Math 151 , Fall 2005, Day 20 Wed. Oct. 12 Hit reload ...After class

Exam 2 a week from Friday.  Covers thru that Monday's HW.
Day 20 (Wed. Oct. 12): Reading: D&V Ch 12, ahead in 13. Reading for Sampling: Ch. 11 pp.  216-7 The Step-by-step simulation effectively takes a random sample of size 3 from the 57 students.  The sampling processs is repeated 10 times.  The sampled individuals are only labeled as to whether they are Varsity or Not, but they could have been given names.  AS13 is good.
Hand in (All D&V p 238ff. unless otherwise noted)
A.  Making & Examining SRS's with SPSS.  Do the assignment on the handout Using SPSS to find a Simple Random Sample. 
1, 4, 6, 7, 8, 9 Do parts a,b,c,d, and e, Save till next time (when you'll do  f and hand them all in. )

23 Sampling methods
21 Quality Control Use a cluster sample. (SPSS) Get the individuals  like this: 
In SPSS, type in values of a variable for case code, with values 61, 62,....80.  Get a sample of size3 & write down which cases are chosen.   Then  choose one from each case.  Consider them labeled from 1 to 12: enter those numbers into a variable.  For each case, take a sample of size 1 to decide which bottle from that case.   (Are we running a risk if we take the same (place) bottle from each case?)  Write down which bottles were chosen. 
AND If we've covered sampling from the Random Number TableWe didn't, so postpone the rest(p. A-49) Do it again! Use line 16, reading across, to first choose 3 cases from 61, 62,....80, then choose a bottle from each case .  You'll get a different sample from your SPSS sample, of course.

19 Accounting

Postpone the rest of Ch. 12:
11 Parent opinion I
15, 16 Phone and cell phone surveys

p. 267 #41 Security
p. 240 #20 Happy workers?  For e, use the Random Number Table (p. A-49) & read across Row 6. 
= = = = = = = = = = = = = = = 
Chapter 13 You can do these now, if you like...
 Hand in answers to these questions on the "Placebo Effect" articles (outside my door/on reserve ) Hand in Monday: 
a) Give two examples of the placebo effect (from the article!)
b) What do researchers believe causes the placebo effect? 
c) In the separate article: "Pill will make you feel better...," what country was surveyed? 

 Read,
  to 
discuss 

p. 265 #29 Home-
coming

Postpone:
p. 239 #13 Wording
the survey
 

 Optional 

Homework questions? Day 19  Add your results from the arm-measurement to the circulating list, and your dots to the circulating dot-plot .
Sample Chosen from a  Population
       (varies)             (fixed, but usually unknown)
Calculate
Numerical summary: Statistic (Latin) Parameter(Greek letter) (D&Vp227)
    Examples:           Sample mean xbar    Population mean mu (µ)
                       Sample st. dev. s    Pop. standard dev. sigma

The actual value of the Statistic will vary, depending on the particular sample.
"Sampling variability" = "sampling error"
The Statistic "estimates" the Parameter.  We hope it is close to the parameter.  If we choose simple random samples, we can understand the pattern of values the statistic can take.
Want sample to be representative of population, statistic to estimate paramater well, but variability happens...

Simple Random Sample (SRS) of size n:   See Day 19 for details:
Sampling  frame.       Using SPSS to Sample. Get Handout.
Other sample designs:  Stratified random, Cluster, Multistage, Systematic
- - - - - - - - - - - - -
Start here Friday:
Sources of Bias in sampling: any systematic failure of a sample (or its method) to represent its population.  (E.g. sampling frame excludes "different" part of population.)

Bad sampling designs:Not using randomness:

Other problems, even with good sampling design: Undercoverage:  of some or other group:  due to sampling frame, voluntary response bias, convenience sample, nonresponse....
Moral(s):  Design and plan to reduce potential biases
          Pretest for remaining problems   (A stitch in time saves 9; or the whole project)
          Report your sampling method and process in detail, so others may critique.

Using Random Number Table to sample (p. A-49)  Example: Ch. 11 pp.  216-7 The Step-by-step simulation effectively takes a random sample of size 3 from the 57 students.
    Every digit, every sequence of digits, is equally likely to be "next" in any direction. (Divisions into 5 is just for legibilty)
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)
                    For example :   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, Start where I say and go across (so everyone who does it right gets the same answer.).  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.

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