32 Chapter 1 What Is Psychology?
collisions than people who do not. How likely,
then, would we be to obtain the difference we
found (or an even larger one) between the experi-
mental group and the control group? If that likeli-
hood is quite low, we can reject the hypothesis that
there is no difference in the real world, and we can
say that the result is statistically significant—that the
difference we found in our study is probably real.
By convention, psychologists consider a result
to be significant if it would be expected to occur by
chance 5 or fewer times in 100 repetitions of the
study. They would then say that the result is sig-
nificant at the .05 (“point oh five”) level, or p<.05,
where p stands for probability and .05 is referred to
as the p value. If, however, the p value is greater than
.05, many researchers would have little confidence
in the study’s result, although they might still want
to do further research to confirm their judgment.
Today, a growing number of psychologists and
other researchers also report their results by using a
statistical formula that creates a confidence interval.
The mean from a particular sample will almost
never be exactly the same as the true mean in the
population. A confidence interval specifies, with a
particular probability, a range a little higher and
lower than the sample mean to help depict where
the true population mean probably lies (Fidler &
Loftus, 2009). As Figure 1.5 shows, if you repeated
your study many times, you would get a somewhat
different sample mean and confidence interval each
time, but most of the intervals would contain the
true population mean (Cumming, 2012).
By the way, many studies similar to our hypo-
thetical one have confirmed the dangers of talking
on a cell phone while driving. In one study, cell
phone users, whether their phones were handheld
or hands-free, were as impaired in their driving
ability as intoxicated drivers were (Strayer, Drews,
& Crouch, 2006). Because of such research, some
states have made it illegal to drive while holding
a cell phone to your ear. Others are considering
making any cell phone use by a driver illegal.
We will revisit this topic, and the general issue of
multitasking, in Chapter 7.Confidence interval A
statistical measure that
provides, with a speci-
fied probability, a range
of values within which a
population mean is likely
to lie.
maniacs and had 15 collisions, whereas the others
were more cautious and had only 5. Perhaps almost
all of the participants had 9, 10, or 11 collisions.
Perhaps the number of accidents ranged from 0
to 15. The mean does not tell us about such vari-
ability in the subjects’ responses. For that, we need
other descriptive statistics. For example, the stan-
dard deviation tells us how clustered or spread out
the individual scores are around the mean; the more
spread out they are, the less typical of everybody the
mean is. Unfortunately, when research is reported
in the news, you usually hear only about the mean.Inferential Statistics:
Asking “So What?” LO 1.19
At this point in our experiment, we have one group
with an average of 10 collisions and another with
an average of 7. Should we break out the cham-
pagne? Hold a press conference? Call our moth-
ers? Better hold off. Perhaps if one group had an
average of 15 collisions and the other an average
of 1, we could get excited. But rarely does a psy-
chological study hit you between the eyes with
a sensationally clear result. In most cases, there
is some possibility that the difference between
the two groups was simply the result of chance.
Despite all of our precautions, perhaps the people
in the cell phone group just happened to be a little
more accident-prone, and their extra 3 collisions
had nothing to do with talking on the phone.
To find out how impressive the data are, psy-
chologists use inferential statistics. These statistics
do not merely describe the findings; they permit
researchers to draw inferences (conclusions based
on evidence) about how meaningful the findings
are. Like descriptive statistics, inferential statistics
involve the application of mathematical formulas
to the data.
Historically, the most commonly used inferen-
tial statistics have been significance tests, which tell
researchers how likely it is that a result occurred
by chance. Let’s hypothesize that in the real world,
people who talk on cell phones have no morestandard deviation A
commonly used measure
of variability that indi-
cates the average differ-
ence between scores in
a distribution and their
mean.
inferential statistics
Statistical procedures
that allow researchers to
draw inferences about
how statistically mean-
ingful a study’s results
are.
significance tests
Statistical tests that
assess how likely it is
that a study’s results
occurred merely by
chance.
Most people assume that “average” means “typical,” but sometimes it doesn’t. Averages can be
misleading if you don’t know the extent to which events deviated from the statistical mean and
how they were distributed.© 1990 Creators Syndicate Inc. By permission of Mell Lazarus and Creators Syndicate