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,
19-month-old rats (equivalent to 60-year-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 skills tests. Although all supplemented rats showed
improvement, those supplemented with blueberry powder showed
the most notable improvement.
1. What is the independent variable? (dietary supplement: none, blueberry, strawberry, and spinach)
2. What are the dependent variables? (memory test and motor skills
test)

Example #2: Does beta-carotene protect against cancer? Beta-carotene 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 beta-carotene
supplement or a placebo,
and their health was studied over their lifetime. Cancer rates
for women taking the beta-carotene supplement did not differ systematically
from the cancer rates of those women taking the placebo.

1. What is the independent variable? (supplements: beta-carotene
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 brakes)

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 variables 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. 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.