Spearman's Rank Correlation Table: Critical Values of rₛ

Spearman's rho Table

Rows: sample size n · Columns: α (one-tailed on the first header row, two-tailed on the second) · Cells: critical rₛ. Reject H₀ if |rₛ| ≥ the cell.

Tip: click any value to highlight its row and column.

How to read this table

1. Rank each variable separately and compute rₛ = 1 − 6Σd² / (n(n² − 1)), where d is the difference in ranks for each pair.
2. Find the row for the number of pairs n and the column for your α.
3. The correlation is significant if |rₛ| is greater than or equal to the table value.

Worked example

In 12 patients the rank correlation between baseline disease score and time to response is rₛ = 0.65. Row 12, two-tailed α = 0.05 gives 0.588, so the correlation is significant at the 5% level. The two-tailed 0.01 value is 0.728, so 0.01 < p < 0.05.

Click the underlined links to highlight the value in the table.

Formula and how the values were computed

For n ≤ 18, values come from the exact permutation distribution of Σd², enumerated over all n! orderings. For larger n they use the Edgeworth series approximation of Best and Roberts (AS 89), which the exact values up to n = 18 show to be accurate to about 0.0001 in probability. Each entry is the smallest attainable rₛ with P(rₛ ≥ r) ≤ α, rounded up.

Frequently asked questions