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Chapter 14
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3. Because the difference was statistically significant, can we conclude that the
working students had an anxiety level that would be considered abnormally
high?
4. If the investigators repeated their study with another sample of working and
non-working university students drawn from the same population, should we
expect that they will obtain a similar result?
5. Your textbook tells you that large sample sizes can produce statistically
significant results that lack importance. The analysis of Beck Anxiety
Inventory scores was based on 78 working students and 30 non-working
students, or a total of 108 students. Would a sample size of 108 be considered
excessively large?
Answers:
1. The researchers would have rejected the null hypothesis.
2. A statistically significant difference is not necessarily a large difference. To
determine whether or not a difference is large, it is a good idea to calculate a
standardized effect size. Exercise 10 provides the information needed to
calculate Cohen’s d, which comes out to be approximately 0.52. Using
Cohen’s guidelines presented in section 14.9 of your textbook, we would
conclude that the effect size is medium.
3. Because the working students’ anxiety test mean is significantly higher than
that of the non-working students, we cannot automatically conclude that the
mean is in the abnormal range. In the article, the authors indicate that the
working students’ mean was in the mild anxiety range and the non-working
students’ mean was in the minimal anxiety range.
4. A statistically significant result implies that the observed outcome is reliable
and would likely reappear if the study were repeated.
5. A total sample size of 108 would not generally be considered excessively
large for testing for a standardized effect size in the vicinity of one-half of a
standard deviation. Samples of 500 or more in each group (i.e., a total of
1,000) students, however, would be considered excessively large for testing
for an effect size approximately equal to 0.5.
Exercise 11
Juvonen, Wang, and Espinoza (2013) investigated social prominence, physical
aggression, and spreading rumors among adolescents at three time points. The outcome
measures were based on peer nominations made individually by each participating
student. Social prominence was assessed by asking students to name grade mates whom
they considered the “coolest”. Physical aggression was measured by asking students to
name grade mates who “start fights or push other kinds around”. Spreading of rumors
was assessed by asking students to name grade mates who “spread nasty rumors about
other kids”. This exercise is only concerned with the results of analyses carried out on
the fall of 8th grade data that were designed to test for gender differences. The table
presented here presents a summary of the analysis results.
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