Pearson

Definition

Pearson correlation coefficient, often denoted as $r$, measures the linear relationship between two variables. Its value ranges from -1 to 1, indicating the strength and direction of the correlation.

5 Must Know Facts For Your Next Test

1. The Pearson correlation coefficient is calculated using the formula: $$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}$$
2. A Pearson correlation of 1 indicates a perfect positive linear relationship, while -1 indicates a perfect negative linear relationship.
3. A Pearson correlation close to 0 suggests no linear relationship between the variables.
4. Pearson's $r$ assumes that both variables are normally distributed and have a linear relationship.
5. The significance of Pearson's $r$ can be tested using a t-test to determine if the observed correlation is significantly different from zero.

Review Questions

• What does a Pearson correlation coefficient tell you about two variables?
• How do you interpret a Pearson correlation coefficient of -0.8?
• What assumptions must be met for the Pearson correlation coefficient to be valid?

Related terms

Spearman's Rank Correlation: A non-parametric measure of rank correlation that assesses how well the relationship between two variables can be described using a monotonic function.

Linear Regression: A statistical method for modeling the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.

Covariance: A measure of how much two random variables change together, indicating whether an increase in one variable corresponds to an increase or decrease in another.