Correlation coefficient r: what it means and how to read it
In the report: r — The correlation coefficient: the strength and direction of the relation, from −1 to 1. Empty when a column has no spread or there are fewer than 2 common rows.
How to read it
How closely two things go together: 0 — no linear relation (a curved one can still exist), 1 — they rise together perfectly along a straight line, −1 — one falls exactly as the other rises. A common guide (Cohen): 0.1 small, 0.3 medium, 0.5 large.
Correlation is not causation: r says that the two go together, not that one causes the other.
In a paper: r(48) = .15, p = .293 — the number in brackets is df.
In plain words
A teacher wondered whether students who sleep more get higher marks. She counted r for 50 students and got 0.5. Zero would mean no straight-line link, and 1 that the 50 students line up perfectly, more sleep always with higher marks. With her 0.5, pick two students at random: the one who slept more also got the higher mark in about 67 pairs out of 100, against 50 for a coin, so many pairs still go the other way. Reports call this a large link. A minus sign would mean the other way, more sleep with lower marks. The number only shows what goes together, not why, and a curved link can hide behind a zero.
Example
The cell with r is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- —
=STATS_PEARSON(Data!A1:T51, "x,y,x1",0.95,"two-sided") - — Returns correlation matrix
=STATS_SPEARMAN(Data!A1:T51, "q1,q2,q3",0.95,"two-sided") - — a matrix, two controls
=STATS_PARTIAL(Data!A1:T51, "x,x1,x2", "age,score")
Where you see it
STATS_PEARSON— Pearson correlation (r).STATS_SPEARMAN— Spearman rank correlation (rho): the correlation for rating scales, ranks and skewed data — does one go up as the other goes up?STATS_PARTIAL— Partial correlation: the Pearson correlation of two variables with the controls held constant (SPSS PARTIAL CORR). Two variables give one correlation, three or more a matrix, as STATS_PEARSON.STATS_ANALYZE— Runs several analyses on one range and returns one report.
Related values
- Kendall’s tau-b — Kendall’s tau-b: pairs of rows ordered the same way in both columns minus pairs ordered the opposite way, over the pairs not tied, from −1 to 1. Empty when a column has no spread or there are fewer than 2 common rows.
- Partial correlation — The correlation of the two columns with the controls held constant: of what is left of both after the linear effect of the controls is removed. Empty when a control is constant or repeats another, or when there are fewer than k + 3 complete rows (k — the number of controls).
- Cohen's d — The effect size: the difference in standard deviations, so it does not depend on the units of the data. Empty when there is no spread.
- Phi — The strength of the relation, from the chi-square: for a 2 × 2 table with the sign of the relation (the sign depends on the order of the categories), for a larger table it equals the square root of χ² / N.
- Cramér's V — The strength of the relation of two categorical variables, from 0 (none) to 1 (one determines the other).
Get it in your sheet
One formula in a cell gives the whole report, Correlation coefficient r included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)