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Related Concept Videos

Wilcoxon Rank-Sum Test01:21

Wilcoxon Rank-Sum Test

The Wilcoxon rank-sum test, also known as the Mann-Whitney U test, is a nonparametric test used to determine if there is a significant difference between the distributions of two independent samples. This test is designed specifically for two independent populations and has the following key requirements:
Wilcoxon Signed-Ranks Test for Median of Single Population01:14

Wilcoxon Signed-Ranks Test for Median of Single Population

The Wilcoxon signed-rank test for the median of a single population is a nonparametric test used to evaluate whether the median of a population differs from a specified value. Unlike parametric tests, it does not require data to follow a normal distribution, making it suitable for non-normal or small samples. The test begins by calculating the difference (d) between each observation and the hypothesized median. The absolute values of these differences are ranked in ascending order, with ties...
Wilcoxon Signed-Ranks Test for Matched Pairs01:09

Wilcoxon Signed-Ranks Test for Matched Pairs

The Wilcoxon signed-rank test for matched pairs evaluates the null hypothesis by combining the ranks of differences with their signs. It essentially tests whether the median of the differences in a population of matched pairs is zero. Since the test incorporates more information than the sign test, it generally yields more trustable conclusions. This test also does not require the data to follow a normal distribution, but two conditions must be met for it to be applicable: (1) the data must...
One-Way ANOVA: Equal Sample Sizes01:15

One-Way ANOVA: Equal Sample Sizes

One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...
One-Way ANOVA: Unequal Sample Sizes01:15

One-Way ANOVA: Unequal Sample Sizes

One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:
Bonferroni Test01:10

Bonferroni Test

The Bonferroni test is a statistical test named after Carlo Emilio Bonferroni, an Italian mathematician best known for Bonferroni inequalities. This statistical test is a type of multiple comparison test to determine which means are different than the rest. Bonferroni test can minimize the Type 1 error by reducing the significance level alpha, which otherwise increases with sample pairs.
The means of different samples are first paired in all possible combinations.
The null hypothesis of the...

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Related Experiment Video

Updated: Jun 19, 2026

Comparison of Predictive Performance of Three Lymph Node Staging Systems in Colorectal Signet Ring Cell Carcinoma Based on Machine Learning Model
07:13

Comparison of Predictive Performance of Three Lymph Node Staging Systems in Colorectal Signet Ring Cell Carcinoma Based on Machine Learning Model

Published on: April 18, 2025

Exemplary data set sample size calculation for Wilcoxon-Mann-Whitney tests.

George Divine1, Alissa Kapke, Suzanne Havstad

  • 1Department of Biostatistics and Research Epidemiology, Henry Ford Hospital, Detroit, Michigan 48202-3450, USA. gdivine1@hfhs.org

Statistics in Medicine
|November 6, 2009
PubMed
Summary
This summary is machine-generated.

A new formula for sample size calculation in Wilcoxon-Mann-Whitney (WMW) tests with ties offers a straightforward approach. The exemplary data set method is asymptotically equivalent, providing similar accuracy to established statistical software for common allocation ratios.

Related Experiment Videos

Last Updated: Jun 19, 2026

Comparison of Predictive Performance of Three Lymph Node Staging Systems in Colorectal Signet Ring Cell Carcinoma Based on Machine Learning Model
07:13

Comparison of Predictive Performance of Three Lymph Node Staging Systems in Colorectal Signet Ring Cell Carcinoma Based on Machine Learning Model

Published on: April 18, 2025

Area of Science:

  • Biostatistics
  • Statistical Methods

Background:

  • Sample size calculation is crucial for the validity of statistical tests.
  • The Wilcoxon-Mann-Whitney (WMW) test is a non-parametric alternative to the t-test, often used when data are not normally distributed.
  • Handling ties in data can complicate sample size estimations for the WMW test.

Purpose of the Study:

  • To present a straightforward formula for sample size calculation in WMW tests with ties.
  • To explore the relationship between the Zhao-Rahardja-Qu (ZRQ) method and the exemplary data set approach for WMW sample size estimation.
  • To compare the accuracy of the ZRQ formula and the exemplary data set method against existing approaches.

Main Methods:

  • Development of a closed-form sample size formula for WMW tests with ties.
  • Application of the exemplary data set approach for WMW sample size estimation.
  • Simulation studies to evaluate the performance of different sample size estimation methods.
  • Comparison with established methods like Kolassa (nQuery Advisor) and O'Brien-Castelloe (SAS 9.2 PROC POWER).

Main Results:

  • The Zhao-Rahardja-Qu formula provides a simple method for WMW sample size calculation with ties.
  • The exemplary data set approach is asymptotically equivalent to the ZRQ method.
  • Both methods yield accurate sample size estimates comparable to existing software for 1:1 and 1:2 allocation ratios.
  • For 1:4 and 1:19 allocation ratios, Kolassa and O'Brien-Castelloe methods may offer higher accuracy.

Conclusions:

  • The ZRQ formula and exemplary data set approach offer practical and accurate solutions for WMW sample size estimation with ties.
  • The exemplary data set approach demonstrates broad utility for sample size estimation beyond the WMW test.
  • Researchers can confidently use these methods, especially for common allocation ratios, simplifying study design.