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Wald-Wolfowitz Runs Test I

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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.
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Related Experiment Video

Updated: Aug 26, 2025

Monitoring Spatial Segregation in Surface Colonizing Microbial Populations

Monitoring Spatial Segregation in Surface Colonizing Microbial Populations

Published on: October 29, 2016

Quantifying ethnic segregation in cities through random walks.

Sandro Sousa^1,2, Vincenzo Nicosia³

¹School of Mathematical Sciences, Queen Mary University of London, London, UK. ssou@itu.dk.

Nature Communications

|October 3, 2022

Summary

This summary is machine-generated.

We introduce new non-parametric measures for spatial segregation using random walks on graphs. These methods consistently estimate segregation and allow for cross-system comparisons, revealing links to socioeconomic deprivation.

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Area of Science:

Urban studies
Spatial analysis
Network science

Background:

Socioeconomic segregation significantly contributes to urban inequalities.
Existing spatial segregation measures have limitations in scale dependency, neglecting spatial correlations, and relying on ad-hoc parameters, hindering cross-system comparisons.

Purpose of the Study:

To propose a novel family of non-parametric measures for spatial distributions.
To enable consistent and comparable estimations of segregation across diverse urban systems.
To analyze ethnic segregation in US and UK metropolitan areas and its association with socioeconomic factors.

Main Methods:

Utilizing the statistics of random walk trajectories on graphs representing spatial systems.
Developing non-parametric measures based on diffusion on graphs to quantify spatial diversity.
Applying these measures to analyze ethnic segregation patterns in metropolitan areas.

Main Results:

The proposed measures provide consistent estimations of segregation in synthetic and real spatial patterns.
Ethnic segregation in US and UK metropolitan areas was analyzed using graph diffusion.
Spatial diversity measures showed strong associations with socioeconomic deprivation.

Conclusions:

The novel graph-based diffusion measures offer a robust and comparable method for assessing spatial segregation.
These measures overcome limitations of traditional methods, allowing for analysis across urban areas of varying characteristics.
The findings highlight a significant link between ethnic segregation, spatial diversity, and socioeconomic deprivation in urban environments.