Detect multiple choice test copying and find cheaters (Compare the similitary of multiple choice responses)
This is the thing for you if you’re interested in finding out who are the cheaters on a multiple choice test. I will spare you the mathematics behind the method save to say that it’s a simple application of matrices.
A square matrix results from some matrix multiplications comparing students against other students and themselves:
Click here to download the Microsoft Excel Spreadsheet
Okay, so you’ve read this far. That means you want some of the math:
Here are some student responses on a 5 question multiple choice test:
We can represent these responses as a matrix of wrong and right answers (binary 1s and 0s):
Above, we have a 3×5 matrix of binary values representing wrong and right responses. We will call this matrix M.
The transpose of this matrix, transpose(M), is also shown above and it is a 5×3 matrix.
N is the number of questions on the test.
The similarity of the responses is determined by:
[ M * transpose(M) + (1-M) * (1-transpose(M)) ] / N * 100%
In words, this is saying:
Correct questions that students being compared have in common plus incorrect questions that students being compared have in common. The result is then converted to a percentage figure.
The more questions you have, the smaller the probability that highly similar papers will arise without collusion.
Remember: for the matrices A and B to be multiplied, the number of columns in A must be the same as the number of rows in B. The resulting matrix will have the same number of rows as A and the same number of columns as B.
Posted in Excel on November 27th, 2007 by me | | 0 Comments
