions. The second focuses on the lower and upper quantiles of the usual difference scores. Methods for comparing quantiles have been derived that typically assume that sampling is from a continuous distribution. There are exceptions, but generally, when sampling from a discrete distribution where tied values are likely, extant Methods can perform poorly, even with a large sample size. One reason is that extant Methods for estimating the standard error can perform poorly. Another is that quantile estimators based on a single-order statistic, or a weighted average of two-order statistics, are not necessarily asymptotically normal. Our main result is that when using the Harrell--Davis estimator, good control over the Type I error probability can be achieved in simulations via a standard Percentile Bootstrap Method, even when there are tied values, provided the sample sizes are not too small. In addition, the two Methods considered here can have substantially higher power than alternative procedures. Using real data, we illustrate how quantile comparisons can be used to gain a deeper understanding of how groups differ.
A. Firat Özdemir - One of the best experts on this subject based on the ideXlab platform.
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A new quantile estimator with weights based on a subsampling approach.
British Journal of Mathematical and Statistical Psychology, 2020Co-Authors: Gözde Navruz, A. Firat ÖzdemirAbstract:Quantiles are widely used in both theoretical and applied statistics, and it is important to be able to deploy appropriate quantile estimators. To improve performance in the lower and upper quantiles, especially with small sample sizes, a new quantile estimator is introduced which is a weighted average of all order statistics. The new estimator, denoted NO, has desirable asymptotic properties. Moreover, it offers practical advantages over four estimators in terms of efficiency in most experimental settings. The Harrell-Davis quantile estimator, the default quantile estimator of the R programming language, the Sfakianakis-Verginis SV2 quantile estimator and a kernel quantile estimator. The NO quantile estimator is also utilized in comparing two independent groups with a Percentile Bootstrap Method and, as expected, it is more successful than other estimators in controlling Type I error rates.
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Quantile estimation and comparing two independent groups with an approach based on Percentile Bootstrap
Communications in Statistics - Simulation and Computation, 2017Co-Authors: Gözde Navruz, A. Firat ÖzdemirAbstract:ABSTRACTAlthough the most common approach for comparing two independent groups is on the basis of some measure of location, determination of the differences in the tails of the groups is often of interest. In this study, Harrell–Davis estimator, Sfakianakis–Verginis estimators and default quantile estimator of R are used in conjunction with a Percentile Bootstrap Method with the aim of comparing two independent groups via the quantiles, and the relative efficiencies of Harrell–Davis and Sfakianakis–Verginis estimators are compared. General performance of Sfakianakis–Verginis estimators was much better than Harrell–Davis estimator in terms of both saving actual type I error and relative efficiency.
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Comparing J independent groups with a Method based on trimmed means
Communications in Statistics - Simulation and Computation, 2017Co-Authors: A. Firat Özdemir, Rand R. Wilcox, Engin YildiztepeAbstract:ABSTRACTThe 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.
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Comparing Measures of Location: Some Small-Sample Results When Distributions Differ in Skewness and Kurtosis Under Heterogeneity of Variances
Communications in Statistics - Simulation and Computation, 2012Co-Authors: A. Firat Özdemir, Rand R. Wilcox, Engin YildiztepeAbstract:This article considers the problem of comparing two independent groups in terms of some measure of location. Nine Methods, including a new Method and a new robust estimator, were compared in terms of actual significance level and power. Simulations were performed using data generated from both theoretical distributions and data stemming from actual studies. For the theoretical distributions, the Bootstrap-t B 2 t Method (with 20% trimming) and Yuen's test (with 10% trimming) performed best. Otherwise, the Bootstrap-t B 2 t Method (with 25% trimming) and a Percentile Bootstrap Method with trimmed means (20% and 25% trimming) or one-step M-estimator performed best.
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Comparing two independent groups: a test based on a one-step M-estimator and Bootstrap-t.
British Journal of Mathematical and Statistical Psychology, 2012Co-Authors: A. Firat ÖzdemirAbstract:A new test is proposed for the problem of comparing two independent groups in terms of some measure of location. The proposed test () uses a one-step M-estimator and a Bootstrap-t Method with the procedure proposed by Ozdemir and Kurt (2006). Eight Methods were compared in terms of actual Type I error and power when the underlying distributions differ in skewness and kurtosis under heterogeneity of variances. For the 21 theoretical distributions, the Yuen test with the Bootstrap-t Method was the most favourable, followed by test. For the five real data sets, the proposed test and Percentile Bootstrap Method with the one-step M-estimator performed best.
David F Garwayheath - One of the best experts on this subject based on the ideXlab platform.
