Stat 301 – Day 9 Fisher’s Exact Test Quantitative Variables.
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Transcript of Stat 301 – Day 9 Fisher’s Exact Test Quantitative Variables.
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Stat 301 – Day 9
Fisher’s Exact Test
Quantitative Variables
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Recap
In analyzing two-way tables, the p-value tells us whether the difference in the group proportions/relative risk could have happened by the random assignment process alone
Simulated the random assignment process to see whether our observed result was extreme
“Fisher’s Exact Test”: Use counting methods to determine the exact probability
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Investigation 1.6.2 (p. 72)
Only 6 of 21 minorities coached at third 24 nonminorities coached at third and 15 at
first How set up two-way table? How define random variable?
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Investigation 1.7.2
Two-way table
successes
Group A
p-value = P(X < 6)
If we let X represent the number of minorities at third, want to find P(X < 6)Hypergeometric with N = 60, M = 30, n = 21
= C(30,6)C(30,15) + … = .0146 C(60, 21)
failures
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Investigation 1.7.2
Two-way table
successes
Group A
p-value = P(X < 6)
If we let X represent the number of minorities at third, want to find P(X < 6)Hypergeometric with N = 60, M = 21, n = 30
= C(21,6)C(39,24) + … = .0146 C(60,30)
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Quiz 6
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Big Picture
Comparing two groups on a categorical response variable Appropriate graphical summary (seg bar graph) Appropriate numerical summaries (conditional
proportions, relative risk, odds ratio) Is the difference statistically significant?
Fisher’s Exact Test: How often get a difference at least this large by the random assignment process alone
Scope of conclusions Cause and effect? Generalize beyond those in study?
Compareresults
Randomized?
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Big Picture
Do it all again! Compare groups on a quantitative response
variable Graphical summaries Numerical summaries Statistical significance Scope of conclusions
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Investigation 2.1.1 (p. 102)
Match the histogram with the variable (“Probability and Statistics for Engineers and Scientists”)
Most important – your justifications
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Stat 301 data
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Stat 301 data
The moral: Try to anticipate variable behavior/explain patterns and deviations from patterns
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Investigation 2.1.2
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Investigation 2.1.2
Aside: History of Statistics and Agriculture www.nass.usda.gov/About_NASS/History_of_Ag_Statistics/
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Investigation 2.1.2
(a) Experiment or observational study?
Imposed seeding/unseeded
Experimental units?
clouds
(b) Explanatory and response variable?
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Investigation 2.1.2
Center Spread Shape Unusual observations
rainfall
treatm
ent
280024002000160012008004000
seeded
unseeded
Always label!!!
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Skip to Minitab detour (p. 110) Course Materials > ISCAM Data Page
Minitab: Chapter 2, Minitab Files, Cloud Seeding.mtw Instructions in text
R: Chapter 2, TXT files, Cloud Seeding.txt Handout
Boxplots Dotplots Descriptive statistics
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Graphical and numerical summaries Five number summary
Median = (41.1+47.3)/2 = 44.2
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Five number summary
UnseededMin=1.0 Q1= 24.4 median=44.2 Q3=163 Max=1202.6
SeededMin=4.1 Q1=92.4 median=221.6 Q3=430 max=2745.6
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Boxplots
936.4IQR 1.5IQR
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Boxplots
164.6
442
23% of data lie above mean
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For Wednesday
Mini-project 1 proposal Finish Investigation 2.1.2 through part (n)
See online solutions, bring questions to class PP 2.1.1 (p. 113)
Combine parts (b) and (g) together (c)-(f) in Blackboard as multiple choice
Investigation 2.1.4 parts (a)-(d) (p. 119-120)