Math 151 , Fall 2006 Wednesday Day 26, Oct. 25 Hit reload...After class, no changes

HW:  Finish Chapter 9.Check p. 228: 9.16, 17, 18, 20 (obs/expt, factors)  Then 21 (choosing groups), then 9.19, 22, 23, 25 (types).   Read Data Ethics, pp. 235-242 if you haven't. Read  Ch. 10 to p. 256.  Exam covers to here., def. of Random Variable (discrete) p. 260.  Check p. 263ff. 10.19, 20, 22, 23, 24, 25, 26, 27.   Read rest (Note Normal distribution is back) . Check 10.21, 28
Hand in Monday after the exam:
 (added to last time's list) p. 256, 10.10 rolling die.  Which obey the probability rules?
p. 265, 10.31 Probability models?  Note, you only are checking whether the model is legitimate, not whether it's correct for the phenomenon described!
p. 261, 10.16 Grades RV
p. 252, 10.6 and 10.7 D&D, 4-sided dice
p. 267, 10.42 Race and ethnicity
If you didn't do it for today: p. 249, 10.3 50, 200 Random digits.  Bring your result for (b) to class to compare with others.  I did it twice, got .06, .09   Applet:  Probability
 Read, to discuss


Optional 



Exam Friday Oct 27 (Day 27), Next class.  Bring one sheet of notes (& calculator).  Chapters 8 and 9 and (part of) 10--through HW assigned Monday.
   Sample exam .  Solutions outside my door and on reserve . In /Friday's class I noted that there is no problem on the sample involving two (or more) factors, but such questions could be on the exam.   6d will not be covered on this term's Exam 3.
I have been known to ask questions on the exam specifically on the "outside" reading, such as the Placebo Effect articles.

Sign-in sheet:  indicate if you want to come early (9:00+).  If you need another accomodation, arrange personally with me.

Jenn's  remaining Clinic hours this week:  Wednesday (today) 6-7:30pm.
I'm available (come to my office) after class, and 12:40-4:00 today. 

Add your results from the 200 "coin flips" with p = .10 to the circulating transparency.

Ch. 9 Designing Experiments, finishing . See Day 22 ,  Day 23 , Day 24

Principles of designing an experiment: Compare groups with different treatments:   Control as much as you can, to make all the groups the same except for treatments, Randomize the rest; Use enough subjects  to average out bad "chance" .
   "Randomized comparative experiment".  Issues, vocabulary....see previous days

Discuss acupuncture, 3 treatments (music, acupuncture wrong, acupuncture right) 
Really 2 sub-experiments;  Acupuncture right vs. acupuncture wrong is blinded placebo-controlled measurement of effect of correct acupuncture.  Acupuncture wrong vs. music is measurement of the placebo effect of having needles stuck in you. 
A little problem:  I just read that listening to music has been shown to lessen pain.  So what can we do about Music/none as a confounding variable here?

Completely randomized experiment: all subjects are allocated at random among the treatments.
Fancier Experimental designs (not "completely randomized") Control extraneous variability by pre-sorting individuals into  homogeneous groups.  (BPS4e pp. 224-226)  Details Day 24
Matched pairs: Compare Control and experimental treatments (i.e. 1 factor, 2values) , each on "half" of a pair (or self.)
Block design:  Sort experimental units into "Blocks" = groups homogeneous on potentially confounding variables
    (No randomization here.)  Within each block, randomize the treatments.

Homework questions:  matched pairs?  Day 25
     probability? Probabilities follow the "common sense" rule for proportions of a whole.  Same rules for proportions of areas, proportions of counts, proportions in histograms, proportions of times in the long run something would happen. 
 Probability Details Day 24 

For Monday: 
Two principles for assigning probabilities:
--Sometimes, a properly chosen sample space will have equally likely outcomes. You can use this to find other probabilities.
--If you pick an individual at random from a population, the probability that one individual will be XYZ is the same as the proportion of XYZ's in the population.
  Random Variable:  (X, Y, Z...) Variable whose value is a numerical outcome of a random phenomenon.  
Probability distribution of X tells us what values X can take and how to assign probabilities to them.     If X has a finite number of possible values (Discrete distributions), nothing new except notation.      P(X < 2) is "Prob. that X is less than 2."  (See Day 24, bottom)
Exam questions?
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