What Counts as a Strong Correlation? It Depends on the Field

A study reports a correlation of 0.3. Is that strong? It depends on whom you ask. In psychology, one influential paper calls it large. A widely used medical guide calls it low. Neither is wrong, because the label is a convention, and conventions differ by field and purpose.

Two scales for the same number

Funder and Ozer argue that in psychological research an r of .10 is small, .20 medium and .30 large, and that r = .40 or more is likely to be a gross overestimate that will rarely appear in a large sample or a replication (Funder and Ozer, 2019). A guide written for medical research, by contrast, describes coefficients from 0.3 to 0.5 as low and anything below 0.3 as negligible (Mukaka, 2012).

What r means for prediction

A practical translation: when you predict one variable from another, the typical prediction error shrinks by a factor of √(1 − r²). At r = 0.3, the typical error is still 95% of what it was without the other variable. At r = 0.5 it is 87%, at r = 0.7 it is 71%, and at r = 0.9 it is 44%.

A correlation of 0.3 therefore barely sharpens a single prediction, though it can matter for decisions about groups or repeated events. Squaring r gives the share of variance explained, 9% at r = .30, yet Funder and Ozer warn that squaring effect sizes can mislead.

A correlation is not strong or weak in itself. It is large or small relative to what you are trying to explain.

Significance is not strength

With 10 observations, an r near 0.63 is needed to reach significance at the 5% level. With 100 observations, 0.20 suffices. The correlation coefficient simulator lets you feel how much scatter hides behind each value.

Precision matters too. An r of 0.30 from 30 observations has a 95% interval of about −0.07 to 0.60, from 100 observations about 0.11 to 0.47, and from 1,000 observations about 0.24 to 0.36. The Pearson correlation calculator gives r and its p-value, and the interval follows from Fisher's z-transformation.

Context decides

Ask what the alternatives are. A 0.3 correlation between a screening test and an outcome may be useless for diagnosing one patient but valuable for a program covering millions. A 0.3 between study hours and grades may be impressive, given how many other factors matter.

And sometimes 0.9 is too low. Two thermometers should agree almost perfectly, and a high correlation can still hide a consistent bias, as our article on wearables versus hospital devices shows.

Outliers and range matter as well. A single extreme point can lift r, and studying only a narrow slice, such as top students, can shrink it. Always look at the scatter plot first.

Match the coefficient to the data

Pearson measures linear association. For ranks or curved but steadily rising patterns, the Spearman calculator and the Kendall tau calculator may fit better, as our guide to choosing a correlation explains. And no coefficient proves cause, as the piece on correlation versus causation reminds us.

Use words with care. Report the number, its interval, the sample size, and your reason for calling it large or small, so readers can judge for themselves.