1. Chapter 3 – Statistics of Two Variables
3.4 Cause and Effect
and
3.5 Critical Analysis

2. Cause and Effect Relationships
5 Main Types
Cause and Effect
Common-Cause Factor
Reverse Cause-and Effect
Accidental Relationship
Presumed Relationship

3. Cause-and-Effect Relationship
A change in the independent variable, x, produces a change in the dependent variable, y
Example:
Hours spent studying and your score on a test

4. Common-Cause Factor
An external variable causes two variables to change in the same way
Example:
A town finds that its revenue from parking fees at a public beach each summer correlated with the local tomato harvest
It is unlikely that the parked cars at the beach have any effect on the tomato crop
Good weather is a common-cause factor that increases both tomato crop and number of people at the beach.

5. Reverse Cause-and-Effect
The dependent and independent variables are reversed
Example:
You find that the longer you stay awake, the more coffee you drink but in reality the more coffee you drink the longer you stay awake

6. Accidental Relationship
A correlation between two variables by random chance
Example:
A positive correlation between the number of females enrolled in an engineering undergraduate program and the number of reality shows on TV

7. Presumed Relationship
A correlation does not seem to be accidental even though no cause-and-effect factor is apparent
Example:
A positive correlation between leadership skills and academic performance

8. Extraneous Variables
Determining the nature of a causal relationship can be further complicated by extraneous variables
Affect/obscure the relationship between an independent and dependent variable
Example:
You might expect a strong positive correlation between term marks and final exam marks
Extraneous factors; time studying for the exam, exam schedule, ability to work under pressure, etc.; impact the exam mark

9. How Do We Reduce Extraneous Variables?
Compare an experimental group to a control group
These two groups should be as similar as possible

10. Sample Size and Technique
Use larger samples whenever possible (larger samples = better analysis)
Small samples are greatly affected by outliers

11. Detecting a Hidden Variable
An extraneous variable that is difficult to recognize

12. Questions to Keep in Mind When Analyzing Data
Is the sampling process free from intentional and unintentional bias?
Could any outliers or extraneous variables influence the results?
Are there any unusual patterns that suggest the presence of a hidden variable?
Has causality been inferred with only corelational evidence?