MATH 251, Probability and Statistics I, Fall 2005, Sept. 30, Day 16 After class

Plus data analysis project, in pairs.   * Handout: *  Preliminary report due 4pm Oct. 14, Day 20.  Final paper 9:30 am Oct.17, Day 22. Pairs:  See Day 15.

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.
Design of experimentsSec 3.2       Day 15
(outline:)
Do something to:    "Experimental Units" = "Subjects"   (cases)
Treatment.  Factor:     Levels.  Response variable(s)

Randomized comparative experiment : Diagrams of design, IPS pp. 202, 205
Completely randomized: all exp. units allocated at random among the treatments.

Principles of designing an experiment (p. 203) Control Randomize Repeat
Statistical Significance (first def.):

Placebo effect and biasing.  "Blind",  "Double blind"

Start here Monday:
New--  How to pick individuals for treatment groups, without Website.  (SPSS has no easy way to pick if you have more than 2 treatments.  Pospone SPSS)
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.  (Sec. 3.3)
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, pp. T4-5, back)
    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.

How to use for Experiment?  Say 12 subjects, want 4 groups  of size 3:  Read the table to choose a sample of size 3.  (Record them).  Continue to read the table.  The next 3 make the next group, the next 3 make the 3rd group, and the remaining 3 make the 4th group.  You don't have to start over for each group; just keep reading.

Fancier Experimental designs (not "completely randomized") Controlextraneous variability by presorting individuals into  homogeneous groups.
Matched pairs: To compare Control and experimental treatments (i.e. 2 levels)
   Sort experimental units into "matching" pairs.   One member of pair gets control, other gets experimental.
                Randomize which.
        Compare within pair, then summarize all comparisons.
  Common: Do the control and experiment to same individual (matched with self). (Randomize order)
        Are right feet bigger than left feet? (not an experiment)      Sunburn salve experiment?

Block design:  Sort experimental units into "Blocks" = groups homogeneous on potentially confounding variables
     e.g. M/F, age, income, weight, fruitflies wild or curly-winged.
    Within each block, randomize the treatments. Compare results  within each block, then summarize all results.
    (Matched pairs is a special case of block design--each pair is a "block".)

e.g. Headache remedies:
   Block:  Habitual coffee/cola drinkers would be affected differently by caffeine.  Blocks:  Caffeine-accustomed +Caffeine-free.  (Diagram)
   Matched pairs (2 treatments):  Compare a dosage (aspirin 500 + caffeine 50 ) to placebo:  Self-paired:  1 month on one treatment  followed by 1 month on the other.  Randomize which goes first--half get placebo first, half get medicine first.