m38 problem set STATISTICS

5 Bivariate Analysis: Measures of Association

Measures of Association

You can look at the totals and determine something about the relationship between the two variables. However, if your variables have multiple categories, it becomes challenging to simply understand associations between variables by simply examining percentages via crosstabs. SPSS makes additional analyses very simple. You should consider two factors:

· Measures of association - Is there an association? How strong/weak is the association? What direction?

· Statistical significance - Does the association that occurs between two variables in the sample actually occur in the population or is it due to chance or sampling error?

There are two directions of information: direct and indirect. For example, most people assume that there is a direct relationship between the amount of time spent studying and GPA. This is a positive relationship. If you your study time ↑, your GPA↑. There is frequently an indirect relationship between party time and GPA: as your party time ↑, your GPA ↓. This is a negative association. If you are examining ordinal or scale variables, you can determine the direction of association. If you are examining nominal variables, you can only determine if there is an association, not any direction of that association.

How do you Measure Association?

Lambda is a measure of association for nominal variables. Lambda ranges from 0.00 to 1.00. A lambda of 0.00 reflects no association between variables (perhaps you wondered if there is a relationship between a respondent having a dog as a child and his/her grade point average). A Lambda of 1.00 is a perfect association (perhaps you questioned the relationship between gender and pregnancy). Lambda does not give you a direction of association: it simply suggests an association between two variables and its strength.

Gamma is a measure of association for ordinal variables. Gamma ranges from -1.00 to 1.00. Again, a Gamma of 0.00 reflects no association; a Gamma of 1.00 reflects a positive perfect relationship between variables; a Gamma of -1.00 reflects a negative perfect relationship between those variables.

Pearson’s r is a measure of association for scale (interval/ratio) variables. Like Gamma, Pearson’s r ranges from -1.00 to 1.00.

Which do I use if I am examining different levels of measurement?

Always use the measure of association of the lowest level of measurement. For example, if you are analyzing a nominal and ordinal variable, use lambda. If you are examining an ordinal and scale pair, use gamma.

What do these values mean?

Here are guidelines for interpreting the strength of association for Lambda, Gamma and Pearson’s r:

Strength of Association	Value (of Lamda, Gamma, Pearson's r)
None	0.00
Weak, uninteresting association	+ .01 - .09
Moderate, worth noting	+ .10 - .29
Evidence of strong association, extremely interesting	+ .30 - .99
Perfect association, strongest possible	+ 1.00