more or less continuous scale of anxiety, we would be dealing with measurement data, and
the data would consist of scores for each subject on that variable. Note that in both situa-
tions the variable is labeled anxiety. As with most distinctions, the one between measure-
ment and categorical data can be pushed too far. The distinction is useful, however, and
the answer to the question of whether a variable is a measurement or a categorical one is
almost always clear in practice.1.2 Descriptive and Inferential Statistics
Returning to our intervention program for stress, once we have chosen the variables to be
measured and the schools have administered the program to the students, we are left with a
collection of raw data—the scores. There are two primary divisions of the field of statistics
that are concerned with the use we make of these data.
Whenever our purpose is merely to describe a set of data, we are employing descriptive
statistics.For example, one of the first things that we would want to do with our data is to
graph them, to calculate means (averages) and other measures, and to look for extreme
scores or oddly shaped distributions of scores. These procedures are called descriptive sta-
tistics because they are primarily aimed at describing the data. Descriptive statistics was
once looked down on as a rather uninteresting field populated primarily by those who drew
distorted-looking graphs for such publications as Timemagazine. Twenty-five years ago
John Tukey developed what he called exploratory statistics, orexploratory data analysis
(EDA).He showed the necessity of paying close attention to the data and examining them
in detail before invoking more technically involved procedures. Some of Tukey’s innova-
tions have made their way into the mainstream of statistics, and will be studied in subse-
quent chapters, and some have not caught on as well. However, the emphasis that Tukey
placed on the need to closely examine your data has been very influential, in part because of
the high esteem in which Tukey was held as a statistician.
After we have described our data in detail and are satisfied that we understand what the
numbers have to say on a superficial level, we will be particularly interested in what is
called inferential statistics.In fact, most of this book will deal with inferential statistics.
In designing our experiment on the effect of stress on self-esteem, we acknowledged that it
was not possible to measure the entire population, and therefore we drew samples from that
population. Our basic questions, however, deal with the population itself. We might want
to ask, for example, about the average self-esteem score for an entire population of students
who could have taken our program, even though all that we really have is the average score
for a sample of students who actually went through the program.
A measure, such as the average self-esteem score, that refers to an entire population is
called a parameter.That same measure, when it is calculated from a sample of data that
we have collected, is called a statistic.Parameters are the real entities of interest, and the
corresponding statistics are guessesat reality. Although most of what we will do in this
book deals with sample statistics (or guesses, if you prefer), keep in mind that the reality
of interest is the corresponding population parameter. We want to infersomething about
the characteristics of the population (parameters) from what we know about the character-
istics of the sample (statistics). In our hypothetical study we are particularly interested in
knowing whether the average self-esteem score of a population of students who poten-
tially might be enrolled in our program is higher, or lower, than the average self-esteem
score of students who might not be enrolled. Again we are dealing with the area of inferen-
tial statistics, because we are inferring characteristics of populations from characteristics
of samples.Section 1.2 Descriptive and Inferential Statistics 5descriptive
statistics
exploratory data
analysis (EDA)
inferential
statistics
parameter
statistic