Measurement Decision Theory

This is a javascript program for Internet Explorer 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; requires Sun Java Runtime Environment).


Prior probability of group membership

   Master p(M)

Non-Master p(N)

Set equal

Probability of a Correct Response

Item 1


Set equal

Item 2


Item 3 



One Examinee's Response Pattern

Item 1 Item 2 Item 3


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


    Master Non-master
True state Master c11= c21=
Non-master c12= c22=



Written 12/2001 IE4/Netscape 4

Revised 02/2009 ie7/ie8 must first move mouse off slider for FF2 and FF3
Tested 09/2014: Chrome v37 and IE 9 with Java 7.0.670.1