WHAT IS THE PEARSON r? | Six Sigma and Beyond: Statistics and Probability, Volume III

WHAT IS THE PEARSON r ?

The Pearson r is simply the mean of the z score products, or

To compute r you do nothing new. You convert every X-score value and every Y-score value to a z score. Then you multiply each z score of X by its z score of Y. You sum the products and divide by the number of pairs. The Pearson r then shows you the extent to which individuals have the same position on these two variables. Because you change both sets of scores to z scores, you do not have to worry that the variables are not measured on the same type of scale. In other words, you can correlate weight with height. Looking at this formula and understanding what it means helps one to understand the concept of correlation. However, using this formula to compute r is computationally a pain in the neck. Can you imagine the time and effort it would take to convert every X score and Y score to a z score? Needless to say, it makes life easier to know that other formulas have been derived from this basic definitional formula. One of the easiest to use is given below:

The terms used in this formula have the following meanings: & pound ; XY = multiply each X by its Y, then sum the results, X = sum of all X, Y ² = square the Y, then sum the results, X ² = square the X, then sum the results, Y = sum of all Y, and N = number of pairs.

The requirements for using the Pearson r are:

Relationship is linear.
Data of the population form a normal distribution curve.
Scattergram is homoscedastic.
Data are at interval level of measurement.

The procedure used for the Pearson r is:

Determine r by the formula
Determine the statistical significance of r when N is smaller than 30.
1. Refer to a Critical Value of the t value in a table.
2. Using a df of N - 2, enter table value.
3. If your r is equal to or greater than the table value found in table of t , reject the null hypothesis.
Determine the statistical significance of r when N is 30 or larger.
1. Compute z = r
2. Consult a z table.
3. Reject the null hypothesis if your z value has a probability of occurring that is equal to or less than your level of significance. For a two-tailed test double the probability shown on the table.