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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.





Replies:
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.

rtopper


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