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Stat 155, Section 2, Last Time. Linear Regression Fit a line to data Least Squares Prediction Residual Diagnostic Plot Producing Data How to Sample? History of Presidential Election Polls. Reading In Textbook. Approximate Reading for Today’s Material: Pages 198-210, 218-225 - PowerPoint PPT Presentation
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Stat 155, Section 2, Last Time
• Linear Regression– Fit a line to data
• Least Squares Prediction
• Residual Diagnostic Plot
• Producing Data
• How to Sample?– History of Presidential Election Polls
Reading In Textbook
Approximate Reading for Today’s Material:
Pages 198-210, 218-225
Approximate Reading for Next Class:
Pages 231-240, 256-257
Common Problem
Adding lines to an Excel Plot
E.g. Textbook problem 2.17
• Plot Data
• Add line with “Add trendline”
• Add line: y = 35+.5x
• Explicitly add least squares fit line
Chapter 3: Producing Data
(how this is done is critical to conclusions)
Section 3.1: Statistical Settings
2 Main Types:
I. Observational Study
II. Designed Experiment
Producing Data
2 Main Types:
I. Observational Study
II. Experiment
(Make Changes, & Study Effect)Apply “treatment” to individuals & measure
“responses”
e.g. Clinical trials for drugs, agricultural trials
(safe? effective?) (max yield?)
Producing Data
2 Main Types:
I. Observational Study
II. Experiment
(common sense)
Caution: Thinking is required for each.
Both if you do statistics & if you need to understand somebody else’s results
Helpful Distinctions(Critical Issue of “Good” vs. “Bad”)
I. Observational Studies:
A. Anecdotal Evidence
Idea: Study just a few cases
Problem: may not be representative
(or worse: only considered for this reason)
e.g. Cures for hiccups
Key Question: how were data chosen?(early medicine: this gave crazy attempts at cures)
Helpful DistinctionsI. Observational Studies:
B. Sampling
Idea: Seek sample representative of population
Challenge: How to sample?
(turns out: not easy)
How to sample?History of Presidential Election Polls
During Campaigns, constantly hear in news “polls say …” How good are these? Why?
1936 Landon vs. Roosevelt Literary Digest Poll: 43% for R
Result: 62% for R
What happened?Sample size not big enough? 2.4 million
Biggest Poll ever done (before or since)
Bias in SamplingBias: Systematically favoring one outcome
(need to think carefully)
Selection Bias: Addresses from L. D.
readers, phone books, club memberships
(representative of population?)
Non-Response Bias: Return-mail survey
(who had time?)
How to sample?1936 Presidential Election (cont.)
Interesting Alternative Poll:
Gallup: 56% for R (sample size ~ 50,000)
Gallup of L.D. 44% for R ( ~ 3,000)
Predicted both correct result (62% for R),
and L. D. error (43% for R)!
(what was better?)
Improved SamplingGallup’s Improvements:
(i) Personal Interviews
(attacks non-response bias)
(ii) Quota Sampling
(attacks selection bias)
Quota SamplingIdea: make “sample like population”
So surveyor chooses people to give:i. Right % male
ii. Right % “young”
iii. Right % “blue collar”
iv. …
This worked well, until …
How to sample?1948 Dewey Truman sample size
Crossley 50% 45%
Gallup 50% 44% 50,000
Roper 53% 38% 15,000
Actual 45% 50% -
Note: Embarassing for polls, famous photo of Truman + Headline “Dewey Wins”
What went wrong?Problem: Unintentional Bias
(surveyors understood bias,
but still made choices)
Lesson: Human Choice can not give a Representative Sample
Surprising Improvement: Random Sampling
Now called “scientific sampling”
Random = Scientific???
Random SamplingKey Idea: “random error” is smaller than
“unintentional bias”, for large enough sample sizes
How large?
Current sample sizes: ~1,000 - 3,000
Note: now << 50,000 used in 1948.
