.Q. 1 I have noted that there are multiple statistics listed within  the crosstabs dialogue box in SPSS, available via the menu command sequence Analyze–>Descriptive Statistics–>Crosstabs. As illustrated in the image below, these include the contingency coefficient, phi and Cramer’s V.

 

 

 

 

 

 

 

 

How can I decide which of these is the appropriate statistic to choose in any one setting?

A. The resource
NOMINAL MEASURES OF CORRELATION: PHI, THE CONTINGENCY COEFFICIENT, AND CRAMER’S V 
should serve as an accessible guide.

.Q. 2   I have noted that Somer’s d also appears in the above SPSS dialogue box. Does this statistic have a special condition for use?

A. This statistic is best used for ordinal data, including Likert scale data, where it is very clear that one variable is the dependent variable and the other the independent variable. A useful example is provided within the resource Somer’s d using SPSS Statistics, where the dependent variable is marathon running time categorized into value ranges and the independent variable is training volume, also categorized into value ranges.  The same resources also lists any other assumptions that need to be checked for legitimate use of Somer’s d. The same resource also provides helpful advice on calculating the statistic using SPSS and interpreting and reporting your corresponding findings.

.Q. 3 How, then, do Lambda and eta fit in, as these statistics are also listed?

A.  Lambda works well within a context where, for two categorical variables, it is meaningful to treat one variable as the dependent and the other as the independent variable.  Lambda serves as a measure of how well the independent variable can explain the variability in the values of the dependent variable. As such, it ranges from 0 (no contribution) to 1 (full contribution).  More details can be accessed under Nominal Variable Association and Lambda and Gamma.

For eta, it is also assumed that there is a dependent and independent variable which can easily be identified as such. However, in this case it is assumed that the dependent variable is measured on an interval scale (for example, a pain scale) and the independent variable ranges over a small number of categories (for example, usually as with type of analgesic received).  Like Lambda, eta measures how well the independent variable can explain the variability in the values of the dependent variable. As such, it also ranges from 0 (no contribution) to 1 (full contribution).

Note that for both Lamba and eta, SPSS will compute the association measure both ways round in terms of which variable is the depenent or independent variable. While this is made explicit in the SPSS output, it is up to you to select the correct choice from the two results in each case, depending on what you already know to be the correct dependent and independent variables.

 

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.Q. 4. And how about the uncertainty coefficient?

The uncertainty coefficient is of interest when measuring the degree and direction of association between two nominal variables where it is not obvious that one of these variables is the independent and the other the dependent variable.  The values of the uncertainty coefficient range from -1 (perfect, or 100%, negative association)  to 1 (perfect, or 100%, positive association), with a value of 0 indicating no association.

 

 

 

 

Measuring the degree of association between variables by Margaret MacDougall is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.