**EDUR 7130
Educational Research On-Line**

**Variables and Scales of Measurement**

**Assigned Readings**

See supplemental readings below.

**Variables**

A __variable__ is simply anything that varies, anything that assumes different
values or categories. For example, sex varies because there is more than one category or
classification: female and male. Race is a variable because there is more than one
category: Asian, Black, Hispanic, etc. Age is a variable because there is more than one
category: 1 year, 2 years, 3 years, etc.

Conversely, a __constant__ is anything that does not vary or take different values
or categories. For example, everyone participating in this course is a student, so that is
not a variable since it does not vary since it has only one category. As another example,
consider a group of white females. With this group, neither race nor sex varies, so race
and sex are constants for these people.

**Exercise: Identifying Variables**

In the following statements, identify the variables.

- What is the relation between intelligence and achievement?
- Do students learn more from a supportive teacher or a non-supportive teacher?
- Are students aged 55 and older more likely to drop out of college than students of ages between 30 and 40?
- What is the relationship between grade point average and dropping out of high school?
- How do three counseling techniques—rational-emotive, gestalt, and no-counseling—differ in their effectiveness in decreasing test anxiety in high school juniors?
- What is the relationship among leadership skills, intelligence, and achievement motivation of high school seniors?

Answers:

- Intelligence and achievement.
- Level of support (with two categories: support/non-support) and student learning.
- Age (with two categories: 55 and over, 30 to 40) and dropping out of college (also with two categories: in or out).
- Grade point average and dropping out of high school (two categories: in or out).
- Counseling techniques (with three categories: rational-emotive, gestalt, and no-counseling) and test anxiety.
- Leadership skills, intelligence, and achievement motivation.

**Scales of Measurement **

Measurement is the process of assigning labels to categories of
variables. Categories of variables carry different properties, which are identified below.
If one can only identify categories, then that variable is referred to as a __nominal__
variable.

If the categories of a variable can be ranked, such as from highest to
lowest or from most to least or from best to worst, then that variable is said to be __ordinal__.

If the categories can be ranked, and if they also represent equal
intervals, then the variable is said to be __interval__. Equal interval means that the
difference between two successive categories are the same. For example, temperature
measured with Fahrenheit has equal intervals; that is, the difference between temperatures
of 30 and 31 degrees is 1 degree, and the difference between 100 and 101 degrees is 1
degree. No matter where on the scale that 1 degree is located, that 1 degree represents
the same amount of heat. Similarly, when using a ruler to measure the length of something,
the difference between 2 and 3 inches is 1 inch, and the difference between 10 and 11
inches is 1 inch -- no matter where on the ruler that 1 inch lies, it still represents the
same amount of distance, so this indicates equal intervals. As another example,
time in the abstract sense never ends or begins. Since time is measured
precisely with equal intervals, such as one second, one minute, etc., it can be
viewed as an interval measure in the abstract.

The last scale is __ratio__. This is just like interval, except that
a variable on the ratio scale has a true zero point--a beginning or ending point.
While time in the abstract (no ending or beginning) sense is interval, in
practice time is a ratio scale of measurement since time is usually measured in
lengths or spans which means time does have a starting or ending point. For
example, when timing someone on a task, the length of time required to complete the task
is a ratio measure since there was a starting (and ending) point in the measurement.
One way to identify ratio variables is to determine whether one can
appropriately make ratios from two measurements. For example, if I measure the
time it takes me to read a passage, and I measure the length of time it takes
you to read the same passage, we can construct a ratio of these two measures. If
it took me 30 seconds and took you 60 seconds, it took you (60/30 = 2) twice as
long to read it. One cannot form such mathematical comparisons with nominal,
ordinal, or interval data. Note that the same can be done with counting
variables. If I have 15 items in my pockets, and you have 5, I have three times
as many items as you (15/5 = 3).

For most purposes, especially in education, the distinction between interval and ratio is not important. In fact, it is difficult to find examples of interval or ratio variables in education.

Below is a table that specifies the criteria that distinguishes the four scales of measurement, and the following table provides examples for each scale.

Scales |
Criteria |

Nominal | categories |

Ordinal | categories, rank |

Interval | categories, rank, equal, interval |

Ratio | categories, rank, equal, interval, true zero point |

Scales |
Examples |

Nominal | types of flowers, sex, dropout/stay-in, vote/abstain |

Ordinal | socioeconomic status (S.E.S.), Likert scales responses, class rank |

Interval | time in abstract (see discussion above), temperature |

Ratio | age, weight, height, time to complete a task |

**Classification of Variables**

In research it is often important to distinguish variables by the supposed or
theoretical function they play. For example, if one states that a child's intelligence
level influences the child's academic achievement in school, then the variable
intelligence thought to have some impact, some effect on academic performance in school.
In this example, intelligence is called the __independent__ variable and academic
achievement is the __dependent__ variable. The logic here holds that achievement
depends, to some degree, upon intelligence, hence it is called a dependent variable. Since
intelligence does not depend upon achievement, intelligence in this example is referred to
as the independent variable.

Here are two methods for identify8ing independent variables (IV) and dependent variables (DV). First, think in terms of chronological sequence--in terms of the time order. Which variable comes first, one's sex or one's achievement in school? Most would answer that one is born with a given sex (female or male), so it naturally precedes achievement in school. The variable that comes first in the time order is the IV and the variable that comes afterwards is the DV.

A second method for identifying the IVs and DVs is the ask yourself about the notion of causality. That is, if one does this with variable A, then what happens to variable B? For example, if one could increase intelligence, then achievement in school may result. But, if one increased achievement school, would this have any logical impact on one's intelligence? In this example, intelligence is the IV because it can affect achievement in school, and achievement is the DV because it is unlikely to affect intelligence.

Alternative labels for IV are __cause__ and __predictor__, and other labels for
the DV are __effect__ and __criterion__.

Often it can be difficult to properly identify whether a variable is nominal, ordinal,
interval, or ratio. A simpler approach is to identify variables as either __qualitative__
(or __categorical__) or __quantitative__ (or __continuous__). A
qualitative/categorical variable is one that has categories that are not ranked--i.e., a
nominal variable. All other variables have categories that can be ranked, therefore the
categories differ by degree. These variables are quantitative or continuous, and are
represented by the ordinal, interval, and ratio scales.

For simplicity, variables that have only two categories, even if they can be ranked, will be referred to as qualitative variables since this will be important later when determining which statistical tests may be used for analysis.

**Practice Exercise**

Here is a practice exercise to help you distinguish between IV and DVs. Using the same practice exercise for IVs and DVs, also determine whether each IV and DV is qualitative or quantitative. To make these determinations, sometimes there will not be enough information about the measurement process--how the variables were actually measured. In these cases, it is important to consider the variable carefully to determine if the variable logically has ranked categories or not. If it appears to have ranked categories, then classify the variable as quantitative. See illustrated examples in the practice exercise for further clarification of this issue.

**Supplemental Reading**

Dr. Jacqueline McLaughlin, Assistant Professor of Biology, and Jane S. Noel, Instructional Development Specialist, of Penn State University provide useful information on variables.

http://www.lv.psu.edu/jxm57/irp/var.htm

Wikipedia entry on scales of measurement (note IQ is identified as interval here; this entry is questionable)..

http://en.wikipedia.org/wiki/Level_of_measurement

Ronald Mayer of San Fransico State University also discusses measurement.

http://online.sfsu.edu/~psych200/unit13/133.htm

Wadsworth provides a nice multi-page discussion of scales of measurement.

Copyright 2000, Bryan W. Griffin

Last revised on