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Find difference between two sets of scores of a single participant?

Posted 8 months ago
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What I am trying to do?

I have a data set which consists of only one undergraduate student's all courses scores. Let's assume, he has completed about 70 courses where 40 courses are related to science and remaining 30 courses are related to arts. Score range of each course is 0 to 100. I am interested to find whether there exists any difference in scores of science and arts related courses. Therefore, I have divided the data; in one group (arts) of data, there are 30 values and in another group (science), there are 40 values.

What did stop me to find the difference?

  • As there is only two groups of data, I could use Student's T Test. However, as student's t test has assumption of independence[ [1]][1], I can not use that formula.

  • William M Connelly answered a question of RG where he remarked when should we use Paired T Test

    Moreover, it is basically only applicable when you have a "before" and "after" value recorded from a single "subject" (a subject could be a cell, a piece of tissue, or a human etc). Really, what it is asking is "is there a systematic difference between the before and after?"

Therefore, I can not use Paired T Test also.

  • The same problems occurred when I wanted to use Non parametric tests like Mann Whitney U Test or Wilcoxon Signed-Rank Test.

My Question

How can I find the score difference of arts related courses (30 courses) and science related courses (40 courses) when there is only one student's data and data are not paired?

Note: I have followed repeated measures related different questions of Stack Exchange. However, I feel sorry to say you that I did not find the answer of my question. Actually, I asked this question here. However, I failed to find the answer.

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