CHAPTER 3
A Closer Look at Assumptions
1
!is is an advanced "apter.
Please ask questions#
CASE STUDY 1: CLOUD SEEDING
Cloud seeding to increase rainfall (randomized
experiment)
52 cumulus clouds
At random 26 were seeded and 26 were controls
Experimenter a
Chapter 1
Drawing Statistical Conclusions
Statistical Sleuthing
Carefully examining data to answer
questions of interest (Ramsey and S!afer)
Estimating the unobservable things of
science
What is an example of an unobservable thing of
science?
Answer: th
M arch 7, 2011
We can possibly resubmit exam the take home part. Due F riday.
Take Home Exam
General
If there is output but not verbiage then there is no points.
We have to wri te down. Less output is better. Only give output that is very
i mportant.
P ro
M arch 3, 2011 Thursday
Regression
yi= 0+ 1xi+ i
i ~ N ( 0, 2)
Assumptions:
1.
2.
3.
4.
Normal distribution
Constant Variance
Independence
Correct Form
Fit X by Y /
F it polynomial / 2, quadratic
First thing you should do after fi tt ing, Polynomial fi t
Feb 24 2011
Homework for Chapter 6 due Wednesday
Will do JMP today.
Chapter 5 summary
Dealt with the f-test, which as used for full and reduced model. ANOVA.
Anova addresses the question: are the means all the same or are they different?
Comparison of > 2
2 17 2011
Case Study 0502
Multiple means f-test ANOVA
Full model everything is there
Reduced model group things together that answer another question
FULL MODEL:
Separate Means model case 0502, seven total groups
REDUCED MODEL:
Two Groups (Spock vs. other
2/10
Chapter 4 stuff today
Test Review as well
Are You Watching This?! Sports
Df
= n1 - 1 + n2 ?
S2p
= (n1 1)*st.dev.1^2 + (n2 -1)*(st.dev2^2)/df Pooled Variance
sp
= Sq Root (s2p)
t
= (X1 X2) / [sp * Sq.root (1/n1) + (1/n2)]
e rror
P value <
P value >
=
F or R IG H T NOW: non-parametr ic means ranks.
Chapter 5.
Concepts are similar but there are things to take advantage of, new questions
to ask, ad some new things to worry about.
Analysis of Variance: ANOVA:
D ifferences in Means.
T wo Sample T-test / AN
Comparisons Among Several
Samples
Stat 511 Chap 5
Stat 511 Chap 5
1
Purpose of this chapter
s
s
s
s
In the previous chapters we compared two groups
In chapter 5 we compare 3 or more groups.
Concepts are similar, but there are things to take
advantage of,
Alternatives to the t-Tools
Stat 511 Chap 4
Stat 511 Chap 4
1
Case Study 1: O-Ring Failures
Stat 511 Chap 4
2
Case Study 1: O-Ring Failures
Stat 511 Chap 4
10
5
0
1
2
3
2
1
1
2
Count
15
3
Count
observational study
s highly unbalanced
s far from normal
s a
A Closer Look at Assumptions
Stat 511 Chapter 3
Cloud Seeding Experiment
Case Study 1
Cloud seeding to increase rainfall
(randomized experiment)
52 cumulus clouds
At random 26 were seeded and 26 were
controls
Experimenter and pilot were blind to the
Inference Using t-Distributions
Chapter 2
511 Chap 2
1
Bumpus Data - Case Study I
Humerus length of adult sparrows in 1898
s 2 groups: perished, survived (after a storm)
s surviving sparrows were stressed
s unequal group sizes (24 and 35)
s observational
Drawing Statistical
Conclusions
Chapter 1
Stat 511 Chap 1
1
Statistical Sleuthing
carefully examining data to answer questions
of interest (Ramsey and Schafer)
l estimating the unobservable things of
science
l What is an example of an unobservable
thing
Alternatives to the t-Tools
Stat 511 Chapter 4
Case Study 1: O-Ring Failures
Observational study
Highly unbalanced
Far from normal
Apparently unequal standard
deviations and larger sample
is associated with smaller
standard deviation
Case Study 2: Cogniti