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

PREVIEW
How likely is it that you will marry someone whose
last name begins with the same letter as your last
name? This may sound like a silly question but it was
the subject of a research study examining factors that
contribute to interpersonal attraction (Jones, Pelham,
Carvallo, & Mirenberg, 2004). In general, research has
demonstrated that people tend to be attracted to others
who are similar to themselves and it appears that
one dimension of similarity is initials. The Jones et al.
study found that individuals are disproportionately
more likely to marry those with surnames that begin
with the same letter as their own. The researchers
began by looking at more than 14,000 marriage records
from Georgia and Florida, and recording the surname
for each groom and the maiden name of each bride.
From these records it is possible to calculate the probability
of randomly matching a bride and a groom whose
last names begin with the same letter. This value was
found to be around 6.5%. Next, the researchers simply
counted number of couples in the sample who shared
the same last initial at the time they were married and
found it to be around 7.7%. Although the difference
between 6.5% and 7.7% may not seem large, for statisticians
it is huge—certainly enough to conclude that it
was not caused by random chance but is clear evidence
of a systematic force that leads people to select partners
who share the same initial. Jones et al. attribute the difference
to egoism—people are attracted to people who
are similar to them.
Although we used the term only once, the central
theme of this discussion is probability. In this chapter
we introduce the concept of probability, examine how it
is applied in several different situations, and discuss its
general role in the field of statistics.
6.1 Introduction to Probability
LEARNING OBJECTIVE
1. Define probability and calculate (from information provided or from frequency
distribution graph) the probability of a specific outcome as a proportion, decimal,
and percentage.
In Chapter 1, we introduced the idea that research studies begin with a general question
about an entire population, but the actual research is conducted using a sample. In this
situation, the role of inferential statistics is to use the sample data as the basis for answering
questions about the population. To accomplish this goal, inferential procedures are
typically built around the concept of probability. Specifically, the relationships between
samples and populations are usually defined in terms of probability.
Suppose, for example, you are selecting a single marble from a jar that contains
50 black and 50 white marbles. (In this example, the jar of marbles is the population and
the single marble to be selected is the sample.) Although you cannot guarantee the exact
outcome of your sample, it is possible to talk about the potential outcomes in terms of
probabilities. In this case, you have a 50–50 chance of getting either color. Now consider
another jar (population) that has 90 black and only 10 white marbles. Again, you cannot
specify the exact outcome of a sample, but now you know that the sample probably will be
a black marble. By knowing the makeup of a population, we can determine the probability
of obtaining specific samples. In this way, probability gives us a connection between populations
and samples, and this connection is the foundation for the inferential statistics to be
presented in the chapters that follow.
You may have noticed that the preceding examples begin with a population and then
use probability to describe the samples that could be obtained. This is exactly backward
from what we want to do with inferential statistics. Remember that the goal of inferential
statistics is to begin with a sample and then answer a general question about the population.
We reach this goal in a two-stage process. In the first stage, we develop probability as
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