If totally sure use a definite, a, b, c response.
If totally unsure use an m response.
If see one definitely wrong a, b, c value, choose among the remaining five on the opposite line.
Indicate preference between two values by d, f, g, i, j, l responses.
Indicate uncertainty between two values by e, h, k responses.
Choice Letter Points Fraction
Correct a b c 30 1.000
Wrong -- -100 0.000
Uninformed m 0 0.769
Near Right d f g i j l 20 0.923
Between Two e h k 10 0.846
Near Wrong d f g i j l -10 0.692
The above point values are set to encourage a, b,c answers only when more than 95% certain.
The indicated fractions can be used for scoring. They represent the amount of the [-100, 30] point-range attainable from answers.
a b c
a 30 -100 -100
b -100 30 -100
c -100 -100 30
d -10 -100 20
e 10 -100 10
f 20 -100 -10
g 20 -10 -100
h 10 10 -100
i -10 20 -100
j -100 20 -10
k -100 10 10
l -100 -10 20
m 0 0 0
The definition of risk is expected loss.
Rows indicate points given to a through m answers when the respective column headings are true.
The loss-matrix values cause minimum risk only when a, b, c is answered when more than 95% certain. Otherwise there is a strong preference for an m response. Thus unless truly knowledgeable about the test question, students not following the rule "answer a, b, c only when certain" fall below the upper levels.