So surveys are much cheaper
(thus many more done now….)
Random Sampling
How Accurate?
• Can (& will) calculate using “probability”
• Justifies term “scientific sampling”
• 2nd improvement over quota sampling
And now for something completely different
Recall
Distribution
of majors of
students in
this course:
Stat 155, Section 2, Majors
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Busine
ss /
Man
.
Biolog
y
Public
Poli
cy /
Health
Pharm
/ Nur
sing
Jour
nalis
m /
Comm
.
Env. S
ci.
Other
Undec
ided
Fre
qu
ency
And now for something completely different
A man goes into a drugstore and asks the pharmacist if he can give him something for the hiccups. The pharmacist promptly reaches out and slaps the man's face."What did you do that for?" the man asks.
And now for something completely different
What did you do that for?" the man asks.
"Well, you don't have the hiccups anymore, do you?“
The man says, "No, but my wife out in the car still does!"
And now for something completely different
An elderly woman went into the doctor's office. When the doctor asked why she was there, she replied, "I'd like to have some birth control pills."
Taken aback, the doctor thought for a minute and then said, "Excuse me, Mrs. Smith, but you're 75 years old. What possible use could you have for birth control pills?"
The woman responded, "They help me sleep better."
And now for something completely different
The woman responded, "They help me sleep better."
The doctor thought some more and continued, "How in the world do birth control pills help you to sleep?"
The woman said, "I put them in my granddaughter's orange juice and I sleep better at night."
Random Sampling
How Accurate?
• Can (& will) calculate using “probability”
• Justifies term “scientific sampling”
• 2nd improvement over quota sampling
Random SamplingWhat is random?
Simple Random Sampling:
Each member of population is
equally likely to be in sample
Key Idea: Different from “just choose some”
Random SamplingAn old (but still fun?) experiment:
Choose a number among 1,2,3,4
Old typical results: about 70% choose “3”
(perhaps you have seen this before…)
Main lesson: human choice does not give “equally likely” (i.e. random sample)
Random Sampling
How to choose a random sample?
Old Approaches:
– Random Number Table
– Roll Dice
Modern Approach:
– Computer Generated
Random SamplingEXCEL generation of random samples:http://stat-or.unc.edu/webspace/postscript/marron/Teaching/stor155-2007/Stor155Eg16.xls
Goal 1: Generate Random Numbers
EXCEL approaches:
• RAND function
• Tools Data Analysis Random
Number Generation
EXCEL Random SamplingGoal 2: Randomly Reorder List
EXCEL approach:
• Highlight block with list & random num’s
• Sort whole thing on numbers
Goal 3: Random Sample from List
• Choose 1st subset from random re-order
• Since, each equally likely in each spot
EXCEL DetailsRAND:
• Not available among “Statistical” functions
• But can find on “All” menu
• Note no (explicit) inputs
• Just put in desired cell
• Drag downwards for several random #s
• Caution: these change on each re-comp.
• Thus not recommended for this
EXCEL DetailsTools Data Analysis Random Number
Generation :• Set: # Variables: 1
Distribution: Uniform (over [0,1])
• Generates Fixed List
(doesn’t change with re-computation)
(note entries are “just numbers”)• Thus stable for later interpretation• Recommended for random sample choice
EXCEL DetailsSorting Lists:
• Highlight Block with Both:
– Names to sort
– Random numbers
• Data Sort Choose Column
• Result is random re-ordering of List
Random Sampling HWHW:
C7: For the letters A – L, use EXCEL to:
(a) Put in a random order.
(b) Choose a random sample of 6.
(Hints: for (a), want each equally likely,
for (b), reorder, and choose a subset)
Random Sampling HWInteresting Question:
What is the % of Male Students at UNC?
