Question

1.Understand how to interpret values, such as lambda, gamma, etc.

2.When is Phi appropriate?

3.When Cramer’s V appropriate?

4.What values can phi take on?

5.What if the table is larger than 2x2?

Answer 1

(1)

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 continuous variables. Like Gamma, Pearson’s r ranges from -1.00 to 1.00.

If you have differing levels of measures, 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.

It is easy to calculate lambda and gamma using SPSS. Go to Analyze, Descriptive Statistics, Crosstabs. Enter your dependent variable in the “row “and the independent variable in the “column” box. Using the GSS 2008 (1500 cases) database, we can test for the association of the independent variable “SEX” and the dependent variable “Happy”.

(5)

The only problem with applying Fisher's exact test to tables larger than 2x2 is that the calculations become much more difficult to do. The 2x2 version is the only one which is even feasible by hand, and so I doubt that Fisher ever imagined the test in larger tables because the computations would have been beyond anything he would have envisaged.

Nevertheless, the test can be applied to any mxn table and some software including Stata and SPSS provide the facility. Even so, the calculation is often approximated using a Monte Carlo approach.

Yes, if the expected cell counts are small, it is better to use an exact test as the chi-squared test is no longer a good approximation in such cases.

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