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)

Inputs

Prior probability of group membership

   Master p(M)

Non-Master p(N)

Set equal

Probability of a Correct Response

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=
 

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