Introductory Statistics and Analytics: A Resampling Perspective

10

CORRELATION

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.

Definition: Correlation

Correlation is an association between the magnitude of one variable and that of another—for example, as x₁ increases, x₂ also increases. Or as x₁ increases, x₂ decreases. Different statistics are used to measure correlation; we will develop and define two in this chapter. ...