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=
 

   

 

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