Page 253 - Statistics for Dummies

Chapter 15: Commonly Used Hypothesis Tests: Formulas and Examples
way according to relevant variables such as age or perhaps weight, or the
same people are used twice (for example, using a pre-test and post-test).
Paired tests are typically used for studies in which someone is testing to see
whether a new treatment, technique, or method works better than an existing
method, without having to worry about other factors about the subjects that
may influence the results (see Chapter 17 for details).
The average difference (tested in this section) isn’t the same as the difference
in the averages (tested in the previous section):
✓ With the difference in averages, you compare the difference in the
means of two separate samples to test the difference in the means of
two different populations.
✓ With the average difference, you match up the subjects so they are
thought of as coming from a single population, and the set of differences
measured for each subject (for example, pre-test versus post-test) are
thought of as one sample. The hypothesis test then boils down to a test
for one population mean (as I explain earlier in this chapter). 237
For example, suppose a researcher wants to see whether teaching students
to read using a computer game gives better results than teaching with a
tried-and-true phonics method. She randomly selects 20 students and puts
them into 10 pairs according to their reading readiness level, age, IQ, and so
on. She randomly selects one student from each pair to learn to read via the
computer game method (abbreviated CM), and the other learns to read using
the phonics method (abbreviated PM). At the end of the study, each student
takes the same reading test. The data are shown in Table 15-1.
Table 15-1 Reading Scores for Computer Game Method
versus Phonics Method
Student Pair Computer Method Phonics Method Difference (CM – PM)
1 85 80 +5
2 80 80 0
3 95 88 +7
4 87 90 –3
5 78 72 +6
6 82 79 +3
7 57 50 +7
8 69 73 –4
9 73 78 –5
10 99 95 +4

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