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4. Take the square root of this total score to ﬁnd the standard error of the difference
of the means between the two groups, S X 1 X 2 ¼
q
S 1
S 2
n 2
n 1 þ
This last step is the one that gives students the most difﬁculty when they are
ﬁnding this standard error using their calculator, because they are in such a hurry to
get to the answer that they forget to carry the square root sign down to the last step,
and thus get a larger number than they should for the standard error.
5.2.1 An example of Formula #1 for the Two-group t-test
Now, let’s use Formula #1 in a situation in which both groups have a sample size
greater than 30.
Suppose that a large university offered several sections of Introductory Biology
101 to undergraduates last semester and that it wanted to compare the results of the
student evaluation form at the end of the course to see if there were gender
differences between males and females. Suppose, further, that Item #12 of the
student evaluation form is the item given in Fig. 5.7 .
Suppose you collect these ratings and determine (using your new Excel skills)
that the 52 men in this course had a mean rating of 55 with a standard deviation of 7,
while the 57 women in this course had a mean rating of 64 with a standard deviation
of 13.
Fig. 5.7 Example of a Rating Scale for Item #12 for Introductory Biology 101 (Practical
Example)
Fig. 5.8 Worksheet Data for Item #12 for Introductory Biology 101
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