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MDM 4UI Classifying Relationships
Classifying Relationships
By virtue of pairing two variables, an association has automatically been created. The
association or relationship may be classified as: cause-and-effect, common cause,
reverse cause-and-effect, accidental or presumed. Moreover, the association does
not have to be linear.
1. Cause-and-effect relationship: A relationship in which a change in the
independent variable (x) produces a change in the dependent variable (y).
Such relationships are sometimes easy to see, especially in the physical processes.
However, often they are difficult to prove!
Examples of those from the physical processes:
There is a cause-and-effect relationship between the human body temperature
and the amount of water retained. A strong negative linear correlation also
exists.
Human alcohol consumption and level of coordination is a cause-and-effect
relationship.
Impact velocity and the distance of the object relative to the Earth’s surface
demonstrate a cause-and-effect phenomenon:
The impact velocity of
an object released d units
above the Earth’s
surface, neglecting air
resistance, can be found
2 gd .
by: v
(Acceleration due to
gravity is a constant g =
9.8 m/s2)
MDM 4UI Classifying Relationships
2. Common-cause relationship: A relationship in which an external variable (z)
causes two variables to change.
Examples:
The revenue from admissions to the local public beach and the local tomato
harvest.
The number cell phones in a country and the country’s life expectancy:
3. Reverse cause-and-effect relationship: A relationship in which the independent
and dependent variables are reversed in a study and a (new) cause-and-effect
relationship is established.
Example:
The general (average) amount of traffic in a city has a cause-and-effect and a
reverse cause-and-effect relationship with the general number of roads built. It
also bears a strong positive correlation.
MDM 4UI Classifying Relationships
4. Accidental relationship: A relationship between two variables that has a
correlation, but it is entirely by coincidence.
Example:
A strong positive correlation exists between students’ marks in Kitchener high
schools and the city’s air quality index.
5. Presumed relationship: It is likely that a cause-and-effect relationship exists
between two variables x and y, between z and y, or even between both x and z on y, but
it is difficult to prove. A relationship is deemed presumed when several factors (such
as x and z) can be “at work” and it is difficult to prove how they create the response
(y). A fishbone diagram may help identify the factors “at work”: x and z (to be
discussed later).
Example:
There is a positive correlation between the earth’s average air temperature and
the concentration of CO2 (carbon dioxide) in the atmosphere.
Remember: (Linear) Correlation does not imply causation.
A correlation between a predictor variable x and a response variable y, even if it
is very strong, is not by itself enough evidence that changes in x actually cause
changes in y.
MDM 4UI Classifying Relationships
Practice Question #1:
Classify each relationship. Provide a brief explanation.
a) The price of butter and price of motorcycles has a strong positive correlation over
many years.
b) The rate of a chemical reaction decreases as temperature decreases.
c) A moderate positive correlation exists between students’ English marks and their
interest level of video games.
Lurking Variables
An extraneous factor, (z) has an effect on the independent variable, the dependent variable,
or both. This extraneous variable is known further as a lurking (or hidden) variable when it
is very difficult to recognize.
A common cause factor is a type of extraneous variable. Extraneous variables are sometimes
referred to as confounding variables. If an extraneous variable z is identified as causing y to
occur, then a cause-and-effect relationship exists between z and y. Hence, the association
between another variable x, and y is deemed an accidental relationship.
Practice Question #2:
A strong positive correlation exists between exam scores (y)
and term grades (x). Identify several extraneous variables.
MDM 4UI Classifying Relationships
Cause-and-Effect Diagrams
In 1943, Dr. Kaoru Ishikawa invented the cause-and-effect diagram (or fishbone diagram).
This tool is used to identify, explore and display in increasing detail, all of the possible
causes of a problem, and to hopefully flush out the root cause(s) of the problem. The general
structure is as follows:
Practice Question #3:
Create a cause-and-effect diagram for why a student may miss questions on a test.
MDM 4UI Classifying Relationships
A control group is the set of members in a study for which the independent variable is held
constant. This contrasts the experimental group, which is the set of members for which the
independent variable is varied. For example, if a study is done to measure the effects of a
new method of learning math, the control group would learn math using the traditional
method and the experimental group would learn via the new method.
Practice Question #4
A medical researcher wants to test a new drug believed to help smokers overcome the
addictive effects of nicotine. Fifty people who want to quit smoking volunteer for the study.
The researcher carefully divided the volunteers into two groups, each with an equal number
of moderate and heavy smokers. One group is given nicotine patches with the new drug,
while the second group uses ordinary nicotine patches. Fourteen people in the first group quit
smoking completely, as do nine people in the second group.
a) Identify the independent variable, dependent variable, control group and experimental
group.
b) Can the researcher conclude the new drug is effective?
MDM 4UI Classifying Relationships
A double blind study is a study where neither the patient nor the physician knows whether
the patient is receiving the treatment of interest or the control treatment. It is the most
rigorous in clinical research design because, in addition to the randomization of subjects
which reduces the risk of bias, it can eliminate the placebo effect.
MDM 4UI Classifying Relationships
Problem Set
Day One
1. For each pair of variables, classify the dominant relationship, and provide a brief explanation of your
choice. Assume a positive linear correlation exists, and the first variable listed is the independent
variable.
a) score on a physics exam, score on a calculus exam
b) population of rabbits, inflation in an economy
c) a person’s “Energy drink” consumption, stress hormone secretion
d) smoking, lung cancer
Final answers are at the bottom of this sheet.
2. Page 200 #2, 3, 5, 6, 7 (note: for #5 the text fails to classify the relationship in the Answers section.
What type of relationship is it?). Remember to always compare your answers with those in the
text’s Answers section.
Day Two
3. Page 200 #4 (do all of 4, but for a) create a fishbone diagram too!), 8, 9, 10, 11 (use EXCEL).
Remember to always compare your answers with those in the text’s Answers section.
Answers for #1:
The ONLY answers possible are:
a) common cause (factor: similar mathematical/scientific skills are required)
b) accidental (purely a coincidence)
c) cause-and-effect (the more caffeine, the more they are secreted, which leads to a short
charge of alertness followed by agitation and eventually tiredness and hunger….this of
course may lead to weight gain too!)
d) presumed (several factors are at work and it is difficult how they create the body to
produce cancerous cells).