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)