## What is the Proportional Reduction in Error (PRE Test)?

The **Proportional Reduction in Error (PRE Test)** is a statistical criterion which quantifies the extent that knowledge about one variable can help us predict another variable.

That is to say, it helps you understand to what degree knowing a variable x can help you to predict another variable y. If there is zero relationship between the variables, knowing x will not help you to predict y. And if there is a perfect correlation, knowing x will allow you to predict y with 100% confidence.

## Example

Let’s say you wanted to know something about individual’s final test scores in a math class. If you know an individual’s height (x), this would tell you nothing about their final test score. A better prediction could be to just use the class mean to predict an individual’s score, but this could come with a very large error, depending on how widely the class scores varied. Knowing how many hours a person studied, or what their previous test scores are, could certainly help you make a better prediction. The better the correlation between the variables (e.g. previous test scores might be a better indicator than hours studied), the greater the proportional reduction in error.

## PRE Values

The better the prediction, the less error there is in that prediction. A PRE statistic takes values between 0 and 1.

- 0 means no reduction in error,
- 1 means that there is perfect prediction—the error is completely eliminated.

Anywhere in between tells you how much error is eliminated. For example, if your independent variable has a PRE of .5, then you have a 50% reduction in error for predicting the dependent variable.

A general rule of thumb:

- 0 to 0.1 is considered weak,
- 0.1 to 0.4 moderate,
- 0.4+ is considered strong.

Not all statistical techniques have PRE interpretations. Two common tests that do are Pearson’s r and the Gamma coefficient (Bailey, 1994).

## Chi-Squared vs. PRE

Measures of association can be grouped into two types: chi-squared, or PRE. Chi-squared based measures of association like phi or V are considered weak and outdated (Bailey, 1994; Hanneman & Kposowa, 2012). This is mostly because of the vague results these measures supply: associations are “weak”, “moderate”, or “strong” and are not easily interpreted by non-statisticians. In addition, the numerical result doesn’t have much meaning to the layperson. For example, an association of .6 is not twice as strong as .3, so it can be difficult to compare results. On the other hand, the numbers given by a proportional reduction in error method do have that exact meaning: an association of .6 is exactly twice as strong as on with .3. This makes it the preferable method, especially in the social sciences, for reporting results for measures of association.

## References

Bailey, K. (1994). Methods of Social Research, 4th Edition.

Hanneman, R. & Kposowa, A. (2012). A. Basic Statistics for Social Research 1st Edition. Jossey-Bass.

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