Find the Best Optimization Method for Creating Test Groups - Mike

[MJNun]

I am looking for a term to describe a sort of "optimization" that I am trying to do.

Hi everybody, I am a college student who unfortunately is not smart enough to be a math major. But nonetheless I am obsessed with statistics and numbers. I have a question:

I need help figuring out a term, or a statistical method to describe and help me solve what I am looking to do.

I will give you the layout of my project (it is not real, just a good way of explaining what i am trying to accomplish):

I gave 40 students a test on Day 1, (test 1, 2, 3, or 4). At random, I gave them either test 1,2,3,4,5 or No test (0) on Day 2. But made sure not to repeat tests so a student cannot take test 2 on both days. I have averaged their scores and listed which students received which tests in my attachment so you can have a visual representation.

What I am trying to do, and what I would like some help on is:
Creating 4 groups of 4 students who only have one test in common
Group 1: (1,0), (2,1), (4,1), (1,5)
Group 2: (2,4), (2,1)*Different person than group 1, (3,2), (2,0)
ect.

But here is where I have trouble (even explaining), I want to make it so that each group is optimized in way that the groups have the highest possible score, while keeping the standard deviation of the groups at a minimum.

So basically is there a term, or analysis method that would help me figure out what I am trying to do. I figured there has to be a way to weight the standard deviation, so that I have the most equal groups possible, while still having the highest scores.

Think of it as if I were assembling a team for a competition, and I wanted to make each group as strong as possible for a single test (the one they have in common), while also making sure they had diversity in their knowledge. This is where I get optimization from, I am trying to optimize my team.

Does this make sense? If not please don't just ignore this, feel free to ask me a question if you are confused, and any help at all will be much appreciated.

- Mike

 

[MJNun]

Just to clarify, I plan on doing this with up to 17 different tests and 200+ students. So this is a simplified version of my goal.

Also, I plan on asking someone who is good with Matlab to write me a code. So if someone could explain to me a statistical analysis method that describes this crazy 'optimization' problem in words that would help me ask a more direct request to someone with Matlab expertise that would be great. Or any of you think you can tackle this with Matlab, that would be incredible.
*A friend of mine said that I might be looking for something that involves Mean Square Error (but he's not a math major either)*

 

[bpet]

Hello MJNun and welcome to the forums.

It's quite a challenge you've set for yourself, and the specific choices of the objectives and constraints are going to be crucial to whether this combinatorial optimisation problem is merely difficult to solve or near impossible.

If math isn't your strong point, then perhaps you can describe more about the actual purpose of the teams?

Otherwise I'd suggest speaking to an expert in Operations Research (particularly in quadratic binary integer programming) who can help to formulate and solve the problem (not necessarily using Matlab).

 

[weetabixharry]

I want to make it so that each group is optimized in way that the groups have the highest possible score, while keeping the standard deviation of the groups at a minimum.

When you say standard deviation, do you mean for each individual student across their own test results? (i.e. they will be preferred if they scored quite strongly across all tests, rather than just acing one or two?) ... or the students' totals within the group (i.e. all members in a given group should be of a similar overall standard?)

Also, what is the idea behind giving some students no test on day 2? I feel like this is a missed opportunity to gather useful data.

 

[blue_raver22]

Hello Mike,

It sounds like you are looking for an optimization method for creating test groups. One approach you could consider is using a technique called "cluster analysis." This method involves grouping data points (in this case, students) based on their similarities and differences in certain variables (such as test scores). You could also incorporate the idea of minimizing standard deviation by using a weighted clustering approach, where you assign a higher weight to the standard deviation in your optimization process.

Another method you could explore is called "simulated annealing," which is a type of optimization algorithm that is often used in situations where there are multiple variables and constraints (such as your desire for diversity in knowledge within the groups). This method involves randomly assigning students to groups and then making small adjustments to the groups in a way that improves the overall score while also satisfying the constraints.

I hope this helps and gives you some ideas for further research. Good luck with your project!