统计分析中检验方法的选择

1.一组样本资料若来自正态总体,可用t检验;若来自非正态总体或总体分布无法确定,可用Wilcoxon符号秩和检验。2.配对设计资料二分类变量,可用McNemar检验;有序多分类变量,可用Wilcoxon符号秩和检验;连续型变量,若来自正态总体,可用配对t检验,否则可用Wilcoxon符号秩和检验。3.两组独立样本连续型变量,若来自正态总体,可用t检验,否则,可用Wilcoxon符号秩和检验;二分类变量,可用χ2检验;无序多分类变量,可用χ2检验;有序多分类变量,宜用Wilcoxon符号秩和检验。4.多组独立样本连续型变量值,来自正态总体且方差相等,可用方差分析;否则,进行数据变换使其满足正态性或方差齐性的要求后,采用方差分析;数据变换仍不能满足条件时,可用Kruskal-Wallis秩和检验。二分类变量或无序多分类变量,可用χ2检验。有序多分类变量宜用Kruskal-Wallis秩和检验。5.随机区组设计连续型变量,来自正态总体且方差相等,可用随机区组设计的方差分析;否则,进行数据变换使其满足正态性或方差齐性的要求后,采用方差分析;数据变换仍不能满足条件时,可用Friedman秩和检验。统计分析中检验方法的选...     

完全随机设计两样本的Wilcoxon检验与K-S检验功效比较

目的 对完全随机设计下两样本比较的Wilcoxon检验与Kolmogorov-Smimov( K-S)检验的功效进行比较.方法 采用Matlab7.5软件编程,利用Monte Carlo方法模拟不同总体条件下两种方法的检验功效.结果 对正态分布,两总体方差比率越大K-S检验的功效越高,而Wilcoxon检验则受方差比率的影响不大；对偏态分布,两检验法在方差不等时功效更高.方差相等且样本量较大的两组数据比较时,Wilcoxon检验功效高于K-S检验；其余情况则K-S检验功效更高；如果样本量足够大,两种方法功效接近.结论当两组样本方差相等且样本量较大时（n≥50）建议采用Wilcoxon检验,而在其他条件下均可采用K-S检验,当效应量ES≥0.8且样本量n≥50时两种方法均可.     

统计分析中检验方法的选择

1．一组样本资料 若来自正态总体，可用t检验；若来自非正态总体或总体分布无法确定，可用Wilcoxon符号秩和检验。 2．配对设计资料 二分类变量，可用McNemar检验；有序多分类变量，可用Wilcoxon符号秩和检验；连续型变量，若来自正态总体，可用配对t检验，否则可用Wilcoxon符号秩和检验。     

统计分析中检验方法的选择

1．一组样本资料 若来自正态总体,可用t检验;若来自非正态总体或总体分布无法确定,可用Wilcoxon符号秩和检验。     

Nemenyi法检验的SAS实现

对于来自正态总体完全随机设计多组样本数据资料的多重比较可以通过方差分析方法来实现.然而,对总体分布未知的数据资料利用方差分析方法来直接进行检验,可能增加统计推断的误差[1].秩和检验是这类数据资料分析的重要工具,因为秩和检验方法并不要求数据资料满足正态性假定.     

统计分析中检验方法的选择

1．一组样本资料若来自正态总体，可用t检验；若来自非正态总体或总体分布无法确定，可用Wilcoxon符号秩和检验。     

t检验和χ2检验常见误用辨析

t检验和χ~2检验分别是定量和定性数据分析中最简单和最常用的统计分析方法。t检验主要用于两组数值型数据平均水平的比较,χ2检验主要用于率和构成比的比较。数据分析过程中,这两种方法非常容易误用。现对这两种方法的应用和常见问题展开讨论。1t检验t检验分为单样本t检验、配对t检验和成组t检验三类。单样本t检验用于比较一个样本均数所代表的未知总体均数与已知总体均数之间的差异,如将某地区某年龄男性身高均值与已知的全国同年龄男性身高均值进行比较时,应采用单样本t检验。配对t检验用于配对设计的两样本均值比较,配对设计主要有两种…     

