**Chapter 3.4 **

Dependent
Variables 1:

Operational Definition and

Level of Measurement

**Chapter 3.4**

Dependent Variables 1:

Operational Definition and

Level of Measurement

Dependent Variables 1:

Operational Definition and

Level of Measurement

**Objectives:**

For any research article, be able to identify the dependent variables (outcome measurements or data). For each, indicate the:

- Conceptual variable
- Operational definition
- Scale (Level) of Measurement

Remember
the variable?

As we said earlier, a variable is a characteristic or feature that varies, or changes. It's opposite is a constant: something that doesn't change. We have talked about the independent variable, the one that differs between groups to be compared. Now we will discuss dependent variables, which are the measurements taken from each subject: the data. These are variables because each subject potentially will have different scores. As with independent variables, whether or not something is a variable or constant will depend upon the particular study. (Back to top)

Dependent
Variables

The outcome variable
measured in each subject, which may be influenced by manipulation of the
independent variable is termed the **dependent variable**. In the example
of quadriceps strengthening, the strengthening protocol used is the independent
variable, and the maximal torque generated isometrically on an isokinetic
dynamometer by the quadriceps muscles is the dependent variable.

Once a basic purpose
or concept of a research project has been established, it is important
to establish the variables that will be studied. Variables are the observable
characteristics or events that assume a range of values during the research.
First the experimenter establishes conceptual variables. Dependent variables
are the outcome measures taken. **Conceptual
variables are the ideas of what needs to be measured. **

For instance,
an investigator may want to measure changes in strength. Strength would
be the conceptual variable. What exactly is strength and how can
it be measured? To answer that question the conceptual variables needs
to be defined in specific measurable terms. **Redefining a variable in
terms of specific, measurable terms is called operationalizing a variable.** The **operationally defined** variable for strength could be maximal
torque generated isometrically on an isokinetic dynamometer by the quadriceps
muscles. Or strength could be defined as the maximum amount of weight
that could be lifted 3 times, or the number of pounds of force that could
be pressed onto a scale. So, this same conceptual variable could be measured
many different ways. In a study, the authors will give the **operational
definition** of the variable that they think is best suited to their
needs.

## Operational Definition

The **operational
definition** of a variable is the specific way in which it is measured
in that study. Another study might measure the same conceptual measure
differently. If you were studying ways of
helping people stop smoking, smoking cessation would be an outcome measure
(dependent variable). You could measure smoking cessation as a person
not smoking a cigarette for 1 month, or as a person who has not smoked
in a year, or a 50% reduction in the number of cigarettes smoked. Clearly
the operational definition of the dependent variable is an important step
in the design of the study. Some
other health related conceptual variables that have many operational definitions:
intelligence, fitness, health, quality of life. Several questionnaires
have been developed to measure these conceptual variables. In a research
article, the operational definition is usually found in the methods section.

In the next chapter, we will further discuss the reliability (consistency), and the validity (accuracy) of operational definitions.

## Scales (or Levels) of Measurement

Levels of measurement of the dependent variable indicate the precision of the measurement. There are 4 levels of measurement: 1) nominal, 2) ordinal, 3) interval and 4) ratio. Interval and ratio data together are also called metric. The level of measurement of the dependent variable is one factor that determines the choice of statistical tests that can be used to analyze the data.

In nominal measurement, the score for each subject is placement into one of two or more categories. These categories are mutually exclusive so a single subject cannot fall into more than one category. Most commonly, nominal data are frequencies or counts of the number of subjects or measurements which fall into each category. Examples of nominal level of measurement include categories such as male/female, hair color, or institutionalized elders/community dwelling elders. This is sometimes termed discontinuous data because each category is discrete and there is no continuity between categories. There is also no implied order in these categories. Despite common myth, one cannot say that blond hair is better or greater than brown hair, black hair or red hair.

An example of a nominal dependent variable: A study done to determine the effectiveness of a new patch to help smokers stop smoking. The outcome measure is smoking status. Each subject falls into one of two categories: smoking or not smoking, or quit and not quit. Another example would be a study to determine whether the incidence of heart attack is different between men and women in Georgia. Each subject is placed and counted in one of two categories: presence or absence of heart attack. A key word that indicates use of the nominal scale is "incidence." If a study measures the incidence of something, it must count the occurrences of that event - and each subject is either a count or no count - so the measure is nominal.

In ordinal measurement, each subject's score is also a discrete measure or category. However, unlike nominal data, there is a distinct and agreed upon order of these groups, categories. The order of this data is symbolized with the use of numbers, but there is no implication of equal intervals between the numbers. For instance in the calculation of a grade point average, grades are designated as A=4, B=3, C=2, D=1 and F=0. Although all students would agree that an A is better than a C, there is no implication that an A is exactly twice as good as a C. Likewise, you cannot add 2 Cs together to get an A. In the case of the smoking study described above, an ordinal measure could be used by asking each subject whether he/she smoked more, less or the same this week as compared with last week. There would be three possible scores for each subject, in a rank order: more is more than same, but you can't tell how much more.

In metric measurement, each subject's score is a number that can be an integer or a fraction. Interval data are continuous data ordered in a logical sequence. Because interval data are continuous, there are equal intervals between all of the numbers and intervening numbers have a meaningful value. Basic algebraic calculations can be done to represent relationships between values.

From lowest to highest

- Nominal: subjects scores are a few named categories
- Ordinal: subjects scores fall into a few categories that can be ordered
- Metric: subjects scores are real numbers with equal intervals

So what measurement level should be used?

First, some variables are inherently nominal in nature. For example, when we need to know subjects' gender or state of residence, nominal data is the natural choice.

Second, many novice researchers overuse the ordinal scale. Better to use a carefully constructed standardized test which measures at the interval level than rank ordering. Two reasons for this are: (Back to top)

- Measuring at the interval level gives you more information because it tells you by how much measures differ.
- Can use more powerful types of analyses when you measure at the interval rather than the ordinal level.

The choice between interval and ratio depends solely on whether it is possible to measure with an absolute zero. When it is possible, we usually do so. For the purposes of statistical analysis, interval and ratio data are treated in the same way.

### An Example Analysis of Variables from the title
of a study:

Water aerobics reduced the intensity of low back pain in pregnant
women.

From this title
alone, you can tell that the **independent variable** is type of exercise
( with 2 or more levels, water aerobics and no water aerobics or some
other type of exercise or control group). The independent variable was
active (for them to conclude that it was the water aerobics that reduced
(i.e., caused the reduction) of low back pain., and subjects were randomly
assigned to one of the groups (This also inferred from the causal conclusion
- should be checked in the text). The groups being compared are two separate
groups of individuals, so they are independent, not paired. However, both
groups were likely compared in a pretest and post-test of low back pain
intensity to assess change, and this independent variable (time of testing)
is a repeated measure. The **dependent variable** was low back pain.
Note that this statement in the title gives you the conceptual variable.
The methods section will tell you the operational definition, that is,
how they low back pain intensity. Although it is possible to measure pain
on a nominal scale (do you have pain or not?). It is more common to assess
pain on an ordinal scale, such as a 1-10 scale. The scale of measurement
depends upon the operational definition.