Today:
- Return Quiz over 9.1-9.3
- p-value < .05 means reject null....
- Next test is next week! It will cover section 8.2 through 10.2/3 -- the F test
- Questions in preparation for the exam?
- Section 10.2: the F test
- Analysis of Variance (ANOVA) F-test: A comparison of
k population means (p. 403)
Decision rule: Accept Ha if p-value <
Test Statistic:
- Conditions of using an F-test (p. 404):
- Completely randomized design to collect the k samples
- All k populations are normally distributed
- All k populations have the same (unknown) standard
deviation
Even so, ANOVA is robust -- even if some of the conditions
above aren't met, it's liable to produce reasonable p-values.
- The F-distribution
- Is skewed right:
- Calculation requires knowing degrees of freedom, numerator
and denominator -- yikes!;) You won't have to worry
about this if you use technology.... The curves above
correspond to different pairs of df, and the .05
rejection region.
- Large values of F signify that it's unlikely that the
means are the same (reject the null!). As you can see,
p-values are in the tail area:
- Examples:
- Example 10.2, using StatCrunch: http://www.nku.edu/~statistics/data/exam10-02.xls
- M&Ms and the F-test
- #1, p. 413: http://www.nku.edu/~statistics/data/c10s02e01.xls
- A t-test is equivalent to an F-test (gives the same p-value): #6, p. 341 (http://www.nku.edu/~statistics/data/c09s02e06.xls)
- Section 10.3: Multiple Comparisons
- The F-test indicates that there is at least one pair of means that
differ: what now? Multiple comparisons....
- We do a t-test on each pair (see page 417), although you won't be
required to do these. The analysis table will be presented, as
in the following example.
- Example: #2, p. 413 (with handout):
http://www.nku.edu/~statistics/data/c10s02e02.xls
- Important point: the more tests (comparisons) that are carried
out, the more likely that one will be significant by
chance (probability of a type I error)
- Section 12.1: Comparing two qualitative variables: the chi-square test
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