Introduction

1. What is Correlation?

Continuous variables in a study can be interrelated with one another, so that they increase/decrease together, or change in opposite directions.

One way to assess the relationship between two continuous variables is correlation. It is a measure of the extent to which two variables are related to each other.

A correlation coefficient is a standardized measure of the relationship between two variables. The most commonly used correlation coefficient is the Pearson’s r. There are other types of correlation coefficients for other purposes, such as Spearman and Kendall's tau-b. In this module, we focus on Pearson’s r (or, most frequently, it's simply known as r). Pearson’s r ranges from -1.0 to +1.0.

Whenever we look at the Pearson’s r value between two variables, we look at two aspects:

• sign (positive or negative): If r > 0, it means that the two variables tend to increase or decrease together. This is known as a positive correlation, in which the two variables tend to change in the same direction. If r < 0, it means that the two variables tend to change in opposite direction. In other words, when one variable increases, the other tends to decrease, and vice versa. This is known as a negative correlation.

• magnitude (the size of the number, regardless of the sign): Values of r that are closer to +1 or -1 (i.e., of a larger magnitude) represent stronger correlation between the two variables. Conversely, values of r that are closer to 0 (i.e., a smaller magnitude) represent weaker correlation between the two variables. The strongest possible correlation is either +1 or -1. The weakest possible correlation is 0.

3. Example 2: Correlation between "PerAttract" and "NumRel"

Another example of a correlational study would be the relationship between perception of attractiveness and number of romantic relationships. Some people claimed that the number of romantic relationships may be related to how people perceive themselves, such as attractiveness. We want to know whether such relationship does exist or not.

Q: How do we test the relationship between “PerAttract” and “NumRel"?

A: We use the “Correlation Matrix” under “Regression” in jamovi.

4. Effect Size interpretation

Same as t-test and ANOVA, we can measure the effect size in correlation analysis. Indeed, we can take the size of the correlation coefficient (e.g., Pearson correlation coefficient r) as a measurement of effect size. Generally, it is used when both variables are continuous (interval or ratio scales). Theoretically, the range of r is from negative one to positive one (-1 to +1). E.g., if r = .47, it means that the variable X and variable Y have a large positive association.