Friedman M检验平均秩的多重比较在SPSS软件的实现

完全随机区组设计的秩和检验(Friedman's test)是随机化区组设计方差分析不满足方差分析条件时采用的方法.随机化区组设计的秩和检验是由M·Friedam在符号检验的基础上提出来的,又称M检验,目的是推断各处理组样本分别代表的总体分布是否不同[1].对于Friedman M检验,在当P＜α(α为检验水准)差异有统计学意义时,可认为多个总体间相比较有差异,但不能说明任何两个总体间均是有差异的.     

RPT对秩和检验的改进及Matlab实现

秩和检验作为一种方便、有效的非参数检验方法,在实际中有着广泛的应用,特别是在总体分布、参数均未知时,可以用来比较两样本的均值〔1〕。本文针对秩和检验对来自非正态总体两样本均值比较可能遇到准     

Wilcoxon配对秩和检验界值表简介

目前采用的配对秩和检验界值表多为单界值,例如 T_(0∶05(n))表示秩和 T≤T_(0∶05(n))的近似概率,在检验步骤中必需计算正秩和及负秩和,以绝对值小者作为 T 与 T_(0∶05(n))比较,判断检验结果。本文在分析秩和分布基础上,提出配对秩和检验的双界值表,在判断检验结果时,可任以正秩和或负秩和与界值相比,形式上与两组比较秩和检验相似、简化配对秩和     

Increasing physicians' awareness of the impact of statistics on research outcomes: comparative power of the t-test and and Wilcoxon Rank-Sum test in small samples applied research

To effectively evaluate medical literature, practicing physicians and medical researchers must understand the impact of statistical tests on research outcomes. Applying inefficient statistics not only increases the need for resources, but more importantly increases the probability of committing a Type I or Type II error. The t-test is one of the most prevalent tests used in the medical field and is the uniformally most powerful unbiased test (UMPU) under normal curve theory. But does it maintain its UMPU properties when assumptions of normality are violated? A Monte Carlo investigation evaluates the comparative power of the independent samples t-test and its nonparametric counterpart, the Wilcoxon Rank-Sum (WRS) test, to violations from population normality, using three commonly occurring distributions and small sample sizes. The t-test was more powerful under relatively symmetric distributions, although the magnitude of the differences was moderate. Under distributions with extreme skews, the WRS held large power advantages. When distributions consist of heavier tails or extreme skews, the WRS should be the test of choice. In turn, when population characteristics are unknown, the WRS is recommended, based on the magnitude of these power differences in extreme skews, and the modest variation in symmetric distributions.     

两个非正态样本同分布检验的非参数法选择

目的 对检验两个非正态样本是否同分布的常用非参数方法进行评价,为合理选择检验方法提供参考依据.方法 采用Matlab7.5软件编程,模拟数据在不同的分布类型、样本量相等或不等、方差齐或不齐、方差与样本量顺向或反向、均数相等或不等等条件下,分别采用Wilcoxon检验、Wald-Wolfowitz游程检验(WWR)、Kolmogorov-Smirnov检验(K-S)和Hollander极端反应检验(Hollander)进行检验.结果 给出4种检验法的Ⅰ型和Ⅱ型误差估计值.结论 当两个总体均数相等时,建议选用Hollander检验;当两个总体方差相等时,建议选用Wilcoxon检验或K-S检验;而在两个总体方差、均数都不相等但差异不大时,则可选用Wilcoxon检验、K-S检验或Hollander检验中的任意一种.     

