Stat 301 – Day 9
Fisher’s Exact Test
Quantitative Variables
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
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?
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
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)
Quiz 6
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?
Big Picture
Do it all again! Compare groups on a quantitative response
variable Graphical summaries Numerical summaries Statistical significance Scope of conclusions
Investigation 2.1.1 (p. 102)
Match the histogram with the variable (“Probability and Statistics for Engineers and Scientists”)
Most important – your justifications
Stat 301 data
Stat 301 data
The moral: Try to anticipate variable behavior/explain patterns and deviations from patterns
Investigation 2.1.2
Investigation 2.1.2
Aside: History of Statistics and Agriculture www.nass.usda.gov/About_NASS/History_of_Ag_Statistics/
Investigation 2.1.2
(a) Experiment or observational study?
Imposed seeding/unseeded
Experimental units?
clouds
(b) Explanatory and response variable?
Investigation 2.1.2
Center Spread Shape Unusual observations
rainfall
treatm
ent
280024002000160012008004000
seeded
unseeded
Always label!!!
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
Graphical and numerical summaries Five number summary
Median = (41.1+47.3)/2 = 44.2
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
Boxplots
936.4IQR 1.5IQR
Boxplots
164.6
442
23% of data lie above mean
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)
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