5E Correlation and Causation

A correlation exists between two variables A and B, when

- higher values of A consistently go with higher values of B, positive correlation.
- higher values of A consistently go with lower values of B, negative correlation.

strength of the correlation: the more closely two variables follow the general trend. In a perfect correlation, all data points lie on a straight line.

The following exercises list pairs of variables.
State possible measurement units for the variables.
Are the variables correlated?
If yes, positively or negatively?
Is the correlation strong or weak?

height and weight:

price and demand
altitude on a mountain hike and surrounding air temperature
weigth of a car and price of car

scatter diagram: each point represents the values of 2 variables.

exercise 9

guidelines for establishing causality:

effect is correlated with suspected cause, while other factors vary
group includes (doesn't include) suspected cause - effect present (absent)
larger amount of suspected cause -> larger amount of effect
if effect has several possible causes, test by eliminating all but one cause and see if the effect is present
if possible, test the suspected cause with an experiment. If the test cannot ethically be performed on humans, consider doing it with cell cultures, or computer models.
try to determine the physical mechanism by which the suspected cause produces the effect.

possible explanations for a correlation:

coincidence
both variables might be directly influenced by some common underlying cause.
one of the variables might cause the other.

Are the phenomena correlated? Positively or negatively? Strongly or weakly? State the correlation clearly.
Then state whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause.

In one US city, the crime rate increased at the same time that the number of people in prison increased
Sales of tea in a local restaurant are positively correlated with ticket sales at the local swimming pool.
You are trying to identify the cause of late afternoon headaches that plague you several days each week. For each of the following observations , explain which of the six guidelines for establishing causality you used and what you concluded:

the headaches only occur only on days that you go to work.
if you stop drinking Coke at lunch, the headaches persist.
in the summer the headaches occur less frequently, if you open the windows of your office slightly. The occur even less often, if you open your office window fully.

Broad levels of confidence in causality:

possible cause: there is a correlation, but one cannot determine whether correlation implies causality (=> start investigation)
probable cause: good reason to suspect that correlation involves cause (=> warrant for search or wiretap)
cause beyond reasonable doubt: found a physical model that is so successful in explaining how one thing causes another that doubting the causality would seem unreasonable (=> usual standard for conviction)

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