Math 151 , Fall 2004, Monday Day 22, Oct. 18 After class Hit reload ...

HW assignment Day 21
Reading: ReRead section  3.2 to p. 196, including Significance p. 193.  Read  Matched pairs and block design pp. 196-8; review ch. 3.    Next:  4.1, 2, 3.  We'll do  4.1, 2, 3.  Skip 4.4 and Skip Ch. 5.

Hand in  Wednesday Matched pairs and blocks  p. 199 3.43 hand strength 3.45 weight loss 3.44 student traders.  The difference in the treatments is whether or not they have software that can make "charts" of past "trends." (If they don't have the software that "highlights trends" they don't have "charts"--they just have lists of numbers giving the price history.) = = = = = = = = = = = = =  Hand in  Wednesday): On a separate sheet:   Prep for ch. 4:  Do p. 216, 4.4 spinning penny  Spin a penny 50 times, keeping track of Heads or Tails.  Bring to class  # of heads , #of spins, proportion that came up heads (# of heads divided by # of spins) = = = = = = = = Postpone Probability: Sec.  4.1  p. 215,  4.1, 2, 3 parameter/statistic

Read, to discuss  (matched pairs)  p. 209 3.72 McDonald's vs Wendy's (two-factor) p. 209 3.71speeding the mail

Optional  (more of same)  p. 203, 3.58 (matched pair) 3.59

Homework questions? 

Example:  Suppose 95% of the subjects  had their headaches cured by treatment 9 and only 25%  by treatment 1 (placebo).  IF the medicine in fact did "no good" that would be a very unlikely outcome.  So we will say the difference in headache cures between treatment 1 and treatment 9 is "statistically significant" and be inclined to believe the medicine "works".
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Fancier Experimental designs (not "completely randomized") Control extraneous variability by pre-sorting 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?
    Aside:  Sampling data, "longitudinal study" following same people through time.
            Works like matched pair to control variability.
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.  (No randomization here.)
    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".)

Exam 2 material ends here.  Questions?  Bring more on Wednesday

Start here Wednesday, after exam questions.
Not in text:  In practice, the ideal requirements may not be met:  Sometimes the treatment cannot be deliberately  imposed and we must observe it (and the response) when it happens. (Can't force people to smoke.)
"Prospective study--retrospective study."
--Prospective:  You get your subjects before something  (e.g. disease) happens to them, can get information from them.  Then it happens (or doesn't).  E.g. enlist 1000 women, collect info, wait 5 years.  See who gets the disease. An observational study, but More like an experiment than
--Retrospective:  Ask people with/without disease what they were/are like.  (Problems: Reliability of remembered info,  matching,  sampling)  (My mother's headaches)

Ch. 4, Probability and Sampling Distributions.
Chance  behavior (a random phenomenon): Unpredictable in the short run,  predictable regular pattern in the long run.
  (Random numbers:  equally likely in the long run.  "Random" in this chapter  is more general--pattern is not necessarily equally likely)
25 digits from the random number table: Individual sets of 25 showed much variability.  Pooled  shows more "flatness" --but still much variability.  You would be right to be skeptical when I told you that your "pick-a-number" choices were not random, on the basis of just this class's data.
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We know that a sample from a population will not exactly represent the population.  If we take a random sample, the behavior of samples will not be individually predictable, but there will be predictable pattern in many random samples from the same population.  Knowing the pattern will be  as good as we can do.