Correlation Coefficiant
Siobhan Michaels
pieces of data. I know how to find it with a calculator, but I have to show
the workings of the manual method using the Pearson Rank Correlation
coefficient. If anyone knows how to use that thing, you will know you have
to rank the data. I'm stuck on that part. I've got some data pieces that are
the same and I don't know how to rank them. My teacher was going on about
something to do with .5's but I didn't get it. Here's my data if anyone can
help me please.
Match No. of goals Rank No. of shots Rank d d^2
1 2 11
2 4 13
3 1 6
4 3 12
5 1 6
6 3 13
7 3 9
8 3 11
9 2 12
10 6 16
11 5 9
12 2 9
13 2 11
14 3 12
15 2 14
Mathman T
As you say, the first job to do when finding the Spearman Coefficient is to
rank the data, in other words, say where each piece of data is in order.
The best way to do this is to write down all the data in order then write
"1, 2, 3,...." underneath the data.
So for example, the 'No. of goals' in your data would look like this:
No. of goals: 6 5 4 3 3 3 3 3 2 2 2 2
2 1 1
Rank order: 1 2 3 4 5 6 7 8 9 10 11 12 13
14 15
But now we have to sort out the fact that some identical data have different
rank numbers (ie the repeated data): clearly this is daft, so we need a
compromise: what you do is work out the average of the rank orders for the
repeated data, and take that as the compromise rank order for each repeat.
So in your goals data, the 3 appears 5 times with ranks 4,5,6,7 and 8, so
work out the average rank (4+5+6+7+8)/5 which comes to 6, so we now take
each 3 to have a rank of 6. In the same way each of the 2's now has a rank
of 11, and each of the 1's now has a rank of 14.5 (which I guess is what
your teacher was referring to).
So now the table of ranks looks like this:
No of goals: 6 5 4 3 3 3 3 3 2 2 2 2
2 1 1
Rank order: 1 2 3 6 6 6 6 6 11 11 11 11 11
14.5 14.5
Now enter these rank numbers against the data in your table.
Next, repeat the operation for the 'No of shots' data.
At this point you can actually get on with the job of calculating the
Spearman Coeff! Fill in the 'd' column in your table, which means the
difference in the two ranks for each row of the table, and obviously the d^2
column is then obtained by squaring the d-values.
Finally, total up the d^2 column (giving a total of T, say) and the formula
for Spearman is
1 - 6T/(n(n^2-1)), where n = number of data, in your case 15.
Let me know what answer you get, and I'll see if it agrees with mine....
Good luck!
Mathman T.
Siobhan Michaels wrote in message <7aegfb$m9d$1...@newnews.global.net.uk>...