Chapter 3 – Statistics of Two Variables

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Presentation transcript:

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?

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