Correlation

Purpose:

A measure of association, or change in relation to one another. Or, how closely a data fits a straight line. There are two big limitations: (1) you can NOT infer causality, and (2) it is only for linear relationships.

Note: Correlation ≠ causation due to a likelihood of a spurious relationship (association without causation). This could be due to coincidence, directionality problem/reverse causality, and the third variable problem.

Context used:

• There must TWO CONTINUOUS variables

• No IV, No DV. Just 2 variables: Var1, Var2

Jamovi Walkthrough:

1. Click "Regression"

2. Click "Correlation Matrix"

3. Enter Var1 and Var2 into the box on the right

4. Check "Person" under "Correlation Coefficients"

5. Check "Report significance" under "Additional Options"

6. Check "Flag significant correlations" under "Additional Options"

Output Interpretation:

Person's r:  Both a test statistic (direction) and measure of effect size (magnitude). (Note: In the social sciences, it is impossible to get a correlation as high as 1.0 due to human behavior. Instead, a magnitude closer to .4 is excellent!). 

If r is closer to 0, there is a WEAK correlation magnitude.

If r is closer to 1, there is a STRONG correlation magnitude. 

If r is positive, there is a POSITIVE correlation direction (both variables move together in the same direction).

If r is negative, there is a NEGATIVE correlation direction (the variables move in opposite directions).

p-value: The probability you detect a meaningful relationship/difference when there is none. We are typically looking for a small value (p < 0.5).

If p < 0.5, reject the null hypothesis. There IS a difference.

If p > 0.5, accept the null hypothesis. There is NO difference.

df: Values in a study that have the freedom to vary and are essential for assessing the importance and validity of the null hypothesis.

APA Format:

Appropriate data visualization: Scatterplots

Sample table: https://apastyle.apa.org/style-grammar-guidelines/tables-figures/sample-tables#correlation

Sample write-up:

IQ and GPA were found to be moderately positively correlated, r(38)= .34, p=.032

Note: plugin the variables, magnitude, direction, df, Person's r, and p-value.

Want to make correlation FUN?

Visit https://www.guessthecorrelation.com/ to test your person's r prediction skills.

Visit https://www.tylervigen.com/spurious-correlations to laugh at some examples of spurious correlation.