
Determination of statistical significance
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 nonmusic 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 nonmusic 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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