Title: Proportional Reduction of Error (PRE) Measures of Association in Tables
Course: UGQuants (SSPS) > Section: Association for Nominal and Ordinal Variables

Proportional Reduction of Error (PRE) Measures of Association in Tables

Both Chi and Yule’s Q produce measures of association by measuring the distance between what we would expect to have if no relationship exists between our variables and the values we can actually observe in our data.  These are different from proportional reduction of error (PRE) coefficients.  PRE measures examine the improvement in predicting values of our dependent variable if we have knowledge of an independent variable.  PRE measures give us a sense of the strength of the relationship between our independent and dependent variable by examining the extent to which one (the Independent Variable, or 'IV') is a predictor of the other (the Dependent Variable, or 'DV'). If the independent variable is a good predictor, then the PRE measure indicates that there is a strong relationship. If the IV is a weak predictor, the PRE measure tells us that there is a weak relationship.

PRE measures are calculated as a fraction, ranging from 0 to 1.  Fundamentally all PRE measures follow the same basic steps:

1 | Identify the mode of the dependent variable
2 | Assume that the mode is correct all of the time
3 | Calculate how often you’d be wrong if you assumed that the mode occurred all the time
4 | For each category of the IV identify the mode for the DV
5 | Calculate how often you’d be wrong if you assumed that the DV mode for each category of the IV occurred all the time (eg WRONG category 1, WRONG category 2, WRONG category 3 etc)
6 | Add all of these category wrongs together to produce a measure of errors predicting the DV WITH knowledge of the IV
7 | Calculate with the appropriate formula

Of course different statistical tests calculate PRE slightly differently.  Three common ones are Lambda, Tau and Gamma.