Think back to the “no fault” study of errors in hospitals. In an experiment, we found that introducing a no-fault reporting system reduced the number of serious errors. We found that there was a relationship between one variable—the type of reporting system—and another variable—a reduction in errors.

The “type of reporting system” is a binary variable. It has just two values: “regular” and “no-fault.”

Often, you may want to determine whether there is a relationship involving the *amount* of something, not just whether it is “on” or “off.”

For example, is there a relationship between employee training and productivity? Training is expensive, and organizations need to know not simply *whether* training helps but also *how much* it helps.

After completing this chapter, you will be able to:

- explain how the vector product sum measures correlation,
- use a resampled vector product sum to test the statistical significance of a measured correlation,
- explain the useful properties of the correlation coefficient, and how it is a standardized version of the vector product sum,
- perform a resampling test of the correlation coefficient,
- state some limitations and cautions when measuring correlation.

Correlation is an association between the magnitude of one variable and that of another—for example, as *x*_{1} increases, *x*_{2} also increases. Or as *x*_{1} increases, *x*_{2} decreases. Different statistics are used to measure correlation; we will develop and define two in this chapter. ...

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