Correlation

Purpose:

A correlation measures the strength and direction of the linear relationship between two continuous variables. It does not imply that one variable causes the other.

Context Used:

  • There must be TWO CONTINUOUS variables.
  • There is no distinction between IV and DV — correlation is symmetric.
If variables are ordinal or the relationship is non-linear, use Spearman's rho instead of Pearson's r.
Do NOT use correlation if: You want to predict one variable from another → use regression | Your variables are categorical → use chi-square | You have more than two variables to examine → consider multiple regression or factor analysis

Assumptions:

  • Continuous variables: Both variables must be measured on a continuous scale.
  • Linearity: The relationship between the two variables should follow a straight-line pattern. Check with a scatterplot.
  • No extreme outliers: Outliers can heavily distort Pearson's r.
  • Normality: Both variables should be approximately normally distributed for significance testing to be accurate.

Jamovi Walkthrough:

  1. Click "Regression"
  2. Click "Correlation Matrix"
  3. Move both variables into the box on the right
  4. Check "Pearson" under "Correlation Coefficients"
  5. Check "Report significance" and "Confidence intervals"
  6. Check "Correlation matrix plot" under "Plot" for a visual

R Walkthrough:

cor.test(df$variable1, df$variable2)

corr.test(df[, c("var1", "var2", "var3")])   # psych package: gives r, p, n

Output Interpretation:

Pearson's r: Ranges from −1.00 to +1.00. The sign indicates direction; the absolute value indicates strength.

|r|Strength
.00 – .09Negligible
.10 – .29Small
.30 – .49Medium
≥ .50Large
  • Positive r: as one variable increases, the other increases.
  • Negative r: as one variable increases, the other decreases.

p-value:

  • If p < .05 → there IS a significant association between the two variables.
  • If p > .05 → there is NO significant association.

df: For correlation, df = N − 2. Report in parentheses after r: e.g., r(38) = .34 means N = 40.

APA Format:

Appropriate data visualization: Scatterplot with line of best fit.

Sample write-up:

A Pearson correlation examined the relationship between [Variable 1] and [Variable 2]. There was a statistically significant [positive/negative] association, r() = , p = , 95% CI [, ]. These results suggest that as [Variable 1] increases, [Variable 2] [increases/decreases].

Note: Report r, df in parentheses, p-value, and 95% CI.

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