Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

184 CHAPTER 6 | Probability
6.5 Looking Ahead to Inferential Statistics
LEARNING OBJECTIVE
7. Explain how probability can be used to evaluate a treatment effect by identifying
likely and very unlikely outcomes.
Probability forms a direct link between samples and the populations from which they come.
As we noted at the beginning of this chapter, this link is the foundation for the inferential
statistics in future chapters. The following example provides a brief preview of how probability
is used in the context of inferential statistics.
We ended Chapter 5 with a demonstration of how inferential statistics are used to help
interpret the results of a research study. A general research situation was shown in Figure 5.10
and is repeated here in Figure 6.20. The research begins with a population that forms a
normal distribution with a mean of μ = 400 and a standard deviation of σ = 20. A sample
is selected from the population and a treatment is administered to the sample. The goal for
the study is to evaluate the effect of the treatment.
To determine whether the treatment has an effect, the researcher simply compares the
treated sample with the original population. If the individuals in the sample have scores
around 400 (the original population mean), then we must conclude that the treatment
appears to have no effect. On the other hand, if the treated individuals have scores that are
noticeably different from 400, then the researcher has evidence that the treatment does have
an effect. Notice that the study is using a sample to help answer a question about a population;
this is the essence of inferential statistics.
The problem for the researcher is determining exactly what is meant by “noticeably different”
from 400. If a treated individual has a score of X = 415, is that enough to say that
the treatment has an effect? What about X = 420 or X = 450? In Chapter 5, we suggested
that z-scores provide one method for solving this problem. Specifically, we suggested that
a z-score value beyond z = 2.00 (or –2.00) was an extreme value and therefore noticeably
different. However, the choice of z = ±2.00 was purely arbitrary. Now we have another
tool, probability, to help us decide exactly where to set the boundaries.
Population
Normal
m 5 400
s 5 20
FIGURE 6.20
A diagram of a research study. A
sample is selected from the population
and receives a treatment. The goal is
to determine whether the treatment
has an effect.
Sample
T
r
e
a
t
m
ent
Treated
sample