could be a high correlation between house numbers and the combined ages of
the house’s occupants but reading any significance into this would be
unfortunate.
Spearman’s correlation
Correlation can be put to other uses. The correlation coefficient can be
adapted to treat ordered data – data where we want to know first, second, third,
and so on, but not necessarily other numerical values.
Occasionally we have only the ranks as data. Let’s look at Albert and Zac, two
strong-minded ice skating judges at a competition who have to evaluate skaters
on artistic merit. It will be a subjective evaluation. Albert and Zac have both won
Olympic medals and are called on to judge the final group which has been
narrowed down to five competitors: Ann, Beth, Charlotte, Dorothy and Ellie. If
Albert and Zac ranked them in exactly the same way, that would be fine but life
is not like that. On the other hand we would not expect Albert to rank them in
one way and Zac to rank them in the very reverse order. The reality is that the
rankings would be in between these two extremes. Albert ranked them 1 to 5
with Ann (the best) followed by Ellie, Beth, Charlotte and finally Dorothy in 5th
position. Zac rated Ellie the best, followed by Beth, Ann, Dorothy and Charlotte.
These rankings can be summarized in a table.
Spearman’s formula
How can we measure the level of agreement between the judges? Spearman’s
correlation coefficient is the instrument mathematicians use to do this for ordered