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Wald-Wolfowitz Runs Test II01:17

Wald-Wolfowitz Runs Test II

292
The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and...
292
Wald-Wolfowitz Runs Test I01:17

Wald-Wolfowitz Runs Test I

700
The Wald-Wolfowitz test, also known as the runs test, is a nonparametric statistical test used to assess the randomness of a sequence of two different types of elements (e.g., positive/negative values, successes/failures). It examines whether the order of the elements in a sequence is random or if there is a pattern or trend present. This nonparametric test applies to any ordered data despite the population and sample data distribution, even if a higher sample size is available.
The test works...
700
Wilcoxon Signed-Ranks Test for Median of Single Population01:14

Wilcoxon Signed-Ranks Test for Median of Single Population

199
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...
199
Wilcoxon Signed-Ranks Test for Matched Pairs01:09

Wilcoxon Signed-Ranks Test for Matched Pairs

187
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...
187
Test for Homogeneity01:23

Test for Homogeneity

2.0K
The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can...
2.0K
Wilcoxon Rank-Sum Test01:21

Wilcoxon Rank-Sum Test

279
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:
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Related Experiment Video

Updated: Aug 9, 2025

Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks
09:49

Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks

Published on: September 25, 2021

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A practical two-sample test for weighted random graphs.

Mingao Yuan1, Qian Wen1

  • 1Department of Statistics, North Dakota State University, Fargo, ND, USA.

Journal of Applied Statistics
|February 23, 2023
PubMed
Summary

This study introduces a new statistical test for comparing two weighted networks, outperforming existing methods for binary graphs. The proposed test statistic is validated for network data analysis and real-world applications.

Keywords:
Two-sample hypothesis testrandom graphweighted graph

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Area of Science:

  • Statistics
  • Machine Learning
  • Network Analysis

Background:

  • Network data analysis is crucial in statistics and machine learning.
  • Existing graph two-sample hypothesis tests are limited to binary graphs, not applicable to weighted networks.
  • Practical network data often involves weights, necessitating new analytical approaches.

Purpose of the Study:

  • To address the challenge of weighted graph two-sample hypothesis testing.
  • To propose a novel and practical test statistic for comparing weighted graph populations.
  • To evaluate the theoretical properties and practical performance of the new test.

Main Methods:

  • Development of a new test statistic for weighted graph comparison.
  • Theoretical analysis of the test statistic's convergence to a standard normal distribution under the null hypothesis.
  • Power analysis of the proposed test statistic.

Main Results:

  • The proposed test statistic converges in distribution to the standard normal distribution.
  • Theoretical analysis confirms the test's statistical validity.
  • Simulation studies demonstrate satisfactory performance and significant outperformance compared to binary graph methods.

Conclusions:

  • The developed test statistic is effective for weighted graph two-sample hypothesis testing.
  • The method offers a practical solution for analyzing real-world weighted network data.
  • The study advances statistical methods for network data analysis.