Spearmans rho

TerrorFirmer

Hi,

I'm looking for a very simplistic example of how you would do this. It needn't be complex, in fact the very opposite - just something to show how it's done, where you get the values for each section, etc. I'm supposed to be doing one, but from just looking at an example that doesn't have an explanation alongside it I don't quite know where the values of X and Y are coming from...

thanks.

2Scoops

Kind of hard to explain it in words but here goes…

The Spearman correlation first reassigns each value in the two variables being correlated (X and Y) a rank score e.g. highest score gets 1, next highest, no matter how much higher, gets 2 etc.

Then it calculates the difference of the 2 ranks (Xrank – Yrank). Then it squares the differences in rank and sums them.

The equation is like this (excuse lack of scientific noation!):

Spearman r = 1 – (6 by sum of squared rank differences) / n(n^2 – 1).

It’s advantage is that it makes no assumption on the distribution of scores and can be used on ordinal data.

X Y X-rank Y-rank D D^2
6 9 3.5 4 -.5 .25
5 8 5.5 5 .5 .25
7 10 2 2 0 0
8 10 1 2 -1 1
2 4 10 8 2 4
5 6 5.5 7 -1.5 2.25
3 3 9 9.5 -.5 .25
4 3 7.5 9.5 -2 4
6 7 3.5 6 -2.5 6.25
4 10 7.5 2 5.5 30.25

Spearman = 1 - 6(48.5)/10(99)
=.71


Edit: can't get the table to come out right

TerrorFirmer

Thanks, appreciate it. But my problem arises when two values are the same - how does it work. I vaguely remember they both get 1.5 or something, but then there was also something about skipping the number '2' then, or something like that...but I can't remember. How do you assign the values of Y, if X is awarding 1 through 10 or whatever for highest values of X?

2Scoops

If you can figure out that table I posted, I included examples. Every time there's a space, that's a new column. You seem to have it already though: when 2 numbers are the same they both get the same number, halfway between the two ranks, then the next number is skipped.

Edit: overlooked one of your questions. You assign the ranks for Y exactly the same as those for X, give the highest rank to the highest value and so on. You will end up with 2 new variables of rank: X-rank and Y-rank, and then you correlate these instead of the original variables.

TerrorFirmer

Thanks. Much appreciated.