1 8 9Statistical Applications
Statistical Applications
In a statistical generalization, we draw inferences concerning a population
from information concerning a sample of that population. If 60 percent of
the population sampled said that they would vote for candidate X, we might
draw the conclusion that roughly 60 percent of the population will vote
for candidate X. With a statistical application (sometimes called a statistical
syllogism), we reason in the reverse direction: From information concerning
a population, we draw a conclusion concerning a member or subset of that
population. Here is an example:
Ninety-seven percent of the Republicans in California voted for Romney.
Marvin is a Republican from California.
[ Marvin voted for Romney.
Such arguments have the following general form:
X percent of Fs have the feature G.
a is an F.
[ a has the feature G.^1
Obviously, when we evaluate the strength of a statistical application, the
percentage of Fs that have the feature G will be important. As the figure ap-
proaches 100 percent, the argument gains strength. Thus, our original argu-
ment concerning Marvin is quite strong. We can also get strong statistical
applications when the figure approaches 0 percent. The following is a strong
inductive argument:
Three percent of the socialists from California voted for Romney.
Maureen is a socialist from California.
[ Maureen did not vote for Romney.
Statistical applications of the kind considered here are strong only if the fig-
ures are close to 100 percent or 0 percent. When the percentages are in the
middle of this range, such statistical applications are weak.
A more interesting problem in evaluating the strength of a statistical ap-
plication concerns the relevance of the premises to the conclusion. In the
above schematic representation, F stands for what is called the reference class.
In our first example, being a Republican from California is the reference
class; in our second example, being a socialist from California is the refer-
ence class. A striking feature of statistical applications is that using different
reference classes can yield incompatible results. To see this, consider the fol-
lowing example:
Three percent of Obama’s relatives voted for Romney.
Marvin is a relative of Obama.
[ Marvin did not vote for Romney.97364_ch08_ptg01_177-194.indd 189 15/11/13 10:44 AM
some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materiallyCopyright 201^3 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights,
affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.