Three-Answers and Thirteen-Responses

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.

Values Between a and m Indicate Belief

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.

Loss Matrix

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.