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we read too much into this, we need to consider that nonsignificant
findings are “inconclusive” because there are lots of reasons why we
might fail to find an effect. First is the possibility that the effect doesn’t
exist (i.e., brain-training doesn’t really work). Second, as we learned
in Chapter 8, our study could be underpowered, with the sample size
not large enough to detect an effect. Thus, our nonsignificant finding
could be a Type II error. Third, it is also possible that our study was not
done well enough to properly test for the effect. If the study design
is substandard, statistical conclusions from that design are suspect.
In our case, we did not even run a proper study. Having a particular
friend group do a task and answer some questions does not qualify as
a scientific study. For a proper study, we would ideally have a random
sample of people with no connection at all to the researcher. We also
should have recruited participants who had never used brain-training,
then randomly assigned half to do the brain-training. This would rule
out the possibility that those who were already using brain-training
were in some way different from the start. To give any possible effect a
fair test, we should also include more participants so we have 80 degrees
of freedom total or more (because at the point and beyond, the cutoff
scores are virtually identical). Finally, any quality study of brain- training
would closely monitor how much participants use the training and
would make sure everyone used it frequently to optimize any potential
benefit. It’s clear that our study had a lot of shortcomings, which is why
we cannot draw any definite conclusions based on what we did.

Your Turn 10.3 a. Step 1: Population and Hypotheses. (1) What
would the populations be? (2) What would the
1. When calculating the variance for the distribu- hypotheses be?
tion of differences between means, why do we add
the variances from both distributions of means? b. Step 2: Build a Comparison Distribution. (1)
What is the comparison distribution? What
2. As part of a health studies minor you’re complet-
ing, you need to take a nutrition class. Last month shape is it? (2) What will be the comparison
following a discussion on the benefits of clean distribution’s mean be? Why? (3) What will be
eating, the class decided to test clean eating’s ben- the estimate of the population variance? (4)
efits by seeing if increases energy. Using a random What is the variance of the two distributions of
2
means? (5) What is the variance (S
number generator, everyone was assigned a num- standard deviation (S Difference ) and
ber. Those who got an even number ate clean for Difference ) of the comparison
a month, while those with an odd number ate nor- distribution?
mally. At the end of the month, everyone took an c. Step 3: Establish Critical Value Cutoff. In
assessment of mental energy where 1 = Low Energy order to know for sure if the group who ate
and 7 = High Energy. Everyone in your nutrition clean had more mental energy, you need to
class follows their randomly assigned diet and gets establish a cutoff score. (1) What three pieces of
a mental energy score. Here are the scores for the information do you need to find the cutoff score
groups: Clean Eating (7, 7, 6, 5, 7) and Non-Clean on the t-table? (2) What is the t-cutoff associ-
Eating (3, 7, 6, 5, 4, 4, 6). ated with this information?

360 S TATIS TI c S F OR L IFE

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