Which method should I use?

Recommendations for: test the strength of association or correlation between two variables

1. Robust CorrelationStatistics

   Robust Correlation is a family of association measures that resist outliers, covering Spearman's rank correlation, Kendall's tau, and the biweight midcorrelation. Drawing on the robust-statistics tradition described by Wilcox (2012) and Shevlyakov & Oja (2016), it measures how strongly two variables move together without being distorted by a few extreme points.

2. Cramer's VStatistics

   Cramer's V is a nonparametric effect-size statistic that measures the strength of association between two categorical variables on a scale from 0 to 1. Introduced by the Swedish mathematician Harald Cramér in his 1946 work Mathematical Methods of Statistics, it generalises the phi coefficient to tables of any size, making it the standard companion statistic to the chi-square test.

3. Spearman CorrelationStatistics

   The Spearman rank correlation coefficient (ρ) is a nonparametric measure of the monotonic association between two variables. Introduced by Charles Spearman in 1904, it converts raw observations to ranks and measures how consistently one variable increases as the other increases, without assuming a normal distribution or a linear relationship.

4. Kendall Tau CorrelationStatistics

   Kendall Tau is a nonparametric rank correlation coefficient introduced by Maurice G. Kendall in 1938 to measure the strength and direction of a monotone association between two ordinal or continuous variables. It is particularly suited to small samples and datasets containing many tied ranks, where the Spearman coefficient can be less stable.

5. Chi-square goodness-of-fit testStatistics

   The chi-square test of independence is a nonparametric hypothesis test that determines whether two categorical variables are statistically associated or independent of one another. Introduced by Karl Pearson in 1900, it remains the standard procedure for analysing contingency tables and requires no assumption of normality — only that observations are independent and that expected cell frequencies are sufficiently large.

6. Chi-square testStatistics

   The chi-square test of independence is a nonparametric hypothesis test that examines whether two categorical variables are associated by comparing observed and expected frequencies in a cross-tabulation. It rests on the chi-square criterion introduced by Karl Pearson in 1900.