Math 151 , Fall '08 Friday Day 24, Oct. 24 Hit reload...after class.

HW:  Finish Chapter 9: read p.224 on.  Check p. 228:  9.19, 22, 23, 25 (types).   Read Data Ethics, pp. 235-242 if you haven't. Next, Read Ch. 10 to p. 256, def. of Random Variable (discrete) p. 260.  Check p. 263ff. 10.19, 20, 22, 23, 24, 25, 26, 27.
Hand in  Monday
p. 226, 9.13 hand strength, MP
p. 231, 9.35 forest CO2

p. 226, 9.15 teaching techn.  Why might I call this a  matched pairs rather than a general block design?   Don't actually do the randomization, but think about what ought to be done; we'll talk about it.
p. 232, 9.40 TV ads, block design.  Use the  Applet, to assign your subjects.  Number your Women and your Men, and show their numbers as well as the group they're in. 
p. 229, 232, 9.27 and 9.39 wine, beer, spirits two ways
+ + + + + + + + + +
Hand in Monday Separate paper:
Hand in answers to these questions on the "Placebo Effect" articles (outside my door/on reserve): 
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?
- - - - - - - - - -
Hand in Wednesday, Day 26:  "Ethics": Read Data Ethics, pp 235-242.  Find at least one other person in the class, and together discuss  one of these questions.  Write up your answers as a pair/trio  (If you have consensus, fine! If you disagree, say who thinks what).  pp. 242-245, # 4 or 5 or 9 or 11 or 13 or 14 or 17

= = Chapter 10: NONE tonight. Start Monday=
p. 249, 10.1 Texas Hold'em

p. 265, 10.30 Sample spaces, free throws
p. 252, 10.5 Sample spaces
..
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
p. 250, 10.4 Probability says..

p. 254, 10.9 Canadian languages, using rules
p. 256, 10.12 Watching TV, RV
p. 261, 10.16 Grades RV
p. 266, 10.37 Land in Canada, 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. 252, 10.6 and 10.7 D&D, 4-sided dice
p. 267, 10.42 Race and ethnicity

p. 256, 10.10 rolling die.  Which obey the probability rules?
p. 268, 10.44 Benford One more discrete probability
Read, to discuss

p. 232, 9.38  spine fractures You lack the information to make a complete design (i.e. how many women at each hospital.)  Sketch in what you can.

 Optional 


p. 226, 9.14 matched and not, more practice
Exam Next Friday Oct 31 (Day 27).  Bring one sheet of notes.  Chapters 8 and 9, all, Some or all of Ch 10 --through HW assigned Monday
   Sample exam available today in class, or in white folder outside my door.  Solutions Here.Note that there is no problem on the sample involving two (or more)" factors" or expressly listing "factors" and "treatments", but such questions could be on the exam. 
I have been known to ask questions on the exam specifically on the "outside" reading, such as the Placebo Effect articles; Bradley effect.
Review Normal distribution: we'll want it soon after the exam. 

Placebo news this morning: Half of doctors prescribe them
Bradley effect:  What is it and why might it be important this year?   Spiral of silence?
Homework questions:  Day 23

Ch. 9 Designing Experiments, Summary. See Day 22 ,  Day 23  for more  notes

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"

More issues:
--Placebo and biasing effects--avoiding:   "Blind",  "Double blind."
--Lack of realism:   Do sociology, psychology experiments generalize to "real life?"
--Subjects are not a random sample from the population. ( Ivy League males, before 1970's.)
--Ethical questions...Milgram. Zimbardo prison. Whole section BPS4e, pp. 235-242

Statistical Significance p.221: An observed effect so large that it would rarely occur by chance (assuming no real difference in treatments) is called "statistically significant".   "So large", "rarely", "by chance" will be defined and quantified in Ch. 6.
  = = = = = = = = = = = = = = = = = = = new today:  See Day 23 for details = = = = = = =

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)
Matched pairs: To compare Control and experimental treatments (i.e. 2 values only)
   Sort experimental units into "matching" pairs.   One member of pair gets control, other gets experimental.  Randomize which.
        Compare within pair, then summarize all comparisons.   Often: matched with self="self-paired"). (Randomize order)
Block design:  Sort experimental units into "Blocks" = groups homogeneous on potentially confounding variables
        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".)   Diagram p. 226

