Math 151 , Spring 2005, Day 20 Wed. March 16 Hit reload ...After class

Exam 2 the Friday after break.  Covers thru that Monday's HW.
Day 20 (Wed. March 16): 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)
1,4,6,7,8, 9 You did parts a,b,c,d, of these; now add  e, 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. OR If we've covered sampling from the Random Number Table(p. A-49) , use line 16, reading across, to first choose 3 cases from 61, 62,....80, then choose a bottle from each case .
19 Accounting

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
 Hand in answers to these questions on the "Placebo Effect" articles (outside my door/on reserve (soon)) 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?

Postpone the rest:
 p257ff.  1,2,4,5,6,10,11,12  Do a: Decide if it is an observational study or an experiment.  If it was an observational = "investigative" study answer that b,c,d,e.  (We'll complete the experiment ones later; start them on a separate page, answering the questions you can so far.)
25 Wine
24 Full moon

 Read,
  to 
discuss 

p. 267 #29 Home-
coming

p. 239 #13 Wording
the survey
 

 Optional 

Homework questions? Day 19  Circulate your random samples from Old Faithful data.
Sampling variability = "sampling error":  Want sample to be representative of population, statistic to estimate paramater well, but variability happens...

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.
Sampling  frame: the list of individuals from the population that you actually choose the sample from.  May differ a little (or a lot!) from the population you desire to study.

Other (good) designs:  See Day 19

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.

Start here Friday:  = = = = = = = = = = = = = = = = = = = = = = = = = =
D&V Ch13  Goal:  show cause-and-effect. Predictor-->Response
Observational Study:  Observe individuals; don't do anything to them; do not influence the responses.  Can indicate strength of relationship, differences, but not cause and effect.  (Often not with samples, but with selected group(s).)  Lurking variables?!? (Fisher:  Smokers smoke to soothe irritabilities that may cause cancer.)
         Retrospective:  gather data after the fact (observe that x% of men hospitalized with heart disease were/are smokers)
         Prospective:  choose individuals in advance. Measure them; or follow them as events happen.  (Framingham Heart Study: 5,209 (2,873 women and 2,336 men) healthy residents between 30 and 60 years of age.  Followed from 1948 to now. A second-generation cohort recruited 1971, Minority group 1995  http://www.framingham.com/heart/)

Experiment: Impose treatments  on individuals, to see how the treatment influences  the response.
Compare treatments' effects.
Do something to:    "Experimental Units" = "Subjects"
   Treatment:  A Specific experimental condition.
   Factor: = Explanatory (Predictor) Variable we manipulate.
        Levels: Specific values of a factor that we set.
   Response variable(s)

E.g. 2 headache medications, in combination?
A two-factor experiment, each with 3 levels. 9 possible treatments.
    Factor A: Aspirin:  levels None, 500 mg, 1000 mg
    Factor B: Caffeine: levels None, 50 mg, 100 mg
Response variable: reported pain relief
Aspirin
None 500 mg 1000 mg
None Treatment 1 Treatment 2 Treatment 3
Caffeine 50 mg Treatment 4 Treatment 5 Treatment 6
100 mg Treatment 7 Treatment 8 Treatment 9

E.g. (Day 13, MRA-95-13 )Corn yield= response variable.  One Factor = Planting rate.  5 Levels=the rates.

Principles of designing a comparative experiment (p. 243)

Results:  Measure differences in the response variable for different treatments (e.g. side by side boxplots)
 "Statistically Significant" differences--too big to have plausibly occurred by chance (compare with variability within treatment)  We'll quantify later.

 
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