(Your chance of date,
or take 100% - to get your chance)
HW:
C8: Print Class Handouthttp://stat-or.unc.edu/webspace/postscript/marron/Teaching/stor155-2007/Stor155HWC8.doc
Random Sampling HWNotes on HW C8:• 3 dumb ways to sample, 1 good one• Goal is to learn about sampling,
Not “get right answer”• Part 1, put symbol for yourself, Ms and Fs
for others• Put both count & % (%100 x count / 25)• Part 2, “tally” is:• Part 4, student phone directory available
in Student Union?
Random Sampling HWNotes on HW C8,
• Hints on Part 4:– For each draw, first draw a “random page”– Tools Data Analysis Random Number
Generation Uniform is one way to do this– In “Uniform”, you need to set “Parameters”, to
0 and “number of pages”.– This gives a random decimal, to get an
integer, round up, using CEILING– In CEILING, set “significance” to 1.
Random Sampling HWNotes on HW C8,
• Hints on Part 4 (cont.):– Next Choose Random Column– Next Choose Random Name– Caution: Different numbers on each page.– Challenge: still make equally likely– Approach: choose larger number.– Approach: when not there, just toss it out– Approach: then do a “redraw”– Also redraw if can’t tell gender
More On SurveysMore Common Sense:
How you ask the question
makes a big difference
HW:
3.57, 3.59
And Now for Something Completely Different
Extreme Bicycling
Need a bicycle helmet there?
And Now for Something Completely Different
And Now for Something Completely Different
And Now for Something Completely Different
And Now for Something Completely Different
More about SamplingThe “simple random sample” (recall “each
equally likely”) can be expensive
(e.g. nationwide political poll, collected by personal interview)
So there are many cheaper variations:– Stratified Sampling– Multi Stage Sampling– See text– And there are many others as well
Sampling for ExperimentsII. Experiments
(Recall I was Observational Studies,
Now take similar look at II)
Terminology:
“treatments” are applied to “individuals”
i.e. to “subjects”
i.e. to “experimental units”
Sampling for ExperimentsA “treatment” is:
a combination of “levels”,
of explanatory variables (quantities),
called “factors”.
E.g. Medicine, Agriculture, …
Sampling for ExperimentsAgriculture Example:
Study how plant growth depends on:
fertilizer and water
So plants = “experiment’l units”, i.e. “subjects”
“Factors” are fertilizer and water,
Each plant gets some “level” of each.
HW on Sampling TerminologyHW:
3.9
3.11
Design of ExperimentsThe “design” of an experiment is the
assignment of levels and treatments to
experimental units
(just as “choice of sample” was critical for
sampling, this is too. There is a huge
literature on this, including current
research)
Design of ExperimentsKey Design Issues:
1. Control
Idea: Eliminate “lurking variable” effects,
by comparing treatments on groups of
similar experimental units.
Controlled Experiments
Common Type: compare “treatment” with
“placebo”, a “sham treatment” that
controls for psychological effects
(think you are better, just because you are
treated, so you are better…)
Called a “blind” experiment
Controlled Experiments
Further Refinement:
“Double Blind” experiment means neither
patient, nor doctor knows is real or not
Eliminates possible doctor bias
Design of Experiments
2. Randomization
Useful method for choosing groups above
(e.g. Treatment and Control)
Recall: Different from “just choose some”,
instead means “make each equally likely”
Design of Experiments2. Randomization
Big Plus: Eliminates biases,
i.e. effects of “lurking variables”
(same as random choice of samples,
again pay price of added variability,
but well worth it)
Design of Experiments3. Replication
Idea: Reduce chance variation by applying
same treatment to several (even many?)
experimental units.
How many replications are needed?
(depends on context: tradeoff between
cost and reduction of variation)
Will build tools to study (based on probability)
Design of ExperimentsFancier Designs
(there are many, some in text)
• Blocks
• Matched Pairs
• Balanced Designs
Example of an Experiment(to tie above ideas together)
Gastric Freezing:
Treatment for stomach ulcers
– Anesthetize patient
– Put balloon in stomach
– Fill with freezing coolant