Settling Rank ties in Excel for a Mann-Whitney U-test

Question

I have some ranked data that looks something like this in an excel spreadsheet.

1.3
1.3
1.3
1.4
1.6
1.6
1.7
1.8
1.9
2
2
2.3
2.3
2.3
2.4
2.7
3.1
3.3
3.3
3.4
3.4
4
4.2
4.5
4.7
4.9
5.8
6.1
6.7

I'm looking to make a calculator for the Mann-Whitney U-test and for that I need to rank these samples, simple enough using the =RANK() function in Excel, but I need to settle ties in the ranks for the test. The Mann-Whitney method involves taking the average of the ranks. For example, my first 3 values are 1.3 so I need excel to assign all 3 of these values the rank of (1+2+3)/3 (=2). At the moment the =RANK() function just ranks all 3 as 1.

I've seen some similar questions here solved using the IF command but have had trouble appling them to my data.

Any help would be greatley appreciated.

Thanks,

Sam

Answer 1

Which version of Excel are you using? If you have Excel 2010 or later then there is a specific function for this, RANK.AVG, e.g. if your data is in A2:A30 use this formula in B2 copied down to rank as required

=RANK.AVG(A2,A$2:A$30,1)

In earlier versions of Excel you can use this formula to give you the same results

=RANK(A2,A$2:A$30,1)+(COUNTIF(A$2:A$30,A2)-1)/2

Answer 2

You can cheat a little to get duplicates with different ranks. You will need a helper column

I'm going to assume the list of numbers starts @ A1...

in B1, enter the formula =A1+ROW()/10000 - this will add on a small amount to the number - not enough to put it into the next value, but enough to distinguish between values

In C1, enter the formula =RANK(B1,$B$1:$B$29,1) to get the new rankings, with no duplicates.

Then copy B1 & C1 down to complete the table. You can hide column B if you don't want the intermediate cells shown