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

Inputs

Prior probability of group membership (must sum to 1.00)
   Master p(M)


 

0.50
Non-Master p(N)

0.50

Set equal

Probability of a Correct Response

Item 1
Masters


 

0.50
Non-Masters


 

0.50

Set equal
Item 2
Masters


 

0.50
Non-Masters


 

0.50

Item 3 
Masters


 

0.50
Non-Masters


 

0.50

One Examinee's Response Pattern
Item 1 2 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
Rewritten to use CSS 4/6/2024