Correcting the Spearman correlation for ties

Every time there is a tie, count the number of people with the same score, and call it t. Then calculate t³ – t. Add up all the t scores, for each variable, and call that t. We’ll call them t_x for display, and t_y for change in testosterone.

There is one tie for change in testosterone (y) – two people have scored 1.06, so t is 2.

We calculate t³ – t = 23 – 2 = 6, because this is the only tie, t_y = 6.

For display behaviour, there are 4 sets of ties:

2 people scored 3.2; t³ – t = 6

2 people scored 3.6; t³ – t = 6

2 people scored 3.8; t³ – t = 6

3 people scored 4.6; t³ – t = 24

2 people scored 5.2; t³ – t = 6

t_x = 6 + 6 + 24 + 6 = 42

Next we calculate T for each variable.

For change in testosterone, we calculate T_x

And for display behaviour:

Finally, we use a different version of the Spearman formula:

See, that was worth it wasn’t it?