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Author:      joe d liu
I am doing a science project about the effect of music on studying.  I
invented the test which has three sections to it.  In the first two sections
there are eight tests and on the last on there are 20 tests.  I tested eight
people with this test alternating music and no music for each test.  I took
the total averages for each part of the test (music and no music separate-
ly). I was Wondering if there was a statistical way to determine if the
differences between the two averages were significant.

Yes, there are several ways. The simplest way, and the first way to try, is to calculate the standard deviation of the data for each experiment. A good reference, which may be in your local public library, is "statistical Treatment of Experimental Data," by Hugh Young.

Let the test average for the music part be _1 and the non-music part be _2.

The "standard error" of the music tests, s1, is s1 = sqrt{ (sum over music tests) [x_i - _1]^2 } / number of music tests with a similar formula for s2. If all of your test scores are independent of one another, statistical theory predicts that if you tested an infinite number of students, 66% of the music scores would be within the range (_1 - s1, _1 + s1). It also predicts that 66% of the non-music scores would be within the range (_2 - s2, _2 + s2). If these two intervals do not overlap, there is a significant difference between the two.

Example: _1 = 77, s1 = 8, _2 = 45, s2 = 30. The two intervals are (71, 85) and (15, 75). Since they overlap, there is not a significant difference between the two results (due to the large standard deviation.


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