+ + + +Start here Monday+ + + +new--finishing Producing Data section: + + + + +
 In practice, you may not be able to do the ideal experiment:  Sometimes the treatments cannot be deliberately  imposed (ethical reasons, practical reasons) and we must observe the explanatory variables (and the response) . (Can't force people to smoke.)   Included in this may be even intrusive measurements, assessments.
Not in text: "Prospective study--retrospective study."  (Both  are observational studies)
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.  ) Some of the problems:  reliability of memory, completeness and reliability of records.  Comparisons are hard.  Others... 
March 14, '07: NYTimes and others: 12.9% of people admitted to the hospital with heart attacks on the weekend are dead a month later.  12% of those admitted during the week are dead a month later.  (Based on records of NJ hospitals 1999-2002).  A significant difference (unlikely to be due to chance) because so many people were involved (probably 13,000 or more).  Weekend people were much less likely to have angioplasty.  But a weekend/weekday difference was apparent even before angioplasty existed.  And they didn't track how sick people were coming in.
 ----Prospective:  choose individuals in advance. Measure them; and follow them, as events happen.  Still have problems of lurking/confounding variables. (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/)

recall: Toward Inference: Table p. 186, Exploratory Data Analysis vs. Statistical Inference
Chapter 10, Probability (intro)
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)

"Probability" of particular something happening: proportion of times it would happen in a very long series of (independent) repetitions of the phenomenon. ..  Applet:  Probability
    (independence:  outcome of one trial (repetition) must not influence the outcome of any other.)
The random number table.  At each place, the probability of any particular one of the 10 digits is 1/10, or .10.     Sets of 25 digits  from the 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.  Not enough to necessarily show the pattern.

Probability Models : (p. 250-256)
Random (Chance)  phenomenon, described by
    Sample space S:  set of all possible outcomes (no overlap of descriptions)
    Event:  any outcome or set of outcomes
    Probability model: S, and a way of assigning a probability to each event.
Sample space depends on what you want to know:
Phenomenon: Flip coin twice.   3 possible sample spaces:
    S1 = {HH, HT, TH, TT}     S2 = {0, 1, 2} number of heads   S3 = {Y, N} both are heads?..

Probability rules:  pp. 253, in words, then in notation.
A an event in sample space S, P(A) is "the probability that  A occurs"
    These rules are all true for proportions in long run (Probabilities), proportion of counts, proportions of areas.
    1.  0 < P(A) < 1   (any probability is a number between 0 and 1. )
    2. P(S) = 1         (all the outcomes together have total probability 1)
    3.  A and B are  disjoint if they have no outcomes in common (can't happen simultaneously.)
        If A and B are disjoint, their probabilities add:  P(A or B) = P(A) + P(B)
    4. For any event A, P(A does not occur) = 1 - P(A)

Pick one person at random from U.S. Pop. (Age 25 +)   Probability = proportion in the population
Sample space:
No HS degree
       HS only     .
1-3 yrs College
 4 + yrs College
Proportion in population.
18.3%
33.9%
24.8%
23.0%
Probability 
.183
.339
.248
.230
P( that the person's education is HS or less) = ?
P(Not finished college or didn't start) = ?

Discrete models: (Can make a list of all members of the sample space)  Make the list, and
Assign a probability to each outcome (>0) so they add to 1.   (Sometimes equal values make sense.)
    Prob. of an event is sum of prob's of its outcomes.

Phenomenon: Flip coin twice.
    S1 = {HH, HT, TH, TT}     S2 = {0, 1, 2} number of heads   S3 = {Y, N} both are heads?
Sample space  | HH | HT | TH | TT |
       Prob's | .25| .25| .25| .25|  P(tail followed by head)=?
Sample space  | 2  |    1    |  0 |  P(at least 1 tail)=?   P(1 of each) = ?
       Prob's | .25|   .50   | .25|  P(at least 1 Head)= ?  P(2 Heads) = ?
Sample space  | Y  |       N      |
       Prob's | .25|     .75      |

Start here Next. "Random variable" language not on the exam.
Often the sample space is naturally expressed in numbers, thus
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."
Flip coin twice. R.V. X = number of heads:  Distribution given by table.
             x| 2  |    1    |  0 |
       P(X=x) | .25|   .50   | .25|  P(X > 1) = ?   Words:  Prob that # heads is > 1
                                     P(X = 2) = ?         Prob that # heads is 2

Sievers home   Math151-Fall08/Dayf24.htm  2:30pm 10/24/08
This page belongs to Sally Sievers who is solely responsible for its content. Please see our statement of responsibility.