Math 151 , Spring 2007 Friday Day 21, March 16
Hit reload....After
class
HW: (Re) read
pp.
133-136. Skip Chapter
6. Read p. 186. Read Chapter 8. Read p. 200 (Other designs)
last. Check p. 206, 8.17-22, 26 at first., then 8.23-25 with
Table B. Ahead, Chapter 9.
Hand in Wednesday after break
I'll make all of this part of Day 21; you don't have to take your book
home if you don't want to.
p. 195, 8.7 Sampling badly on campus
- - - -
p. 199 8.9 Apartment living, SRS. Use Table B.
p. 209, 8.36 Area code sample, SRS Use Table B.
p. 211, 8.45 random digit dialing,Sampling frame.
p. 210, 8.41 random digit characteristics
We got to here.
p.209-10, 8.38 b only Traffic lights
p. 208, 8.30 movie viewing
|
Read, to discuss
p.195, 8.8 more Sampling badly on campus
We got to here.
p. 211, 8.47 guns
- - - -
p. 204, 8.14, 8.15 biases.
p. 208, 8.31 world affairs
p. 211, 8.46 wording survey questions
|
Optional
p. 209, 8.35 Use table B (more
practice)
We got to here.
p. 209, 8.34 seat belt use
|
Exams returned today.
| problem # |
total
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
10|0
|
| possible |
100 |
20 |
4 |
20 |
26 |
10 |
10 |
10 |
|
9|04
|
| max |
100 |
20 |
4 |
20 |
26 |
10 |
10 |
10 |
|
8|4457799
|
| Q3 |
85 |
16 |
4 |
18 |
22 |
10 |
10 |
10 |
|
7|1133589
|
| Med |
75 |
14 |
4 |
16 |
20 |
7 |
10 |
8 |
|
6|0139
|
| Q1 |
63 |
12 |
4 |
14 |
11 |
6 |
9 |
8 |
|
5|66
|
| min |
41 |
2 |
0 |
9 |
0 |
3 |
4 |
0 |
|
4|19
|
Difficulties with decimal places! #7, .0013 = 13 in 10,000!
Reading .1 for 1 in table, etc.
#4: Faster means fewer seconds--the left hand side of the curve!
Solutions
= = = = = = = = = = = = = = = = = = = = = = = = =
= = = = = = =
If you were absent WED>>Pick a
digit (from
0,1,2,3,4,5,6,7,8,9).
Write it down. Write it to the left of your name on the sign in
sheet .
Homework questions? Day
20
Ch.
8&9: Producing Data:
Aim:
create data sets that will allow us to make inferences to a
larger
world than just the data we have.
Recall: Details See Day 20
Observational
Study: vs. Experiment: ; Confounding:
Ch. 8 p. 192ff. Sampling
Population /Sample: Hope:
Sample will be
representative
of the population.
>> Sampling design: Describes exactly how sample is
to be chosen from population.
(SAMPLING) BIAS: The design of a study is biased if
it systematically favors certain outcomes.
New stuff:
Check our "sample" of digits
People systematically favor 7's, 3's? Stay away from 1, 9,
middle.
Sample survey: (attempt to) choose a representative
sample from a large, varied population. Not Easy!
Some issues: What population do we want
to understand? What exactly do we want to measure?
Non-probability samples (sampling badly):
- Voluntary response sample ( from a general appeal--Ann
Landers,
Cosmo, Hite Report, call-in and "instant polls" ): biased
toward strong
opinions,
esp. negative. (Contenteds don't bother.) www.vote.com,
- Convenience sample (whatever/whoever looks good, is handy) Unlikely
to be representative. Digits. Math 151 is a convenience
sample from Wells for heights, shoe size, major...
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 (p.200).
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, p.686)
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.
Check our "sample" of digits
People systematically favor 7's, 3's? Stay away
from 1, 9, middle.
Just as much variability from the random number table
(probably more than you would anticipate)
but no systematic patterns.
We got to here.
+ + + + + + + + + + + + + + + + + +
Some more sources of
bias, even
in probability samples (p. 201-3):
**Undercoverage: Some groups in the population are left
out, or slighted, in the process of choosing the sample.
One possible source of undercoverage: Sampling
frame: Moore p. 211 problem 8.45: 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. (Often a "list" that already
exists.) 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".
**Response bias Lies, bad memory, pleasing interviewer
(nutrition
surveys) Interview technique
**Wording of questions Confusing? Leading? Limiting choices?
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