STATISTC 111 Chapter 11: Stats Chapter 11 Notes
11.1 Illegitimate Correlations
- Watch out for these problems with correlations:
- Outliers can substantially inflate or deflate correlations
- Groups combined inapporpriately may mask relationships
11.2 Legitimate Correlation Does Not Imply Causation
11.3 Some Reasons for Relationships Between Variables
- Some reasons two variable could be related:
- The explanatory variable is the direct cause of the response variable
- The response variable is causing a change in the explanatory variables
- The explanatory variable is a contributing but not sole cause of the response
variable
- Confounding variables may be responsible for the observed relationship
- Both variables may result from a common cause
- Both variables are changing over time
- The association may be nothing more than coincidence
11.4 Confirming Causation
- Evidence Possible Causation from Observational Studies
- There is a reasonable explanation of cause and effect
- The connection happens under varying conditions
- Potential confounding variables are ruled out
- There is a “dose-response” relationship
Key Concepts
- An outlier in a scatterplot that fits the pattern of the rest of the data will increase the
correlation
- An outlier that does not fit the pattern of the rest of the data can substantially
decrease the correlation, depending on where it falls
- Combining two or more groups in a scatterplot can distort the relationship between the
explanatory and response variable
- It is better to use a separate symbol in the plot to identify group membership
- There are many reasons that two variable could be related other than a direct cause-
and-effect connection
- The most common reason is that there are confounding variables that are related
to the explanatory variable and affect the response variable
- If two variables are both changing consistently over time, they may show a relationship
with each other, even though there is no direct causal association
- Although a direct causal link between two variables cannot to be made based on an
observational study, there are features of the relationship that can help support a
possible causal connection
- These include having a reasonable explanation, observing the relationship under
varying conditions, ruling out potential confounding variables, and finding a dose-
response relationship
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Document Summary
Watch out for these problems with correlations: Outliers can substantially inflate or deflate correlations. Some reasons two variable could be related: The explanatory variable is the direct cause of the response variable. The response variable is causing a change in the explanatory variables. The explanatory variable is a contributing but not sole cause of the response variable. Confounding variables may be responsible for the observed relationship. Both variables may result from a common cause. The association may be nothing more than coincidence. There is a reasonable explanation of cause and effect. An outlier in a scatterplot that fits the pattern of the rest of the data will increase the correlation. An outlier that does not fit the pattern of the rest of the data can substantially decrease the correlation, depending on where it falls. Combining two or more groups in a scatterplot can distort the relationship between the explanatory and response variable.
