Understanding Psychology (10th Ed)

population
All the members of a 
group of interest.
sample
A representative subgroup 
of a population of interest.
inferential statistics
The branch of 
statistics that uses data from samples 
to make predictions about the larger 
population from which the sample is 
drawn.
Key Concepts 
How do we generalize 
from data? 
How can we determine the 
nature of a relationship, and 
the signifi cance of diff erences, 
between two sets of scores?
M O D U L E 5 8 
Using Statistics to Answer 
Questions: Inferential Statistics 
and Correlation 
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 Module 
58 
Using Statistics to Answer Questions: Inferential Statistics and Correlation 
A-15
if 90 heads did appear, the odds would be that the coin or the fl ipping process 
was rigged. 
Inferential statistics are used to mathematically determine the probability of 
observed events. By using inferential statistics to evaluate the result of an experiment, 
psychologists are able to calculate the likelihood that the difference is a refl ection of 
a true difference between populations. For example, suppose we fi nd that the mean 
on an anxiety scale is 68 for smokers and 48 for nonsmokers. Inferential statistical 
procedures allow us to determine whether this difference is really meaningful or 
whether we might expect the same difference to occur merely because of chance fac-
tors (Gaffney & Henry, 2007). 
The results of inferential statistical procedures are described in terms of mea-
sures of signifi cance. To a psychologist, a signifi cant outcome is one in which the 
observed outcome would be expected to have occurred only by chance with a 
probability of .05 or less. Put another way, a signifi cant difference between two 
means says that there are only 5 chances out of 100 (or less) that the difference an 
experimenter has found is due to chance rather than to an actual difference between 
the means.
Obtaining a signifi cant outcome in a study does not necessarily imply that the 
results of an experiment have real-world importance. An experiment may demon-
strate that two groups differ signifi cantly from one another, but the meaning of the 
differences in terms of what occurs outside the laboratory may be limited. Still, 
fi nding a signifi cant outcome tells us something important: The differences a 
researcher has found are overwhelmingly likely to be true differences that are not 
only due to chance.
The Correlation Coeffi
cient: 
Measuring Relationships
How do we know if television viewing is related to aggression, if reading romance 
novels is related to sexual behavior, or if mothers’ IQs are related to their daugh-
ters’ IQs? 
Each of these questions revolves around the issue of the degree of relationship 
between two variables. One way of answering them is to draw a scatterplot, a means 
of graphically illustrating the relationship between two variables. We would fi rst 
collect two sets of paired measures and assign one score to the horizontal axis (vari-
able x ) and the other score to the vertical axis (variable y ). Then we would draw a 
dot at the place where the two scores meet on the graph. The fi rst two scatterplots 
in Figure 1 present typical situations. In (a) and (b), there is a positive relationship
in which high values of variable x are associated with high values of variable y and 
low values of x are associated with low values of y . In (c) and (d), there is a negative