Spearmans rank

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Method 1 of 3: By Hand

1

Draw your data table. This will organize the information you need to calculate Spearman's Rank Correlation Coefficient. You will need:

6 Columns, with headers as shown below.

As many rows as you have pairs of data.

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2

Fill in the first two columns with your pairs of data.

3

In your third column rank the data in your first column from 1 to n (the number of data you have). Give the lowest number a rank of 1, the next lowest number a rank of 2, and so on.

4

In your fourth column do the same as in step 3, but instead rank the second column.

If two (or more) pieces of data in one column are the same, find the mean of the ranks as if those pieces of data had been ranked normally, then rank the data with this mean.

In the example at right, there are two 5s that would otherwise have ranks of 2 and 3. Since there are two 5s, take the mean of their ranks. The mean of 2 and 3 is 2.5, so assign the rank 2.5 to both 5s.

5

In the "d" column calculate the difference between the two numbers in each pair of ranks. That is, if one is ranked 1 and the other 3 the difference would be 2. (The sign doesn't matter, since the next step is to square this number.)

6

7

Square each of the numbers in the "d" column and write these values in the "d2" column.

8

Add up all the data in the "d2" column. This value is Σd2.

9

Choose one of these formulae:

If there was no tie in previous steps, insert this value into the simplified Spearman's Rank Correlation Coefficient formula

The closer to 1 the more positive the correlation is 0 is no correlation and -1 is negative correlation