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=

Prob of being a master =

Prob of being a non-master = 



Software to generate, calibrate and score MDT data can be found at (version .888, April 2009)


This applet accompanies Rudner, L.M. (2009). Scoring and Classifying Examinees Using Measurement Decision Theory. Practical Assessment Research & Evaluation, 14(8). Available online .


It was written 12/2001 IE4/Netscape 4 and revised 02/2009 IE7/IE8; Must move mouse off slider for FF2 and FF3