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Statistics in Plain English, Third Edition
interest in ways that influence the outcome of the study, then it is a perfectly acceptable method of
selecting a sample.
Types of Variables and Scales of Measurement
In social science research, a number of terms are used to describe different types of variables.
A variable is pretty much anything that can be codified and has more than a single value
(e.g., income, gender, age, height, attitudes about school, score on a meas ure of depression). A
constant, in contrast, has only a single score. For example, if every member of a sample is male,
the “gender” category is a constant. Types of variables include quantitative (or continuous)
and qualitative (or categorical). A quantitative variable is one that is scored in such a way that
the numbers, or values, indicate some sort of amount. For example, height is a quantitative (or
continuous) variable because higher scores on this variable indicate a greater amount of height.
In contrast, qualitative variables are those for which the assigned values do not indicate more or
less of a certain quality. If I conduct a study to compare the eating habits of people from Maine,
New Mexico, and Wyoming, my “state” variable has three values (e.g., 1 = Maine, 2 = New
Mexico, 3 = Wyoming). Notice that a value of 3 on this variable is not more than a value of 1 or
2—it is simply different. e labels represent qualitative differences in location, not quantitative
differences. A commonly used qualitative variable in social science research is the dichotomous
variable. is is a variable that has two different categories (e.g., male and female).
Most statistics textbooks describe four different scales of meas ure ment for variables: nomi-
nal, ordinal, interval, and ratio. A nominally scaled variable is one in which the labels that
are used to identify the different levels of the variable have no weight, or numeric value. For
example, researchers often want to examine whether men and women differ on some variable
(e.g., income). To conduct statistics using most computer software, this gender variable would
need to be scored using numbers to represent each group. For example, men may be labeled “0”
and women may be labeled “1.” In this case, a value of 1 does not indicate a higher score than a
value of 0. Rather, 0 and 1 are simply names, or labels, that have been assigned to each group.
With ordinal variables, the values do have weight. If I wanted to know the 10 richest people
in America, the wealthiest American would receive a score of 1, the next richest a score of 2, and
so on through 10. Notice that while this scoring system tells me where each of the wealthiest 10
Americans stands in relation to the others (e.g., Bill Gates is 1, Oprah Winfrey is 8, etc.), it does
not tell me how much distance there is between each score. So while I know that the wealthiest
American is richer than the second wealthiest, I do not know if he has one dollar more or one
billion dollars more. Variables scored using either interval and ratio scales, in contrast, contain
information about both relative value and distance. For example, if I know that one member of
my sample is 58 inches tall, another is 60 inches tall, and a third is 66 inches tall, I know who
is tallest and how much taller or shorter each member of my sample is in relation to the others.
Because my height variable is measured using inches, and all inches are equal in length, the
height variable is measured using a scale of equal intervals and provides information about both
relative position and distance. Both interval and ratio scales use measures with equal distances
between each unit. Ratio scales also include a zero value (e.g., air temperature using the Celsius
scale of meas ure ment). Figure 1.2 provides an illustration of the difference between ordinal and
interval/ratio scales of meas ure ment.
Research Designs
ere are a variety of research methods and designs employed by social scientists. Sometimes
researchers use an experimental design. In this type of research, the experimenter divides the
cases in the sample into different groups and then compares the groups on one or more variables