Variables
Prerequisites
none
Learning Objectives
 Define and distinguish between independent and dependent variables
 Define and distinguish between discrete and continuous variables
 Define and distinguish between qualitative and quantitative variables
Independent and dependent
variables
Variables are properties or characteristics of
some event, object, or person that can take on different values
or amounts (as opposed to constants such as π
that do not vary). When conducting research, experimenters often
manipulate variables. For example, an experimenter might compare
the effectiveness of four types of antidepressants. In this
case, the variable is "type of antidepressant." When
a variable is manipulated by an experimenter, it is called an independent
variable. The experiment seeks to determine the effect of
the independent variable on relief from depression. In this
example, relief from depression is called a dependent
variable. In general the independent variable is manipulated
by the experimenter and its effects on the dependent variable
are measured.
Example #1: Can blueberries
slow down aging? A study indicates that antioxidants found in
blueberries may slow down the process of aging. In this study,
19month old rats (equivalent to 60year old humans) were fed
either their standard diet or a diet supplemented by either blueberry,
strawberry, or spinach powder. After eight weeks, the rats were
given memory and motor tests. Although all supplemented rats showed
improvement, those supplemented with blue berry powder showed
the most notable improvement.
1. What is the independent variable? (diet: blueberries or no
blueberries)
2. What are the dependent variables? (memory test and motor skills
test)
More information on the blueberry study
Example #2: Does beta
carotene protect against cancer? Betacarotene supplements
have been thought to protect against cancer. However, a study
published in the Journal of the National Cancer Institute suggests
this is false. The study was conducted with 39,000 women aged
45 and up. These women were randomly assigned to receive a betacarotene
supplement or a placebo,
and their health was studied over their lifetime. Cancer rates
for women taking the betacarotene supplement did not differ systematically
from the cancer rates of those women taking the placebo.
1. What is the independent variable? (supplements: betacarotene
or placebo)
2. What is the dependent variable? (occurrence of cancer)
Example #3: How bright is right? An automobile
manufacturer wants to know how bright brake lights should be in
order to minimize the time required for the driver of a following
car to realize that the car in front is stopping and to hit the
brakes.
1. What is the independent variable? (brightness of brake lights)
2. What is the dependent variable? (time to hit brake)
Levels of an Independent Variable
If an experiment compares an experimental treatment
with a control treatment, then the independent variable (type
of treatment) has two levels: experimental and control. If an
experiment were comparing five types of diets, then the independent
variable (type of diet) would have 5 levels. In general, the number
of levels of an independent variable is the number of experimental
conditions.
Qualitative and
Quantitative Variables
An important distinction between variables
is between qualitative
variables and quantitative
variables. Qualitative variable are those that express a
qualitative attribute such as hair color, eye color, religion,
favorite movie, gender, and so on. The values of a qualitative
variable do not imply a numerical ordering. Values of the variable “religion”
differ qualitatively; no ordering of religions is implied. Qualitative
variables are sometimes referred to as categorical
variables. Values on qualitative variables do not imply
order, they are simply categories. Quantitative variables
are those variables that are measured in terms of numbers.
Some examples of quantitative variables are height, weight,
and shoe size.
In the study on the effect of diet discussed above,
the independent variable was type of supplement: none, strawberry,
blueberry, and spinach. The variable "type of supplement"
is a qualitative variable; there is nothing quantitative about
it. In contrast, the dependent variable "memory test"
is a quantitative variable since memory performance was measured
on a quantitative scale (number correct).
Discrete and Continuous
Variables
Variables such as number of children in a household
are called discrete
variables since the possible scores are discrete points on
the scale. For example, a household could have three children
or six children, but not 4.53 children. Other variables such as
"time to respond to a question" are continuous
variables since the scale is continuous and not made up of
discrete steps. The response time could be 1.64 seconds, or it
could be 1.64237123922121 seconds. Of course, the practicalities
of measurement preclude most measured variables from being truly
continuous.
