Correlation analysis quantifies the degree to which two variables vary together. If two variables are independent, then the *value* of one variable has no relationship to the *value* of the other variable. If they are correlated, then the *value* of one is related to the *value* of the other. Figure 5.1 illustrates this relationship. For example, when an increase in one variable corresponds to an increase in the other, a positive correlation results. However, when an increase in one variable leads to a decrease in the other, a negative correlation results.

A commonly used correlation measure is Pearson’s r. Pearson’s r has the following characteristics:

**Non-unit tied:**allows for comparisons between variables measured using different units**Strength of the relationship:**assesses the strength of the relationship between the variables**Direction of the relationship:**provides an indication of the direction of that relationship**Statistical measure:**provides a statistical measure of that relationship

Pearson’s correlation coefficient measures the *linear* association between two variables and ranges between -1.0 ≤ r ≤ 1.0.

When ** r is near -1.0** then there is a strong linear negative association, that is, a low value for x tends to imply a high value for y.

When

**r = 0**, there is no linear association, There may be an association, just not a linear one.

When

**then there is a strong positive linear association, that is, a low value of x tends to imply a low value for y.**

*r*is near +1.0Remember that just because you can compute a **correlation** between two variables, it does **NOT** necessarily imply that one **causes** the other. Social/demographic data (e.g., census data) are usually correlated with each other at some level.

### Try This!

For fun: try and guess the correlation value using this correlation applet.

Interactively build a scatterplot and control the number of points and the correlation coefficient value.