Math 151 , Fall 2004, Friday Day 19, October
8
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HW Reading: Ch. 3 thru 3.1. Ahead
in
3.2
Hand in
Wednesday
Ch.3.1, Sampling
p. 170, 3.4employed women Also:
What is the sampling frame? (Def. p. 179, #3.13)
3.6 letters to Congress
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p. 173 3.7 SRS
p. 207, 3.65 SRS
p. 184, 3.26 Random digits
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p. 185 3.30 survey questions
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p. 181 3.16 bigger sample size
p.185 3.31 sampling error for men |
Read, to discuss
Ch.3 Intro:
p. 170, 3.5 pop, samp...
3.18 novel--pop, samp.
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Sampling
p. 183, 3.22 president
3.23black police
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p.180 3.14 ring-no-answer
3.15 2 campaign questions
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Optional
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p. 3.24SRS
Probability Samples (other): InfoHere
p. 176 3.11 stratified sample,
accounts
3.12 multistage design, schoolkids
p. 184, 3.27,Systematic.
3.28 same chance for each. SRS?
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= = = = = = = = = = = = = = = = = = = = = = = = =
= = = = = = = = = = =
Pick a digit (from 0,1,2,3,4,5,6,7,8,9) (if
you didn't last time) Write it down.
Association--->>
Causation?Day
17
Chapters 1 and 2 have covered analyzing
data
that was given to us--what it said about itself.
Informally, develop
guesses,
suspicions, hypotheses about the world the data came from.
Ch.
3: Producing Data:
Aim:
create data sets that will allow us to make inferences to a
larger
world than just the data we have.
Observational
Study: Observes individuals, measures variables, does not
influence the responses. (3.1)
Take Sample from a population, examine it....
Experiment:
Imposes
treatment
on individuals, to see how the treatment
influences the response.
(3.2)
Confounding: Two variables
(explanatory
or lurking) are confounded when you can't sort out their
effects
on a response variable.
______________________
Ch. 3.1 Designing Samples
>>Population: Entire group that we want information
about.
>>Sample: The part of the population we actually
examine.
Hope: Sample will be
representative
of the population.
(SAMPLING) BIAS: The design of a study is biased if
it systematically favors certain outcomes.
Check our "sample" of digits
Some refinements:
*Sampling frame: Moore p. 179 problem 3.13: the group from which
the sample is actually chosen--as different from the
"population"--the
group you want information about. The sampling frame is often,
unfortunately,
smaller than the population. The sample is (usually
much) smaller than the sampling frame.
* "Chosen" sample may not turn out to be actual sample, if some
individuals
don't respond--"Nonresponse", p. 178.
Non-probability samples:
-
Voluntary response sample ( from a general appeal--Ann
Landers,
Cosmo, Hite Report): biased toward strong
opinions,
esp. negative. (Contenteds don't bother.) www.vote.com, vice presidential debate
-
Convenience sample (whatever/whoever looks good, is handy) Unlikely
to be representative. Digits.
Simple Random Sample (SRS)
of size
n: n
individuals
chosen in such a way that every possible set of n
individuals has an equal chance of being chosen.
A probability sample.
HOW? A chance mechanism: Cards, dice, computer program, or
Table of random digits (Simulates rolling a die with 0,1,....9,
over and over...) (Table B, back flyleaf)
Every digit, every sequence of digits, is equally
likely to be "next" in any direction.
To use: label everyone in the population
with a number.
Important: Every labeling number needs the
same
number of digits.
To label 9 people, use the labels 1,2,3,....9
(1-digit
chunks)
To label 15 people, use the labels 01, 02, ...10,
11, ...15 (2-digit chunks)
To label 125 people, use the labels 001, 002, ...
124, 125 (3-digit chunks)
Pick a place (at random) in the table, start reading
across in that size chunk. Get n eligible
numbers (discard repeats)
Read Row 150: 07511
88915
41267 16853 84569 79367 ..
From 9 people, a sample n = 5: 0,7,
5,
1,
1, 8, 8, 9,
1, 5, 4, (sample is individuals 7, 5, 1, 8, 9)
From 15 people, a sample 07,
51, 18, 89, 15,
41, 26, 71, 68, 53, 84, 56, 97, 93, 67.... keep reading,
go to next line (or back to top line) if you need
more. Individuals 7, 15,...are chosen using this line.
From 125 people, a sample 075,
118,
891, 541, 267, 168, 538, 456, 979, 367...keep reading.
Individuals
75, 118, ...
Why the same number of digits in each
label?
Each individual 3-digit chunk is as likely as any other 3-digit
chunk.
But a 1- or 2-digit chunk is more likely than any 3-digit chunk. So
2 will come up more often than 12, but 02 will come
up
just as often as 12.
Why across? For consistency
on
HW, go the way they say (so you get the answer in the book).
In practice, you can read up, down, backwards, as long as you decide
beforehand, and don't change in the middle of choosing the sample.
Sources of bias,
even
in probability samples:
-
Undercoverage: some groups left out or slighted in choosing
the
sample (cf. sampling frame)
-
Nonresponse: some individuals chosen 1) can't be
contacted
2) refuse to answer
Census: 2.3 million uncounted in 2000 (3 million
in 1990) estimated...
Mail surveys:
- Response bias Lies, bad memory, pleasing interviewer
(nutrition
surveys) Interview technique
-
Wording of questions Confusing? Leading? Limiting choices?
Inference to the population: Sample
results
will vary.
Different samples will represent the population with
differing
accuracy.
Well-designed Random (probability) sampling will avoid
systematic
bias.
In general, A larger random sample will
give
more accurate information about the population than a smaller
random
sample.
More kinds of probability samples:
We will focus on the mathematics of the SRS,
the most basic. In practice, more sophisticated sampling
methods
may be preferred. The math needed to analyze their effects is
beyond
our course.
Optional:
Here
are some other ways to design a probability sample.
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