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).

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=   Prob of being a master = Prob of being a non-master =

This applet accompanies Rudner, L.M. (2009). Scoring and Classifying Examinees Using Measurement Decision Theory. Practical Assessment Research & Evaluation, 14(8). Available online http://pareonline.net/getvn.asp?v=14&n=8 .