Mathematical Correlation Doesn’t Mean Cause and Effect
A. Causal Relationship: A causal relationship is a relationship in which one thing causes another thing to
happen or change.
Note1: A correlation or association between two variables does not mean that a cause and effect relationship is
present. But the reverse is true: Causation implies strong association aka high r2.
B. Cause and Effect Association: A causal relationship in which a change in the independent variable will
directly produce an effect in the dependent variable
Examples:
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Coffee consumption and bathroom breaks
Price of gas and bicycle sales
Movie attendance and average daily rainfall amounts
Increase production line speed, increase number of units produced
Deposits increase savings account balance
C. Reversal Cause and Effect Association: A causal relationship in which a change in the dependent variable
will directly produce an effect in the independent variable. This is a Cause and effect relationship in which the
dependent and independent variables have been reversed (often not intentionally).
Examples:
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Flooding and average daily rainfall amounts (flooding does not cause the rain!)
Children’s height and age (being tall does not make you older!)
BMI and hours of exercise (having a low BMI does not cause you to exercise more.)
Cancer causes smoking (reversed cause and effect variables.)
D. Common Cause Relationship: A causal relationship in which simultaneous changes in two variables (x & y)
are due to changes in a third variable (z). Z is the independent variable (aka lurking variable) where x and y are
both dependant variables of z.
Examples:
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Price of cat food and the price of cafeteria food (the cost of meat increasing would be the common cause)
Proportion of recycled household material and electricity consumption (environmental attitudes are the
common cause)
Price of French wine in Canada and the price of Russian caviar in Canada (shipping costs could be the
common cause)
Ice cream consumption and the number of drowning (correlation is due to heat: More sales and swimming.)
E. Accidental Relationship: A situation where an observed correlation between two variables does NOT signify
any kind of causal relationship between the variables. In spite of a high r2 value, it is an accident or coincidence!
Examples:
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Number of reality TV shows and number of females in engineering programs (no causal connection)
Birth rate and the price of gas (unrelated factors…or are they in fact linked?...more data needed…)
The inflation rate and I-pod touch sales (inelastic product)
Ozone levels and cell phone use (strong, negative, linear correlation, yet they are unrelated…)
F. Presumed Relationship: A correlation does not seem to be accidental even though no cause-and-effect
relationship or common-cause factor if apparent.
Examples:
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People’s level of fitness and the number of adventure movies they watched
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Students who are strong in Math and students who are strong in Science
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Students who are strong in English and students who are strong in History
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Relationship between people who exceed the speed limit and people who watch Fast & Furious movies
For example, you might expect to see a strong positive correlation between term marks and final
examinations
results for students in your class because both of these variables are affected by each student’s aptitude and
study habits. However, there are extraneous factors that could affect the examination results, including the
time each student has to study before the examination, the individual examination schedules, and varying
abilities to
work well under pressure.
Control Groups
Example 2: 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
divides
the volunteers into two groups, each with an equal number of moderate and heavy smokers. One group is
given
nicotine patch with the new drug, while the second group uses ordinary nicotine patches. Fourteen people in
the
first group quit smoking completely, as do nine in the second group.
a) Identify the experimental group, the control group, the independent variable, and the dependent variable.
Experimental Group- Control Group Independent Variable Dependent Variableb) Can the researcher conclude that the new drug is effective?
c) What further study should the researcher do?
In order to reduce the effect of extraneous variables, researches often compare an experimental group
(group with new drug in ex 2) to a control group (group with old drug in ex 2). These two groups should be
as similar as possible so that extraneous variables will have approximately the same effect on both groups
(both groups had an equal number of moderate and heavy smokers). The researchers vary the independent
variable (the new drug) for the experimental group but not for the control group (old drug). Any difference in
the dependent variables (number who quit) for the two groups can then be attributed to the changes in the
independent variable