How are several numbers related? (correlation matrix)

In brief

Three or more number columns, and the question is how each is related to each other one (for example study time, motivation, sleep and grade). Statable calculates all pairs at once and shows them as a matrix: the correlation in the lower triangle, followed by a table with n, p and 95% confidence interval per pair. For exactly two columns, "Are two things related?" is the right route (with scatter plot and controlling for a third number).

Pearson or Spearman

One type applies to the whole matrix. Statable suggests Spearman as soon as a column is ordinal or has at most 7 distinct values (for example Likert answers), otherwise Pearson - as for a single correlation. The switch in the result changes the type for all pairs.

Many pairs: Holm correction

Five columns give 10 pairs, ten columns 45. Even without any real relationship, one easily falls below .05 by chance. The switch "Holm-adjust the p values" adjusts the p values for the number of pairs (as R p.adjust). It is off by default, as in SPSS. If you had a specific question about one pair beforehand, you can report that pair without correction; if you are searching the matrix for relationships, turn Holm on.

Missing values

Each pair uses everyone who has answers in both columns (pairwise deletion, as in SPSS and PSPP). So n can differ from pair to pair; the table states it.

Reading the result

• The matrix is numbered: row 3, column 1 is the relationship of the third with the first column. The upper triangle stays empty because it would repeat the same.
• Rule of thumb for |r|: from .1 weak, from .3 moderate, from .5 strong.
• The sentence states how many pairs are clear, and the strongest and weakest pair. The line for your paper names the three strongest pairs; a paper usually shows the matrix as a table.
• Statable puts no stars on the values: p is given per pair in the table.

mpg - wt: r(30) = −.87, p < .001; mpg - hp: r(30) = −.78, p < .001; wt - drat: r(30) = −.71, p < .001

For specialists

Statable calculates itself: Pearson with p via t (n − 2 degrees of freedom) and CI via Fisher z, Spearman with p via t (as R cor.test(exact = FALSE)), Holm as p.adjust; checked against R. PSPP gives the Pearson values (CORRELATIONS /MISSING=PAIRWISE) for comparison.