Transcript Correlation

Correlations
The invalid assumption that correlation
implies cause is probably among the
two or three most serious and common
errors of human reasoning.
Stephen J. Gould
Biologist
Diet Soda and Heart/Stroke Risk
Diet Soda and Heart/Stroke Risk
Definition of Terms
• Correlation: A measure of the strength of
the relationship between two variables.
(Think “predictive power.”)
- Strength: 0 to 1
- 0 indicates no relationship (no predictive
power)
- 1 indicates a perfect relationship (perfect
predictive power)
- Direction: Positive (+) or negative (–)
Scatterplot Example (with outlier)
Correlation Coefficient Estimation
Straight Line
Corn on the Cob
Football
Circular
1.00
0.75
0.50
0.00
Up & Right
Down & Right
Positive
Negative
An outlier will move the
correlation coefficient
closer to zero.
Beware: Correlation = 0.816 for All
Correlations: So What?
• It’s all about predicting one variable given
another. That’s useful all by itself.
• Correlations don’t provide evidence of a cause
and effect relationship, but they are often
interpreted that way.
• The best way to establish a strong argument for
a cause and effect relationship is through
experimentation (manipulating one variable to
see its effect on another—while holding all other
variables constant).
Correlations: Application
• You’re a Peace Corps Volunteer in an African
village and you’re responsible for dispensing a
drug called Praziquantel. It is a drug given to
children for treatment of schistosomiasis—the
second most socioeconomically devastating
disease after malaria.
• The dose for each child depends on their body
weight: 40mg of Praziquantel per kilo.
• Unfortunately, there are no scales in the village
where you are working. What can you do?
Correlations: Hint
Correlations: Solution
“Height poles (Tablet Poles)
have been constructed, made of
straight lengths of hard-wood,
to measure the height of each
child. The poles are marked to
show the correct number of
Praziquantel tablets, to the
nearest half tablet, that should
be given for each child,
depending on their height.”
http://www.schoolsandhealth.org/sites/PChild/Pages/TabletPoleforPraziquantel.aspx
HOD1700 Exam Score Predictions
HOD1700 Exam Completion Time
Correlation: Example 1
Correlation: Example 2
Correlation: Example 3
In-Class Exercise
“It’s such a fine line between clever and stupid.”
– David St. Hubbins (Spinal Tap)
Propose a Causal Relationship
• You will be given 18 graphs of trend data
– 9 where something is increasing over time
– 9 where something is decreasing over time
• If you were to plot any one of these
datasets against any other, you would find
a large correlation (positive or negative).
• Your job is to propose a plausible cause
and effect relationship between any two.
Unemployment in Franklin, TN
Home Completions in Franklin, TN
Correlation Between the Two