Transcript Making Comparisons

Making Comparisons
• All hypothesis testing follows a common logic
of comparison
• Null hypothesis and alternative hypothesis
– mutually exclusive
– exhaustive
• Experimental design and control group
• “Republicans have higher income than
Democrats”?
Methods of Making Comparisons
Independent Variable
Categorical
Continuous
measures
measures
(nominal or
(interval or ratio)
ordinal)
Categorical
Cross-Tabulation &
measures
(Chapter 10)
(Chapter 7) Chi(nominal
Logistic Regression
square
Dependent or ordinal)
Variable Continuous
Compare Means &
(Chapter 8)
measures
(Chapter 9)
Correlation &
(interval or
Dummy Variables Linear Regression
ratio)
Cross-tabulation
• Relationship between two (or more) variables
– Joint frequency distribution
– Contingency table
• Observations should be independent of each
other
– One person’s response should tell us nothing
about another person’s response
• Mutually exclusive and exhaustive categories
Cross-tabulation
• If the null hypothesis is true, the independent
variable has no effect on the dependent
variable
• The expected frequency for each cell
Male
Female
Total
Pro-
?
?
20
Anti-
?
?
80
Total
50
50
100
Expected Frequency of Each Cell
• Expected frequency in the ith row and the jth
column ……… (Eij)
• Total counts in the ith row ……… (Ti)
• Total counts in the jth column ……… (Tj)
• Total counts in the table ……… (N)
Inferences about Sample Means
• Hypothesis testing is an inferential process
• Using limited information to reach a general
conclusion
• Observable evidence from the sample data
• Unobservable fact about the population
• Formulate a specific, testable research
hypothesis about the population
Null Hypothesis
• no effect, no difference, no change, no
relationship, no pattern, no …
• any pattern in the sample data is due to
random sampling error
Errors in Hypothesis Testing
• Type I Error
– A researcher finds evidence for a significant result
when, in fact, there is no effect (no relationship) in
the population.
– The researcher has, by chance, selected an
extreme sample that appears to show the
existence of an effect when there is none.
– The p-value identifies the probability of a Type I
error.