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Cramer’s V

 

Cramer’s V. A correlation coefficient that may be used with nominal data. It is often included with chi-square test reports.


More details about Cramer's V.

Cramér's V is a measure of association for categorical data, particularly useful when examining the strength of the relationship between two nominal variables. It provides a value between 0 (no association) and 1 (perfect association), making it an excellent follow-up measure after conducting a Chi-Square test. Here's the formula:

V = √(χ² / (n × min(k - 1, r - 1)))

Where:

  • χ² is the Chi-Square statistic.

  • n is the total number of observations.

  • k is the number of categories in one variable.

  • r is the number of categories in the other variable.

Example: Preferences for Therapy Types and Age Groups

Imagine a psychology researcher is studying whether preferences for therapy (e.g., Cognitive Behavioral Therapy (CBT), Group Therapy, Art Therapy) are associated with age groups (Youth, Adults, Elderly). The observed data is:

Age GroupCBTGroup TherapyArt TherapyTotal
Youth20151045
Adults30252075
Elderly1015530
Total605535150

Suppose the Chi-Square statistic (χ²) for this data is 10.5.

Step 1: Plug Values Into the Formula

We know:

  • χ² = 10.5 (calculated from the Chi-Square test).

  • n = 150 (total number of observations).

  • k = 3 (categories of therapy types).

  • r = 3 (categories of age groups).

  • The smaller of k - 1 and r - 1 is 2 (min(3 - 1, 3 - 1)).

Now substitute these values: V = √(χ² / (n × min(k - 1, r - 1)))  V = √(10.5 / (150 × 2))  V = √(10.5 / 300)  V = √0.035  V ≈ 0.187

Step 2: Interpret the Result

The Cramér's V value is 0.187, which indicates a weak association between therapy preferences and age groups. While there is some relationship, it is not strong based on this analysis.

Cramér's V is particularly useful because it adjusts for the number of categories, unlike the Chi-Square value alone, providing a standardized measure of association.




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NOTICE:

The information about scales and measures is provided for clinicians and researchers based on professional publications. The links to authors, materials, and references can change. You may be able to locate details by contacting the main author of the original article or another author on the article list.


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Geoffrey W. Sutton PhD is Emeritus Professor of Psychology who publishes book and articles about clinical and social psychology including the psychology of religion. Website:     www.suttong.com

   

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