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a novel distribution of visual field test points to improve the correlation between structure function measurements
Investigative Ophthalmology & Visual Science, 2012Co-Authors: Rin Asaoka, David F Garwayheath, Richard A Russell, Rizwan Malik, David P. CrabbAbstract:PURPOSE: To create a new visual field (VF) test grid centered at the optic disc (disc-centered field [DCF]) and to infer the combination of VF test points (structure-function field [SFF]), taken from the DCF and the conventional fovea-centered 24-2 grid (24-2) of standard automated perimetry, which yields the strongest sectorial correlation between structure-function measurements of retinal nerve fiber layer (RNFL) thickness and VF sensitivity. MethodS: In 50 eyes with ocular hypertension or open angle glaucoma, the DCF and 24-2 VF were measured with a humphrey field analyzer II (Full Threshold strategy) and RNFL thickness was measured with Stratus optical coherence tomography. test points from the DCF and 24-2 VF Were combined and divided into 12 sectors according to the spatial distribution of the RNFL. A novel VF for structure-function studies was established using the following criteria: each sector must contain at least one or two test points (depending on the sector's location), and the combination of test points which yields the strongest structure-function correlation is selected. RESULTS: The SFF consisted of 40 test points. The structure-function correlation for the SFF was compared with the standard 24-2 VF; a multiple-comparison test for dependent groups was carried out using a Percentile Bootstrap Method, which indicated that the sector correlation coefficients in the SFF were significantly higher than those in the 24-2 VF. CONCLUSIONS: The SFF, with fewer test locations, has a stronger structure-function correlation than the 24-2 VF. This improved correlation may help clinicians to better interpret functional measurements in relation to structural measurements.
Florence Clark - One of the best experts on this subject based on the ideXlab platform.
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Comparing robust regression lines associated with two dependent groups when there is heteroscedasticity
Computational Statistics, 2014Co-Authors: Rand R. Wilcox, Florence ClarkAbstract:The paper deals with three approaches to comparing the regression lines corresponding to two dependent groups when using a robust estimator. The focus is on the Theil–Sen estimator with some comments about alternative estimators that might be used. The first approach is to test the global hypothesis that the two groups have equal intercepts and slopes in a manner that allows a heteroscedastic error term. The second approach is to test the hypothesis of equal intercepts, ignoring the slopes, and testing the hypothesis of equal slopes, ignoring the intercepts. The third approach is to test the hypothesis that the regression lines differ at a specified design point. This last goal corresponds to the classic Johnson and Neyman Method when dealing with independent groups and when using the ordinary least squares regression estimator. Based on extant studies, there are guesses about how to proceed in a manner that will provide reasonably accurate control over the Type I error probability: Use some type of Percentile Bootstrap Method. (Methods that assume the regression estimator is asymptotically normal were not considered for reasons reviewed in the paper.) But there are no simulation results providing some sense of how well they perform when dealing with a relatively small sample size. Data from the Well Elderly II study are used to illustrate that the choice between the ordinary least squares estimator and the Theil–Sen estimator can make a practical difference.
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Comparing two independent groups via the lower and upper quantiles
Journal of Statistical Computation and Simulation, 2013Co-Authors: Rand R. Wilcox, David M. Erceg-hurn, Florence Clark, Mike CarlsonAbstract:The most common strategy for comparing two independent groups is in terms of some measure of location intended to reflect the typical observation. However, it can be informative and important to compare the lower and upper quantiles as well, but when there are tied values, extant techniques suffer from practical concerns reviewed in the paper. For the special case where the goal is to compare the medians, a slight generalization of the Percentile Bootstrap Method performs well in terms of controlling Type I errors when there are tied values [Wilcox RR. Comparing medians. Comput. Statist. Data Anal. 2006;51:1934–1943]. But our results indicate that when the goal is to compare the quartiles, or quantiles close to zero or one, this approach is highly unsatisfactory when the quantiles are estimated using a single order statistic or a weighted average of two order statistics. The main result in this paper is that when using the Harrell–Davis estimator, which uses all of the order statistics to estimate a quant...
Engin Yildiztepe - One of the best experts on this subject based on the ideXlab platform.
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Comparing J independent groups with a Method based on trimmed means
Communications in Statistics - Simulation and Computation, 2017Co-Authors: A. Firat Özdemir, Rand R. Wilcox, Engin YildiztepeAbstract:ABSTRACTThe 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.
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Comparing Measures of Location: Some Small-Sample Results When Distributions Differ in Skewness and Kurtosis Under Heterogeneity of Variances
Communications in Statistics - Simulation and Computation, 2012Co-Authors: A. Firat Özdemir, Rand R. Wilcox, Engin YildiztepeAbstract:This article considers the problem of comparing two independent groups in terms of some measure of location. Nine Methods, including a new Method and a new robust estimator, were compared in terms of actual significance level and power. Simulations were performed using data generated from both theoretical distributions and data stemming from actual studies. For the theoretical distributions, the Bootstrap-t B 2 t Method (with 20% trimming) and Yuen's test (with 10% trimming) performed best. Otherwise, the Bootstrap-t B 2 t Method (with 25% trimming) and a Percentile Bootstrap Method with trimmed means (20% and 25% trimming) or one-step M-estimator performed best.