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Related Concept Videos

Correlation01:09

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In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
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Friedman Two-way Analysis of Variance by Ranks01:21

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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...
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Coefficient of Correlation01:12

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The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
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In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a...
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Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
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The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable, x, and the dependent variable, y. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:
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An inequality for correlations in unidimensional monotone latent variable models for binary variables.

Jules L Ellis1

  • 1School of Psychology and Artificial Intelligence, Radboud University Nijmegen, P.O. Box 9104, 6500 HE, Nijmegen, The Netherlands, j.ellis@psych.ru.nl.

Psychometrika
|March 25, 2014
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Summary

A new model for binary items shows that the negative logarithm of correlations must satisfy a triangle inequality. This finding provides bounds for item correlations and is useful for scale analysis.

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Area of Science:

  • Psychometrics
  • Statistical Modeling

Background:

  • Unidimensional monotone latent variable models are used for analyzing binary data.
  • Assessing the quality of scales requires understanding item interrelationships.

Purpose of the Study:

  • To identify a novel mathematical restriction implied by unidimensional monotone latent variable models for binary items.
  • To explore the implications of this restriction for scale analysis.

Main Methods:

  • Mathematical derivation of a restriction on item correlations within a unidimensional monotone latent variable model.
  • Comparison of the derived restriction with existing criteria such as nonnegativity of correlations, coefficient H, and manifest monotonicity.

Main Results:

  • The negative logarithm of item correlations satisfies the triangle inequality.
  • This inequality is a necessary condition implied by the model, unlike other criteria.
  • The inequality establishes both lower and upper bounds for item correlations based on a third item.

Conclusions:

  • The triangle inequality for the negative logarithm of correlations is a key property of unidimensional monotone latent variable models.
  • This property offers a new tool for scale analysis, enhancing the assessment of scale properties within Mokken's framework.