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

Suppose we have R possible choices and each of these is equally likely to be the true one.

If we consider a discrepancy as the difference between the true choice and the one given by a subject then

The expected total discrepancy of the absolute value of discrepancies equals

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

with the average sum of the absolute values of discrepancies per rating equal to

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

For example the table below gives all the abs(discrepancies) for the case where 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

= $$\sum_{k=1}^4 (k=1)k$$.

The average sum of abs(discrepancies) per rating = 20/4 = 5.

None: FAQ/ranksum (last edited 2013-03-08 10:17:10 by localhost)