FAQ/ranksum - CBU statistics Wiki

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What is the expected total discrepancy score in a R choice task?

Suppose we have R choices from 1 to k and each of these is equally likely to be the true rank. The expected total rank of the absolute value of discrepancies equals

$$\sum_{k=1}^R (k=1)k $$

For example

R = 4

k=1

k=2

k=3

k=4

True Rank

0

1

2

3

1

1

0

1

2

2

2

1

0

1

3

3

2

1

0

4

Expected total score assuming random guesses at true rank = 2(1+2+3)+2(1+1+2)= 20 = 1x2 + 2x3 + 3x4 = $$\sum_{k=1}^4 (k=1)k $$.