Robustness of the two independent samples t-test when applied to ordinal scaled data

One may encounter the application of the two independent samples t-test to ordinal scaled data (for example, data that assume only the values 0, 1, 2, 3) from small samples. This situation clearly violates the underlying normality assumption for the t-test and one cannot appeal to large sample theory for validity. In this paper we report the results of an investigation of the t-test's robustness when applied to data of this form for samples of sizes 5 to 20. Our approach consists of complete enumeration of the sampling distributions and comparison of actual levels of significance with the significance level expected if the data followed a normal distribution. We demonstrate under general conditions the robustness of the t-test in that the maximum actual level of significance is close to the declared level.     

Calculation of power and sample size with bounded outcome scores

The two-sample Wilcoxon rank sum test is the most popular non-parametric test for the comparison of two samples when the underlying distributions are not normal. Although the underlying distributions need not be known in detail to calculate the null distribution of the test statistic, parametric assumptions are often made to determine the power of the test or the sample size. We encountered difficulties with this approach in the planning of a recent clinical trial in stroke patients. It is shown that, for power and sample size estimation, it can be dangerous to apply the classical formulae routinely, especially with outcome scores having a U-shaped or a J-shaped distribution. As an example we have taken the Barthel index, a quality-of-life outcome measure in stroke patients. Further, we have investigated alternative methods by means of Monte Carlo simulation. The distributional characteristics of the estimated powers were compared. Our findings suggest more appropriate computer software is necessary for the calculation of power and sample size when efficacy is measured by a non-parametric method.     

Effect of unequal censoring on the size and power of the logrank and Wilcoxon types of tests for survival data

This paper examines the effect of random unequal censoring on the size and power of two-sample logrank and Wilcoxon types of tests for comparing two survival distributions by simulation with small samples from censored exponential distributions. We compared equal-sized samples of n = 8, 16, and 32 with 1000 (size) and 500 (power) simulation trials for 16 combinations of the censoring proportions of 0, 20, 40, and 60 per cent in each of the two samples. For n = 8, the asymptotic normality (AN), Peto-Peto, and the two Wilcoxon-type tests performed at nominal 5 per cent size expectations, but the Mantel test exceeded the 5 per cent size acceptance region in 6 of 16 censoring combinations. For n = 16 and 32, all tests showed proper size, with the Peto-Peto test being most conservative in the presence of unequal censoring. We compared powers of all tests for exponential hazard ratios of 1·4 and 2·0. The Mantel test showed 90 to 95 per cent power efficiency relative to the parametric AN test. Both Wilcoxon tests performed identically and had the lowest relative power of all tests examined but appeared most robust to the differential censoring patterns studied. A modified version of the Peto-Peto test showed power comparable to the Mantel test.     

A modified Wilcoxon test for non‐negative distributions with a clump of zeros

Comparing two samples with a continuous non‐negative score, e.g. a utility score over [0, 1], with a substantial proportion, say 50 per cent, scoring 0 presents distributional problems for most standard tests. A Wilcoxon rank test can be used, but the large number of ties reduces power. I propose a new test, the Wilcoxon rank‐sum test performed after removing an equal (and maximal) number of 0's from each sample. This test recovers much of the power. Compared with a (directional) modification of a two‐part test proposed by Lachenbruch, the truncated Wilcoxon has similar power when the non‐zero scores are independent of the proportion of zeros, but, unlike the two‐part test, the truncated Wilcoxon is relatively unaffected when these processes are dependent. Copyright © 2009 John Wiley & Sons, Ltd.     

