Cramer's V measures the strength of association between categorical variables in a contingency table. It complements a chi-square test for independence: chi-square indicates whether an association is statistically significant, while Cramer's V indicates how large it is. section 9.0 section 9.7
Interpret Cramer's V as a value between 0 and 1:
- 0 indicates absolutely no association between the variables. section 9.7
- 1 indicates a strong association. section 9.7
- Values at or below 0.2 are generally considered small, around 0.5 medium, and at or above 0.8 large. section 20.3
NBA rest and wins
Ask whether the number of days off before an NBA regular-season game is associated with wins and losses. After preparing the contingency table as chisq_table and running the chi-square test, calculate the effect size in R: cramer.v(chisq_table) ## [1] 0.2359978 cramerV(chisq_table) ## Cramer V ## 0.236 Both functions return essentially the same result. The association between rest and wins or losses is statistically meaningful in the accompanying chi-square analysis, but its Cramer's V of about 0.24 indicates a small effect. The effect size supplements rather than replaces significance testing. section 9.7 section 9.8
library(tidyverse) library(sqldf) library(gtools) library(gplots) library(vcd) library(questionr) library(rcompanion)
Use questionr or rcompanion for Cramer's V; the surrounding workflow also supports contingency-table visualization with gplots and vcd. section 9.1
