Statistics Definitions > Correlation Coefficient Formula
Also see: Correlation Coefficient (How to Find it).
Watch the video or read the article below:
Correlation Coefficient Formula: Overview.
Correlation coefficient formulas are used to find how strong a relationship is between data. The formulas return a value between -1 and 1, where:
- 1 indicates a strong positive relationship.
- -1 indicates a strong negative relationship.
- A result of zero indicates no relationship at all.
- A correlation coefficient of 1 means that for every positive increase of 1 in one variable, there is a positive increase of 1 in the other.
- A correlation coefficient of -1 means that for every positive increase of 1 in one variable, there is a negative decrease of 1 in the other.
- Zero means that for every increase, there isn’t a positive or negative increase. The two just aren’t related.
The absolute value of the correlation coefficient gives us the relationship strength. The larger the number, the stronger the relationship. For example, |-.75| = .75, which has a stronger relationship than .65.
Like the explanation? Check out the Practically Cheating Statistics Handbook, which has hundreds of step-by-step, worked out problems!
Types of correlation coefficient formulas.
There are several types of correlation coefficient formulas.
One of the most commonly used formulas in stats is Pearson’s correlation coefficient formula. In fact, if you’re taking a basic stats class, this is the one you’ll probably use:
Two other formulas are commonly used: the sample correlation coefficient and the population correlation coefficient.
Sample correlation coefficient
Population correlation coefficient
Other similar formulas you might come across that involve correlation:
- Intraclass Correlation.
- Kendall’s Tau.
- Moran’s I.
- Partial Correlation.
- Point Biserial Correlation.
- Polychoric Correlation.
- Spearman Rank Correlation.
- Tetrachoric Correlation.
Check out my Youtube channel for more tips and help with statistics!
Correlation Formula: TI 83
If you’re taking AP Statistics, you won’t actually have to work the correlation formula by hand. You’ll use your graphing calculator. Here’s how to find r on a TI83.
Step 2: Press the STAT button.
Step 3: Scroll right to the CALC menu.
Step 4: Scroll down to 4:LinReg(ax+b), then press ENTER. The output willshow “r” at the very bottom of the list.
Tip: If you don’t see r, turn Diagnostic ON (click here for instructions), then perform the steps again.