Directional-sum test for nonparametric Behrens-Fisher problem with applications to the dietary intervention trial

2021 ◽  
pp. 096228022110028
Author(s):  
Zhen Meng ◽  
Qinglong Yang ◽  
Qizhai Li ◽  
Baoxue Zhang

For a nonparametric Behrens-Fisher problem, a directional-sum test is proposed based on division-combination strategy. A one-layer wild bootstrap procedure is given to calculate its statistical significance. We conduct simulation studies with data generated from lognormal, t and Laplace distributions to show that the proposed test can control the type I error rates properly and is more powerful than the existing rank-sum and maximum-type tests under most of the considered scenarios. Applications to the dietary intervention trial further show the performance of the proposed test.

2016 ◽  
Vol 5 (5) ◽  
pp. 16 ◽  
Author(s):  
Guolong Zhao

To evaluate a drug, statistical significance alone is insufficient and clinical significance is also necessary. This paper explains how to analyze clinical data with considering both statistical and clinical significance. The analysis is practiced by combining a confidence interval under null hypothesis with that under non-null hypothesis. The combination conveys one of the four possible results: (i) both significant, (ii) only significant in the former, (iii) only significant in the latter or (iv) neither significant. The four results constitute a quadripartite procedure. Corresponding tests are mentioned for describing Type I error rates and power. The empirical coverage is exhibited by Monte Carlo simulations. In superiority trials, the four results are interpreted as clinical superiority, statistical superiority, non-superiority and indeterminate respectively. The interpretation is opposite in inferiority trials. The combination poses a deflated Type I error rate, a decreased power and an increased sample size. The four results may helpful for a meticulous evaluation of drugs. Of these, non-superiority is another profile of equivalence and so it can also be used to interpret equivalence. This approach may prepare a convenience for interpreting discordant cases. Nevertheless, a larger data set is usually needed. An example is taken from a real trial in naturally acquired influenza.


2019 ◽  
Vol 189 (3) ◽  
pp. 235-242 ◽  
Author(s):  
Chia-Chun Wang ◽  
Wen-Chung Lee

Abstract Random-effects meta-analysis is one of the mainstream methods for research synthesis. The heterogeneity in meta-analyses is usually assumed to follow a normal distribution. This is actually a strong assumption, but one that often receives little attention and is used without justification. Although methods for assessing the normality assumption are readily available, they cannot be used directly because the included studies have different within-study standard errors. Here we present a standardization framework for evaluation of the normality assumption and examine its performance in random-effects meta-analyses with simulation studies and real examples. We use both a formal statistical test and a quantile-quantile plot for visualization. Simulation studies show that our normality test has well-controlled type I error rates and reasonable power. We also illustrate the real-world significance of examining the normality assumption with examples. Investigating the normality assumption can provide valuable information for further analysis or clinical application. We recommend routine examination of the normality assumption with the proposed framework in future meta-analyses.


2018 ◽  
Vol 8 (2) ◽  
pp. 58-71
Author(s):  
Richard L. Gorsuch ◽  
Curtis Lehmann

Approximations for Chi-square and F distributions can both be computed to provide a p-value, or probability of Type I error, to evaluate statistical significance. Although Chi-square has been used traditionally for tests of count data and nominal or categorical criterion variables (such as contingency tables) and F ratios for tests of non-nominal or continuous criterion variables (such as regression and analysis of variance), we demonstrate that either statistic can be applied in both situations. We used data simulation studies to examine when one statistic may be more accurate than the other for estimating Type I error rates across different types of analysis (count data/contingencies, dichotomous, and non-nominal) and across sample sizes (Ns) ranging from 20 to 160 (using 25,000 replications for simulating p-value derived from either Chi-squares or F-ratios). Our results showed that those derived from F ratios were generally closer to nominal Type I error rates than those derived from Chi-squares. The p-values derived from F ratios were more consistent for contingency table count data than those derived from Chi-squares. The smaller than 100 the N was, the more discrepant p-values derived from Chi-squares were from the nominal p-value. Only when the N was greater than 80 did the p-values from Chi-square tests become as accurate as those derived from F ratios in reproducing the nominal p-values. Thus, there was no evidence of any need for special treatment of dichotomous dependent variables. The most accurate and/or consistent p's were derived from F ratios. We conclude that Chi-square should be replaced generally with the F ratio as the statistic of choice and that the Chi-square test should only be taught as history.


2019 ◽  
Vol 14 (2) ◽  
pp. 399-425 ◽  
Author(s):  
Haolun Shi ◽  
Guosheng Yin

2014 ◽  
Vol 38 (2) ◽  
pp. 109-112 ◽  
Author(s):  
Daniel Furtado Ferreira

Sisvar is a statistical analysis system with a large usage by the scientific community to produce statistical analyses and to produce scientific results and conclusions. The large use of the statistical procedures of Sisvar by the scientific community is due to it being accurate, precise, simple and robust. With many options of analysis, Sisvar has a not so largely used analysis that is the multiple comparison procedures using bootstrap approaches. This paper aims to review this subject and to show some advantages of using Sisvar to perform such analysis to compare treatments means. Tests like Dunnett, Tukey, Student-Newman-Keuls and Scott-Knott are performed alternatively by bootstrap methods and show greater power and better controls of experimentwise type I error rates under non-normal, asymmetric, platykurtic or leptokurtic distributions.


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