Six Sigma and Beyond: Statistics and Probability, Volume III

Here is a list of the possible tests (most of which have been discussed in this chapter) used on the STATISTICS subcommand used with the CROSSTABS command:

• Chi-square

• Phi for 2 — 2 tables,

• Cramer's V for larger tables

• Contingency coefficient

• Lambda

• Uncertainty coefficient

  • Kendall's tau-b

  • Kendall's tau-c

  • Gamma

  • Somers' d

  • Eta

  • Pearson's r

How can you measure the strength of the relationship between categorical variables ? Here is a summary of the things that you need to know:

• Many measures of association can be used to measure the strength of the relationship between two categorical variables.

• Measures of association differ in the way they define association.

• You should select a measure to use based on the characteristics of the data and how you want to define association.

• The chi-square statistic is not a good measure of association. Its value does not tell you anything about the strength of the relationship between two variables.

• Measures of proportional reduction in error (PRE) compare the error you make when you predict values of one variable based on values of another with the error when you predict them without information about the other variable.

• Special measures of association are available for ordinal variables. They are based on counting the number of concordant pairs (as one variable increases, so does the other) and the number of discordant pairs (as one variable increases , the other decreases).