Ever wonder what claims like "**social support is associated with greater levels of happiness**", or "**exercise is related to mental wellness**" really mean?

In order to make sense of these claims, you'll need to first understand the concept of **statistical correlation**.

## What is statistical correlation?

**Statistical correlation **indicates the **size **and **direction** of a relationship between two or more **variables**.

It describes how much two variables are **linearly related** — if you can draw a straight line when explaining the relationship on a graph, then the two variables have a linear relationship.

Information from a correlation** can help you predict, to some level of accuracy**, one variable if you have the value of the other.

Correlations can be

**positive**or**negative**.They can also be

**strong**or**weak**.

### For example:

Joyce, a statistician, has found that **variable 1** (height) and **variable 2** (weight) are positively correlated. If Joyce knows the correlational relationship between height and weight, she can use this information to predict, with **some** accuracy, someone's height if she knows their weight.

## What is correlation NOT?

It's important to understand what correlation **is**, but it is just as important to understand what correlation is **not**.

**Understanding a correlation doesn't mean you can predict something with 100% accuracy!**

In the previous example, Joyce couldn't predict with 100% accuracy that someone 5 foot 2 inches would weigh 115 pounds. She could, however, use correlation and the understanding of the relationship of the two variables to predict **close** to the correct weight, **some of the time.**

The accuracy of your prediction is based on how** strong** the correlation is.

## What is Causation?

Causation refers to a cause-and-effect relationship. It means that one thing led to —* or directly caused *— the other. Think of pushing a glass off of a table: your push *caused* the glass to fall — it was directly related.

A common error is thinking that if two variables are correlated, it means that one causes the other — this isn't necessarily true!

Take for example heating costs and ice skate sales. These two things could be positively correlated — when heating costs go up, so do skate sales — but heating costs don't *cause *ice skate sales to increase. In fact, in this example, a **third variable** like outside temperature likely impacted both.

## What does a positive correlation mean?

A **positive correlation** means that **as one variable increases**, the **other variable increases as well**. Both are moving in the same direction.

### Example 1:

**Number of years of education **and **mid-life income level**: the more years of education you have, the higher your salary is likely to be in the middle of your life.

### Example 2:

**Hours spent lifting weights **and general **strength**: the more hours you spend lifting weights, the more your strength will likely increase.

## ⚡Knowledge Check!

Albert recently read an article that ice cream sales are correlated with sunburns.

#### Quiz

Does this mean that ice cream causes people to burn?

## What does a negative correlation mean?

A **negative correlation** is a relationship where two variables tend to be associated in opposite directions with one another. As one variable goes down, the other goes up (and vice versa).

### Example 1:

**Hours of sleep** and **irritability**. As hours of sleep go down, irritability tends to go up.

### Example 2:

As **number of hours of TV watched **goes up, **grade point average** in students tends to go down.

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## This Byte has been authored by

### Robin H

Volunteer Learning Designer