Calculating Pearson Product Moment Correlation

Correlational Analysis

Used to identify associations between 2 variables at the interval and ratio level

Pearson Product-Moment Correlation Symbol

R (the value is always in between -1.00 and +1.00 and a 0 indicates no relationship) (indicative of the slope/regression line)

Negative Correlation (Pearson Correlation)

Indicates that higher values of x are associated with lower values of y

Pearson Correlation Positive Weak Effect Size

0.00 to <0.30

Pearson Correlation Positive Moderate Effect Size

0.30 to 0.49

Pearson Correlation Positive Strong Effect Size

0.50 or greater

Pearson Correlation Negative Weak Effect Size

0.00 to < -0.30

Pearson Correlation Negative Moderate Effect Size

-0.49 to -0.30

Pearson Correlation Negative Strong Effect Size

-1.00 to -0.50

Variables for Pearson Correlation

Attributional (characteristics of the participant), must be measured as continuous at the interval/ratio level 

Pearson Correlation Assumptions

Interval or ratio level data, at least one normally distributed variable, independent observation, homoscedasticity 

Homoscedasticity

Evenly dispersed both above and below the regression line (indicates a linear relationship) and reflect equal variance of both variables

Pearson Correlation Formula

R = (Sample Size) (xy) - (x) (y) ÷ √[sample size (x²) - (x)²][(sample size) (y²) - (y)²]

After establishing the statistical significance of r, we must now determine

Clinical Importance

Coefficient of Determination

(R²) x 100%

What does coefficient of determination represent?

Percentage of variance shared between the 2 variables