Correlation - Statistics Study Guide

Understanding Correlation

**Correlation** measures the strength and direction of the relationship between two variables. A positive correlation means that as one variable increases, the other also increases. A negative correlation means that as one variable increases, the other decreases.

Types of Correlation

There are three types of correlation:

  • Positive Correlation: When both variables move in the same direction.
  • Negative Correlation: When the variables move in opposite directions.
  • No Correlation: When there is no discernible relationship between the variables.

Example: Positive Correlation

Example 1: There is a positive correlation between the number of hours studied and the grades received on a test. As the number of hours studied increases, the test score tends to increase as well.

As hours studied → increases, grade → increases (positive correlation).

Example: Negative Correlation

Example 2: There is a negative correlation between the number of hours spent watching TV and the grades received on a test. As the number of hours spent watching TV increases, the test score tends to decrease.

As hours watching TV → increases, grade → decreases (negative correlation).

Example: No Correlation

Example 3: There is no correlation between a person’s shoe size and their test scores. A person’s shoe size has no impact on their performance on a test.

As shoe size → increases, grade → does not change (no correlation).

Try It Yourself:

Identify the type of correlation based on the following example:

As the amount of rainfall increases, the number of people visiting the beach decreases.

Hint: Think about whether the two variables are moving in the same direction (positive), opposite directions (negative), or if there's no relationship at all (no correlation).