How to Interpret Gamma Coefficients

By Peter Flom

The gamma coefficient is a measure of the relationship between two ordinal variables. These could be continuous (such as age and weight) or discrete (such as "none," "a little," "some," "a lot"). Gamma is one kind of correlation measure, but unlike the better-known Pearson's coefficient (often labeled r), gamma is not much affected by outliers (highly unusual points, such as a 10-year-old who weighs 200 pounds). The gamma coefficient deals well with data that have many ties.

Determine if gamma is above zero, below zero or very near zero. Gamma below zero means a negative or inverse relationship; that is, as one thing goes up, the other goes down. For example, if you asked people about "agreement with Obama" and "agreement with the Tea Party," you would expect a negative relationship. Gamma above zero means a positive relationship; as one variable goes up, the other goes up, e.g., "agreement with Obama" and "likelihood of voting for Obama in 2012"). Gamma near zero means very little relationship (for instance "agreement with Obama" and "preference for a dog versus a cat").

Determine the strength of the relationship. Gamma, like other correlation coefficients, ranges from -1 to +1. -1 and +1 each indicate perfect relationships. No relationship is indicated by 0. How far from 0 gamma needs to be to be considered "strong" or "moderate" varies with the field of study.

Interpret gamma as a proportion. You can also interpret gamma as the proportion of pairs of ranks that agree in ranking out of all possible pairs. That is, if gamma = +1, it means that each person in your study agrees exactly on how he or she ranks the two variables. For example, it would mean that every person who said "agree very strongly" about Obama also said "very likely" to vote for him in 2012, and so on for each rank.

About the Author

Peter Flom is a statistician and a learning-disabled adult. He has been writing for many years and has been published in many academic journals in fields such as psychology, drug addiction, epidemiology and others. He holds a Ph.D. in psychometrics from Fordham University.