Analysis of small sample size studies using nonparametric bootstrap test with pooled resampling method

Experimental studies in biomedical research frequently pose analytical problems related to small sample size. In such studies, there are conflicting findings regarding the choice of parametric and nonparametric analysis, especially with non‐normal data. In such instances, some methodologists questioned the validity of parametric tests and suggested nonparametric tests. In contrast, other methodologists found nonparametric tests to be too conservative and less powerful and thus preferred using parametric tests. Some researchers have recommended using a bootstrap test; however, this method also has small sample size limitation. We used a pooled method in nonparametric bootstrap test that may overcome the problem related with small samples in hypothesis testing. The present study compared nonparametric bootstrap test with pooled resampling method corresponding to parametric, nonparametric, and permutation tests through extensive simulations under various conditions and using real data examples. The nonparametric pooled bootstrap t‐test provided equal or greater power for comparing two means as compared with unpaired t‐test, Welch t‐test, Wilcoxon rank sum test, and permutation test while maintaining type I error probability for any conditions except for Cauchy and extreme variable lognormal distributions. In such cases, we suggest using an exact Wilcoxon rank sum test. Nonparametric bootstrap paired t‐test also provided better performance than other alternatives. Nonparametric bootstrap test provided benefit over exact Kruskal–Wallis test. We suggest using nonparametric bootstrap test with pooled resampling method for comparing paired or unpaired means and for validating the one way analysis of variance test results for non‐normal data in small sample size studies. Copyright © 2017 John Wiley & Sons, Ltd.     

Robustness and power of analysis of covariance applied to ordinal scaled data as arising in randomized controlled trials

In clinical trials comparing two treatments, ordinal scales of three, four or five points are often used to assess severity, both prior to and after treatment. Analysis of covariance is an attractive technique, however, the data clearly violate the normality assumption and in the presence of small samples, and large sample theory may not apply. The robustness and power of various versions of parametric analysis of covariance applied to small samples of ordinal scaled data are investigated through computer simulation. Subjects are randomized to one of two competing treatments and the pre-treatment, or baseline, assessment is used as the covariate. We compare two parametric analysis of covariance tests that vary according to the treatment of the homogeneity of regressions slopes and the two independent samples t-test on difference scores. Under the null hypothesis of no difference in adjusted treatment means, we estimated actual significance levels by comparing observed test statistics to appropriate critical values from the F- and t-distributions for nominal significance levels of 0.10, 0.05, 0.02 and 0.01. We estimated power by similar comparisons under various alternative hypotheses. The model which assumes homogeneous slopes and the t-test on difference scores were robust in the presence of three, four and five point ordinal scales. The hierarchical approach which first tests for homogeneity of regression slopes and then fits separate slopes if there is significant non-homogeneity produced significance levels that exceeded the nominal levels especially when the sample sizes were small. The model which assumes homogeneous regression slopes produced the highest power among competing tests for all of the configurations investigated. The t-test on difference scores also produced good power in the presence of small samples.     

Power in the phenotypic extremes: a simulation study of power in discovery and replication of rare variants

Next‐generation sequencing technologies are making it possible to study the role of rare variants in human disease. Many studies balance statistical power with cost‐effectiveness by (a) sampling from phenotypic extremes and (b) utilizing a two‐stage design. Two‐stage designs include a broad‐based discovery phase and selection of a subset of potential causal genes/variants to be further examined in independent samples. We evaluate three parameters: first, the gain in statistical power due to extreme sampling to discover causal variants; second, the informativeness of initial (Phase I) association statistics to select genes/variants for follow‐up; third, the impact of extreme and random sampling in (Phase 2) replication. We present a quantitative method to select individuals from the phenotypic extremes of a binary trait, and simulate disease association studies under a variety of sample sizes and sampling schemes. First, we find that while studies sampling from extremes have excellent power to discover rare variants, they have limited power to associate them to phenotype—suggesting high false‐negative rates for upcoming studies. Second, consistent with previous studies, we find that the effect sizes estimated in these studies are expected to be systematically larger compared with the overall population effect size; in a well‐cited lipids study, we estimate the reported effect to be twofold larger. Third, replication studies require large samples from the general population to have sufficient power; extreme sampling could reduce the required sample size as much as fourfold. Our observations offer practical guidance for the design and interpretation of studies that utilize extreme sampling. Genet. Epidemiol. 35: 236‐246, 2011. © 2011 Wiley‐Liss, Inc.