Generate all possible group scores based on combinations of individuals

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Morgan
Morgan 2022-6-14
编辑： Morgan 2022-6-19
I want to compare actual group scores to hypothetical scores cosnidering all possible combinations of individuals.
I'd like to plot out the actual group scores to that of all possible combinations (i.e., Actual scores for groups vs possible scores of nCr groups) for each item.
Is there a function to generate possible groupings and plot their scores?
Thank you!
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David Goodmanson
David Goodmanson 2022-6-15
Hi Jeff,
good point, I had not considered group ID so either you would or would not have a factor of factorial(20).
Morgan
Morgan 2022-6-15
Jeff, yes I want to consider all possible ways of forming 20 groups of size 3 that can be formed out of 60 individuals. I don’t need to see the group IDs, I am mainly interested in comparing the plots for my actual groups’ data to that of what could have been formed

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Jeff Miller
Jeff Miller 2022-6-16
Morgan, my point was that "all possible ways" is just too many in this case. By my calculations, if your computer could process one million different group assignments per second, it would still take about 3*(10^52) years to process all of the possible combinations.
A more practical approach is to generate many random group assignments and compare the plots for your actual data again what would happen with random divisions into groups. The code might look something like this:
nIterations = 100; % Increase to a very large number.
GroupAssignment = repmat(1:20,1,3); % 3 members in each of 20 groups.
for iIter=1:nIterations
RandomAssignment = randperm(60);
currentGroup = GroupAssignment(RandomAssignment);
% Now currentGroup(j) is the random group assignment of score j, j=1..60
% Do whatever computation you want for this random assignment of scores to groups,
% and save the result of that computation so that you can see what happens
% over many random groups.
end
% Now tabulate the results across all the random group assignments.
% You haven't looked at all of the possible ones, but if nIterations is
% large then you have probably looked at enough to get a good idea of what
% might happen by chance with other group assignments.

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