Assuming that the sample is truly random, we not only can estimate certain character-
istics of the population, but also can have a very good idea of how accurate our estimates
are. To the extent that the sample is not random, our estimates may or may not be meaning-
ful, because the sample may or may not accurately reflect the entire population.
Randomness has at least two aspects that we need to consider. The first has to do with
whether the sample reflects the population to which it is intended to make inferences. This
primarily involves random sampling from the population and leads to what is called
external validity.External validity refers to the question of whether the sample reflects
the population. A sample drawn from a small town in Nebraska would not produce a valid
estimate of the percentage of the U.S. population that is Hispanic—nor would a sample
drawn solely from the American Southwest. On the other hand, a sample from a small town
in Nebraska might give us a reasonable estimate of the reaction time of people to stimuli
presented suddenly. Right here you see one of the problems with discussing random sam-
pling. A nonrandom sample of subjects or participants may still be useful for us if we can
convince ourselves and others that it closely resembles what we would obtain if we could
take a truly random sample. On the other hand, if our nonrandom sample is not representa-
tive of what we would obtain with a truly random sample, our ability to draw inferences is
compromised and our results might be very misleading.
Before going on, let us clear up one point that tends to confuse many people. The prob-
lem is that one person’s sample might be another person’s population. For example, if I
were to conduct a study on the effectiveness of this book as a teaching instrument, one
class’s scores on an examination might be considered by me to be a sample, albeit a non-
random one, of the population of scores of all students using, or potentially using, this
book. The class instructor, on the other hand, is probably not terribly concerned about this
book, but instead cares only about his or her own students. He or she would regard the
same set of scores as a population. In turn, someone interested in the teaching of statistics
might regard my population (everyone using my book) as a very nonrandom sample from a
larger population (everyone using any textbook in statistics). Thus, the definition of a pop-
ulation depends on what you are interested in studying.
In our stress study it is highly unlikely that we would seriously consider drawing a truly
random sample of U.S. high school students and administering the stress management pro-
gram to them. It is simply impractical to do so. How then are we going to take advantage
of methods and procedures based on the assumption of random sampling? The only way
that we can do this is to be careful to apply those methods and procedures only when we
have faith that our results would generally represent the population of interest. If we can’t
make this assumption, we need to redesign our study. The issue is not one of statistical re-
finement so much as it is one of common sense. To the extent that we think that our sample
is not representative of U.S. high school students, we must limit our interpretation of the
results. To the extent that the sample is representative of the population, our estimates have
validity.
The second aspect of randomness concerns random assignment.Whereas random
selection concerns the sourceof our data and is important for generalizing the results of
our study to the whole population, random assignment of subjects (once selected) to
treatment groups is fundamental to the integrity of our experiment. Here we are speaking
about what is calledinternal validity.We want to ensure that the results we obtain are
the result of the differences in the way we treat our groups, not a result of who we hap-
pen to place in those groups. If, for example, we put all of the timid students in our sam-
ple in one group and all of the assertive students in another group, it is very likely that
our results are as much or more a function of group assignment than of the treatments
we applied to those groups. In actual practice, random assignment is usually far more
important than random sampling.Section 1.1 Important Terms 3external validity
random
assignment
internal validity