Lesson 4 of 6 · 14 min

The Spearman rank correlation test

When the data are not normal, contain outliers or are already ranks, replace each value by its rank and correlate the ranks instead.

In short

The Spearman rank correlation $r_S$ is essentially the Pearson correlation calculated on ranks; it is a non-parametric measure.
Rank each variable within its own sample, largest = 1. Tied values share the average of the ranks they occupy.
$r_S = 1 - 6\sum d_i^2/[n(n^2-1)]$ , where $d_i$ is the difference in ranks for pair i.
Like r, $r_S$ runs from −1 (rankings exactly reversed) to +1 (identical rankings).
Testing: small samples need a special table of critical values; for large samples (n > 30) use the usual t-statistic with n − 2 df.

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