Significance of the partial correlation: what it means and how to read it

In the report: Significance — The p of the partial correlation, as SPSS names it, for the chosen alternative. Empty in the same cases as Correlation.

How to read it

Below 0.05 — the relation holds even with the controls held constant.

In plain words

A researcher looked at age and reading in 50 children with the same years in school. They still went together a little. Was that just chance? Significance came out 0.03: if age and reading had no link in such children, chance alone would give a link this strong only about 3 times in 100. Below 5 times in 100, a link is usually called hard to put down to chance alone. Now she can say that age and reading seem to go together even with the same years in school. Had chance given such a link 40 times in 100, it would show up by luck all the time, and she would keep quiet.

How it is computed

p from t = r · √(df / (1 − r²)), df = n − 2 − k

Example

The cell with Significance is selected in each report; point at a label to see its note.

— the sample data (50 rows) the examples use
— x1 and x2 with age held constant =STATS_PARTIAL(Data!A1:T51, "x1,x2", "age")

Where you see it

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.

Alternative hypothesis — The hypothesis tested: two-sided — the means differ in either direction; greater — the first is larger; less — the first is smaller.
Exact significance — The exact p of U (Dineen and Blakesley), shown only for small groups without ties, as SPSS; for a two-sided test twice the one-tailed p.
Margin of error — Half the width of a two-sided interval: the t quantile times the standard error.
Width of the interval — Upper − Lower.
Estimate within the interval — TRUE (1) when the slope of the data lies inside the interval.

Get it in your sheet

One formula in a cell gives the whole report, Significance of the partial correlation included. ALS Stats is a free add-on for Google Sheets™.

Install ALS Stats from Google Workspace Marketplace (opens in a new tab)