## How do you calculate Pearson product-moment correlation?

Pearson called his equation the product moment correlation coefficient. We typically now refer to it as the Pearson’s r. The calculation is based on the concept of the Z scores; specifically, taking the mean of the Z score products from the X and Y variables….PRACTICE PROBLEM #3.

X | Y |
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4 | 6 |

1 | 3 |

### What is Pearson product-moment coefficient of correlation r?

Definition. The Pearson product-moment correlation coefficient is a measure of the linear relationship between two questions/measures/variables, X and Y. The correlation value can range from +1 to -1. A positive correlation (e.g., +0.32) means there is a positive relationship between X and Y.

#### Why do we use Pearson product-moment correlation?

Pearson’s correlation is utilized when you have two quantitative variables and you wish to see if there is a linear relationship between those variables. Your research hypothesis would represent that by stating that one score affects the other in a certain way. The correlation is affected by the size and sign of the r.

**How do you calculate Pearson r?**

Now the calculation of the Pearson R is as follows,

- r = (n (∑xy)- (∑x)(∑y))/(√ [n ∑x2-(∑x)2][n ∑y2– (∑y)2 )
- r = (6 * (13937)- (202)(409)) / (√ [6 *7280 -(202)2] * [6 * 28365- (409)2 )
- r = (6 * (13937)- (202) * (409))/(√ [6 *7280 -(202)2] * [6 * 28365- (409)2 )
- r = (83622- 82618)/(√ [43680 -40804] * [170190- 167281 )

**How do I use Pearson r?**

To use Pearson correlation, your data must meet the following requirements:

- Two or more continuous variables (i.e., interval or ratio level)
- Cases must have non-missing values on both variables.
- Linear relationship between the variables.
- Independent cases (i.e., independence of observations)
- Bivariate normality.

## What does a significant Pearson product-moment correlation coefficient r between two variables mean?

The Pearson correlation coefficient, r, can take a range of values from +1 to -1. A value of 0 indicates that there is no association between the two variables. A value greater than 0 indicates a positive association; that is, as the value of one variable increases, so does the value of the other variable.

### What does Pearson’s r tell you?

Pearson’s r is a numerical summary of the strength of the linear association between the variables. If the variables tend to go up and down together, the correlation coefficient will be positive.

#### What is a good Pearson correlation?

Calculating a Pearson correlation coefficient requires the assumption that the relationship between the two variables is linear. The relationship between two variables is generally considered strong when their r value is larger than 0.7.

**How do you describe correlation results?**

A correlation of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation. If the correlation coefficient is greater than zero, it is a positive relationship. Conversely, if the value is less than zero, it is a negative relationship.