When you hear the term Test of Association in statistics, it usually means the Chi-Square Test. However, it’s used in an informal sense to mean many things. Loosely speaking, any time you’re trying to find out if two variables are linked in some way, you’re testing for association. Depending on the context, you could be using a diagram (like a scatter plot) to show an association between variables or using a hypothesis test to demonstrate statistically that relationships exist between variables.
A bivariate association test involves one independent variable and one dependent variable. Multivariate association tests involve more than two variables.
Test Vs. Measure of Association
Typically, a Measure of Association quantifies the relationship between two groups. A Test takes this a step further and assigns statistical significance to your results. What can get a little confusing is that some authors will lump all tests and measures in the same theoretical basket (calling them all “tests”). There is a subtle difference between the two (a test is a bit more rigorous than a measure), but for practical purposes you probably won’t be aware of a difference.
Common Measures of Association
The relative risk or odds ratio can show how strong the association is between risk factors and traits. These are not hypothesis tests though, so you won’t know if your results are statistically significant.
Common Tests for Association
- The chi square test for association (also called the chi-square test for independence) is used to find a relationship between two categorical variables. As well as association, the test can be used to demonstrate non-association as well.
- The Cochran-Mantel-Haenszel (CMH) Test studies data from different sources, or from stratified data from one source.
- Fisher’s Exact Test is used as an alternative to chi-square when you have a small sample size.
- The gamma coefficient tells us how closely two pairs of data points “match”. As well as testing for an association between points, it indicates how strong the relationship is.
- Goodman Kruska’s Gamma is a test for ranked variables.
References
Gonzalez-Chica, D. et al. (2015). Test of association: which one is the most appropriate for my study? An Bras Dermatol.Jul-Aug; 90(4): 523–528.
Liu, J. et a;. (2015). Practical Approaches to Causal Relationship Exploration. Springer.
Statistical Tests of Association. Retrieved March 2, 2019 from: http://hihg.med.miami.edu/code/http/modules/education/Design/CoursePageContent.asp?ID=188