|
Size: 87
Comment:
|
Size: 906
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 1: | Line 1: |
| Describe FAQ/ranksum here. | = What is the expected total rank in a R choice task? = |
| Line 3: | Line 3: |
| = What is the expected total rank 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 ||||||||<style="TEXT-ALIGN: center"> '''k=1''' || '''k=2''' || '''k=3''' || '''k=4''' || '''True Rank''' || ||||||||<style="TEXT-ALIGN: center"> '''0''' || '''1''' || '''2''' || '''3''' || '''1''' || ||||||||<style="TEXT-ALIGN: center"> '''1''' || '''0''' || '''1''' || '''2''' || '''2''' || ||||||||<style="TEXT-ALIGN: center"> '''2''' || '''1''' || '''0''' || '''1''' || '''3''' || ||||||||<style="TEXT-ALIGN: center"> '''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 = $$\sum_{k=1}^4 (k=1)k $$. |
What is the expected total rank 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 = $$\sum_{k=1}^4 (k=1)k $$.