Cause & Effect Relationships
A strong correlation does not always prove that the changes in one variable cause
changes in the other. There are various types and degrees of causal relationships
between variables:
Cause & Effect Relationship – a relationship in which a change in the independent
variable (x) produces a change in the dependent variable (y)
example: increasing the height from which you drop an object increases its impact
velocity
Common-Cause Factor – an external variable that causes two variables to change in
the same way
example: suppose that a town finds that its revenue from parking fees at the public
beach correlates with the local tomato harvest. It is extremely unlikely that cars
parked at the beach have any effect on the tomato crop. Instead, good weather is a
common-cause factor that increases both the tomato crop and the number of people
who park at the beach.
Reverse Cause & Effect Relationship - a relationship in which the presumed
dependent and independent variables are reversed in the process of establishing
causality
example: suppose that a researcher observes a positive linear correlation between the
amount of coffee consumed by a group of medical students and their levels of anxiety.
The researcher theorizes that drinking coffee causes nervousness, but instead finds
that nervous people are more likely to drink coffee.
Accidental Relationship – a correlation between two variables that occurs by random
change
example: the number of females enrolled in engineering programs and the number of
“reality” TV shows have both increased over the past several years. These two
variables have a positive linear correlation, but it is entirely coincidental.
Presumed Relationship – a correlation that does not seem to be accidental, even
though no cause-and-effect relationship or common-cause factor is apparent.
example: suppose you found a correlation between people’s level of fitness and the
number of adventure movies they watched. It seems logical that a physically fit person
might prefer adventure movies, but it would be difficult to find a common cause or to
prove that one variable affects the other.
For each example, specify the type of causal relationship between each of the
pairs of variables:
A strong positive correlation is observed in
a regression analysis between the price of
butter (dependent variable) and the price
of motorcycles (independent variable).
A strong negative correlation is observed
in a regression analysis between ozone
levels (dependent variable) and cell phone
sales (independent variable).
A strong positive correlation is observed in
a regression analysis between the rate of
reaction (dependent variable) and
temperature (independent variable).
A strong positive correlation is observed in
a regression analysis between leadership
ability (measured by the number of times
an individual assumes a leadership role in
extracurricular activities - dependent
variable) and academic achievement
(independent variable).
A strong positive correlation is observed in
a regression analysis between the number
of roads (dependent variable) and the
amount of traffic congestion (independent
variable).
Example
A medical researcher wants to test a new drug believed to help smokers overcome
the additive effects of nicotine. Fifty people who want to quit smoking volunteer
for the study. The researcher divides the volunteers into two groups. One group is
given nicotine patches with the new drug, while the second group uses just the
nicotine patch. Fourteen people in the first group quit smoking completely, as do
nine people from the second group.
a) Identify the experimental group, the control group, the independent and the
dependent variable.
b) Can the researcher conclude that the new drug is effective?
c) What further study should the researcher do?