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. .

Data Entry

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. Note, however, that the rank-ordering process is computationally intensive and might take a while, depending on the speed of your computer. Because the time required for rank-ordering increases exponentially as a function of sample size, this calculator is not recommended for cases where the number of XY pairs is greater than about N=40. If you use it with samples larger than this, be prepared to wait a moment.

Raw data can also be imported via the 'Data Import' box. When importing data from a spreadsheet, the paired values of X and Y must be in the form of two adjacent columns. Within the spreadsheet application, select and copy the two columns of data. Then return to this page, click the cursor into the data-import box and perform the 'Paste' operation.

Make sure that the final line in the data-import box is not followed by a carriage return. (An extra carriage return at the end of the list will be interpreted as an extra data entry whose value is zero. Importing data via the copy and paste procedure will almost always produce an extra carriage return at the end of a column.) After the bivariate list has been pasted into the data-import box, click the cursor immediately to the right of the final entry in the list, then press the down-arrow key. If an extra line is present, the cursor will move downward. Extra lines can be removed by pressing the down arrow key until the cursor no longer moves, and then pressing the 'Backspace' key (on a Mac platform, 'delete') until the cursor stands immediately to the right of the final entry.

After verifying that there is no extra line in the data-import box, click the button labeled «Import Raw Data».

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 Data Import pairs X Y X Y
 n rs t df
 P one-tailed two-tailed
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Disregard these cells.
They are merely place holders.