Spearman Rank Order Correlation Coefficient

The logic and computational details of rank-order correlation
are described in Subchapter 3b of Concepts and Applications.

This page will calculate rs , the Spearman rank-order correlation coefficient, for a bivariate set of paired XY rankings.

If your values of X and Y have already been ranked, these ranks can be entered directly into the cells headed by the label 'Ranks.' In this case, please note that the sums of ranks for X and Y must both be equal to [n(n+1)]/2. If this equality is not satisfied, you will receive a message asking you to examine your data entry for errors.

If your values of X and Y have not yet been rank- ordered, they can be entered into the cells labeled 'Raw Data' and the ranking will be performed automatically.

After data have been entered, click one or the other of the «Calculate» buttons according to whether you are starting out with ranks or raw data. If you wish to perform another analysis with a different set of data: click the «Reset» button if the value of n for the new set of data is exactly ; click the Reload or Refresh button of your browser if the value of n is greater or smaller than  .


Data EntryQ
Ranks for
 		Raw Data for
pairs
 		X
 		Y
 		X
 		Y



n
 		rs
 		t
 		df
  P   one-tailed
two-tailed
Note that t is not a good approximation of the sampling distribution of rs when n is less than 10. For values of n less than 10, you should use the following table of critical values of rs, which shows the values of + or —rs required for significance at the .05 level, for both a directional and a non-directional test.
n
 		directional
 		non-
directional
5
 		.90
 		1.00
6
 		.83
 		.89
7
 		.72
 		.79
8
 		.62
 		.72
9
 		.60
 		.70
Home Click this link only if you did not arrive here via the VassarStats main page.














































Disregard these cells.
They are merely place holders.