Are two things related? (correlation)

In brief

Two number columns are checked for whether higher values in one go together with higher values (positive sign) or lower values (negative sign) in the other. Statable preselects between Pearson, Spearman and Kendall; the switch on the page changes the type. PSPP cannot do rank correlations; Statable calculates Spearman and Kendall itself.

Which correlation Statable chooses

• Pearson (r): both columns are numbers with many distinct values. Measures the linear relationship.
• Spearman (rs): if at least one column is ordinal or has at most 7 distinct values (for example Likert answers). The rank positions are compared.
• Kendall (τb): also a rank correlation, often more reliable with many tied values and small samples. With an equally strong relationship τb is smaller than r and rs; the strength in the result sentence is converted accordingly.

The page states the reason for the preselection in one sentence; sentence, line for the paper and report follow the chosen type.

Requirements

• Pearson: both variables interval/ratio, relationship approximately linear (the scatter plot shows this); outliers can change r strongly.
• Spearman and Kendall: only a rank order is needed; captures any steadily rising or falling relationship. Outliers have less influence.
• At least 3 people with answers in both columns.

Reading the result

r, rs and τb lie between -1 and +1. Rule of thumb for |r|: from 0.1 weak, from 0.3 moderate, from 0.5 strong. The confidence interval shows how precisely the value is estimated. A relationship does not establish cause and effect.

Pearson: r(118) = .34, p < .001, 95% CI [.17, .49]

Spearman: rs(118) = .31, p < .001, 95% CI [.14, .46]

Kendall: τb = .22, p < .001, n = 120, 95% CI [.10, .33]

Typical examples

• Study time and exam grade: Pearson.
• Agreement (1 to 5) and number of semesters: Spearman.
• How are they related at the same age? See "Relationship without the influence of a third number".
• Three or more columns at once: see "How are several numbers related?" (correlation matrix).

For specialists

PSPP 2.1.3 has no command for rank correlations (NONPAR CORR); PSPP calculates Pearson.