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Related Concept Videos

Wald-Wolfowitz Runs Test I01:17

Wald-Wolfowitz Runs Test I

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...
Wald-Wolfowitz Runs Test II01:17

Wald-Wolfowitz Runs Test II

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 0s. In...
Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures from...
Ranks01:02

Ranks

Unlike parametric methods, nonparametric statistics are ideal for nominal and ordinal data, requiring fewer assumptions about the population's nature or distribution. This makes nonparametric methods easier to apply and interpret, as they do not depend on parameters like mean or standard deviation. One common approach in nonparametric analysis is to sort data according to a specific criterion. For instance, we might arrange weather data from hottest to coldest days in a month or rank cities...
Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).
Kendall's Tau Test01:16

Kendall's Tau Test

Kendall's tau test, also known as the Kendall rank coefficient test, is a nonparametric method for assessing association between two variables. This test is particularly useful for identifying significant correlations when the distributions of the sample and population are unknown. Developed in 1938 by the British statistician Sir Maurice George Kendall, the tau coefficient (denoted as τ) serves as a rank correlation coefficient, with values ranging from -1 to +1.
A τ value of +1 indicates that...

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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
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Empirical likelihood-based tests for stochastic ordering.

Hammou El Barmi1, Ian W McKeague

  • 1Department of Statistics and Computer Information Systems, Baruch College, The City University of New York, One Baruch Way, New York, NY 10010, USA.

Bernoulli : Official Journal of the Bernoulli Society for Mathematical Statistics and Probability
|July 23, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a new statistical test for stochastic ordering between distributions using empirical likelihood. The novel method shows improved power for comparing historical data, such as Roman Emperor rule lengths.

Keywords:
distribution-freenonparametric likelihood ratio testingorder restricted inference

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Area of Science:

  • Statistics
  • Probability Theory
  • Econometrics

Background:

  • Stochastic ordering is a key concept for comparing probability distributions.
  • Existing methods for testing stochastic ordering have limitations in power and applicability.
  • Empirical likelihood methods offer a non-parametric approach to statistical inference.

Purpose of the Study:

  • To develop a novel empirical likelihood-based test for stochastic ordering of univariate distributions.
  • To provide a distribution-free asymptotic null distribution for the proposed test statistic.
  • To assess the practical utility and power of the new test in historical analysis.

Main Methods:

  • Development of an empirical likelihood approach for hypothesis testing.
  • Construction of a test statistic by integrating a localized empirical likelihood statistic.
  • Asymptotic analysis to derive the null distribution in terms of Brownian bridge processes.

Main Results:

  • The proposed test statistic has a simple, distribution-free asymptotic null distribution.
  • The empirical likelihood test demonstrates substantially improved power compared to existing methods.
  • The method is successfully applied to analyze the lengths of Roman Emperor reigns.

Conclusions:

  • The empirical likelihood approach provides a powerful and flexible tool for testing stochastic ordering.
  • This method offers a significant advancement over previous statistical tests for distribution comparison.
  • The findings have implications for statistical analysis in various fields, including historical studies.