Skip to main content

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.




Creating Surveys on AMAZON    or   GOOGLE  Worldwide










Resource Links: 

All Measures A – Z Test Index

Spirituality Measures A - Z

Statistical Concepts A - Z

See Chi Square


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.


Post Author


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

   

Books available on   AMAZON       and the   GOOGLE STORE

 

Connections

   FACEBOOK   Geoff W. Sutton  

  

   X  @Geoff.W.Sutton

 

   PINTEREST  www.pinterest.com/GeoffWSutton

 

Read many published articles and book samples on:

 

 

 

  ResearchGate   Geoffrey W Sutton 

  Academia   Geoff W Sutton   

 





Labels:

Comments

Post a Comment

Popular posts from this blog

Academic Self-Efficacy Scale ASE

  Overview The  Academic Self-Efficacy Scale is an application of Self-Efficacy Theory   to examine the relationship between self-efficacy and academic performance using 8-items rated on a 7-point scale. The work of Chemers et al. (2001) has been widely cited. Format The 8-items are rated on a 7-point Likert-type scale ranging from 1 = Very Untrue to 7 = Very True. Sample Items 2. I know how to take notes. 6. I usually do very well in school and at academic tasks.   Reliability, Validity, and Other Research notes In the article describing the development and use of the ASE, the authors observed: “As predicted, academic self-efficacy was significantly and directly related to academic expectations and academic performance.” (Chemers et al., 2001, p. 61)   Sutton et al. (2011) reported Cronbach's alpha of .83 in their study of academic self-esteem and personal strengths. ASE was highly positively correlated with ACT scores (.24) and GPA (.39)....
Post a Comment
Read more

Rotterdam Emotional Intelligence Scale (REIS)

  Scale name: Rotterdam Emotional Intelligence Scale (REIS) Scales overview : The Rotterdam Emotional Intelligence Scale (REIS) is a 28-item measure of emotional intelligence having four subscales. Authors: Pekaar, Keri A., Bakker, Arnold B., van der Linden, Dimitri, & Born, Marise Ph. Response Type: All items are rated on a 5-point Likert type scale ranging from 1 (totally disagree to 5 (totally agree). Subscales = 4   Following are the four subscales with a sample item. Self-focused emotion appraisal( 1. I always know how I feel.) Other-focused emotion appraisal ( 8. I am aware of the emotions of the people around me.) Self-focused emotion regulation ( 15. I am in control of my own emotions.) Other-focused emotion regulation ( 22. I can make someone else feel differently.)   Reliability and Validity “The results indicate that the REIS follows a four-factorial structure and can be reliably measured with 28 items. The REIS was strongly correl...
Post a Comment
Read more

Spiritual Bypass Scale (SBS-13)

  Assessment name:   Spiritual Bypass Scale-13 (SBS-13) Scale overview: To assess the observed spiritual bypassing phenomenon, Fox et al. (2017) developed the 13 item Spiritual Bypass Scale . Authors: Fox, Cashwell, and Picciotto    [ Read more about Spiritual Bypassing in Psychotherapy] Response Type: The 13 items are rated on a four-point scale of agreement. Scale items Data analyses from two ethnically diverse US adult samples supported two factors (Psychological Avoidance, PA; Spiritualizing, SP). PA example: When I am in pain, I believe God will deliver me from it SP example: When someone I know is in trouble, I believe it is because they have done something wrong spiritually.   Psychometric properties Cronbach’salphas: Total scale = .85, PA = .82; Sp = .75. The total SBS score was associated with the ASPIRES subscales except for connectedness. PA was associated with depression and SP with stress and anxiety (DASS-21). The over...
Post a Comment
Read more