Chapter 3 – Statistics of Two Variables

3.4 Cause and Effect and

3.5 Critical Analysis

Cause and Effect Relationships

• 5 Main Types– Cause and Effect– Common-Cause Factor– Reverse Cause-and Effect – Accidental Relationship– Presumed Relationship

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

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.

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

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

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

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

How Do We Reduce Extraneous Variables?

• Compare an experimental group to a control group– These two groups should be as similar as possible

Sample Size and Technique

• Use larger samples whenever possible (larger samples = better analysis)

• Small samples are greatly affected by outliers

Detecting a Hidden Variable

• An extraneous variable that is difficult to recognize

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?