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## Measurement Decision Theory

This is a javascript program that will allow you to experiment with different Measurement Decision Theory inputs and see the resultant outputs using different decision rules. (takes time to load)

Master p(M)

Non-Master p(N)

Set equal

Item 1
Masters

Non-Masters

Set equal

Item 2
Masters

Non-Masters

Item 3
Masters

Non-Masters

### One Examinee's Response Pattern

Item 1 Item 2 Item 3
Correct
Incorrect

### Alternate Decision Rules

Maximum Likelihood - select the mastery state most likely to have produced the response pattern z =[]

Prob of z for Masters = p(z|Master) =
=
Prob of z for Non-masters = p(z|Non-master) =
=

Maximum A Posteriori probability of group membership (MAP)  - select the group membership with the highest posterior probability
Prob of being a master = k * p(M|z) = k * p(z|M) * p(M) = P(M)
=
Prob of being a non-master = k * p(N|z) = k*p(z|N)*p(N) = P(N)
=

Bayes Optimal - select the group membership that has the lowest selection cost.
For this approach, you need to specify a cost structure.
 Costs for each decision when the examinee is a true master or non-master Decision Master Non-master True state Master c11= c21= Non-master c12= c22=