Math 151 , Day 39,  Friday, May 2, 2008 .after class. Hit reload .

HW Day39   Review  Ch. 15, to p. 376. Then 377-79,Table C. Optional: Two-sided Tests from Confidence intervals pp. 379-80
Reread first part and read rest of Ch. 16, to p. 396. Optional: Lightly, for the words and concepts of power, effect size, type I and II errors  pp. 396 to 402.  Check p. 405, 16.20, 16.24, 16.25 (c you should be able to take for granted.) 16.26 (they say b--but you can't really do probabilities on the nonresponse and other errors, so I don't think this is a well posed answer.  A better answer would talk about how much you can trust the interval) 16.27  Ch 17 outlines this section of the book.
Start reading Ch. 18:  We'll repeat the CI and test work, only with s instead of sigma, and t instead of z. 

Hand in  Monday.   Remember, the P-value applet can be used to check any P-value computation.

P-value and significance: All you need to know to do these (p. 371): If P is less than the "alpha" number, the outcome is statistically significant at the "alpha" level
p. 372, 15.15, 16 (more of the same problems.  #15, P = .1894., # 16, P = .0359 )
p. 372 15.17 ultramarathoners

Complete all problems in Setups and Calculations section, Days 37 and 38:
 For 15.18, 19, 37, 38, 42, 43,44 You wrote down your H's, your xbar, found z and P, and made a rough sketch of the normal dist. when H0 is true and the direction(s) of evidence for Ha. And marked your z on it.  Now: Use table C with these z's to find "bracketing"  numbers for P:   ___< P < ___.  Check that your P calculated last time is actually between these bracketing numbers.

Two more Table C's:
p.379 15.21&22  significance, Table C, 1 and 2 sided
p. 379 15.23 23 significance, Table C, 2 sided

Cautions about significance tests (and CI's). These problems mostly cover old ideas, carried forward. You should be able to do them, after reading the assigned parts of Ch. 16.
p. 393, 16.5 Is it significant?
p. 394-5 16.6&7  Acid rain.  Do them by hand, and on the Applet.  You should, of course, get (close to) the same answers both ways.
p. 395, 16.8 Acid rain, Confidence intervals.  (there are only 3, not 6, since #6 and #7 are the "same" problem)
p. 396 16.9 rich parents and education

p. 407. 16.32 evidence, pacemakers
p. 407, 16.34 a, b. larger samples
p. 407, 16.35 significance is good for...
p. 408 16.36 sensitive questions (CI)
p. 408 16.37 college degrees (CI)
p. 408 16.39 supermarket shoppers (The data are in order, so a stemplot is easy)
p. 409 16.43 comparing package designs (What did they not tell us that we would want to know?)
p. 409, 16.44 island life (correlation coefficient)
p. 409, 16.45 helping welfare mothers  (The Clinton "welfare reform" depended, probably too much, on studies of this sort)
Postpone the rest.  Yes.
 p. 397, 16.10 searching for ESP
 p. 408 16.40 success of trainees
p. 408 16.41 schizophrenia markers

 Read, 
to discuss
p. 391, 16.3 environment

p. 407,  16.31 sampling at the mall
 Optional 

(more practice)
p. 389, 16.1 TV poll

p. 391, 16.2 red lights
For your "real" shoebox results:  Write your xbars , z's, P-values, and <.10 (Y/N) (one on each pad--yellow or white).
Real shoeboxes last term,
   Your shoeboxes + Your simulation of shoebox results:  (10 each, for mean of 20, mean of 24) 
To the circulating pad: Add your total # where P < .10, (your # of simulations should be 10). I did it 25 times each: My page of results

Exams returned.  Comments   Solutions         
Buffer against one low hour exam:
The final % exam grade minus 10 points will be substituted for the lowest hour exam grade, if it is higher.

Examples:
Ex1 Ex2 Ex3
 Ex4 final % final -10
Student 1 Original 85 80 85
 60 85 75, replaces lower 60
Treated 85 80 85
 75 85 <--ß These will be used.
Student 2 Original 85 80 80
 70 75 65, lower than 70, don't replace.
Treated 85 80 80
 70 75
Student 3 Original 85 50 75
 55 85 75, replaces lower 50
Treated 85 75 75
 55 85 <--ßThese will be used

This is to encourage  all to try to put it together for the (cumulative!) final.

Final exam: Tues. May 13, 7-10 pm (evening!)  If this is a problem for you, please email me soon.  
   Alternative-- Wed. morning is most favored so far..
  Full exam schedule is at   http://www.wells.edu/pdfs/finals.pdf
     Registrar's page with link to this and other good stuff: http://www.wells.edu/academic/regist.htm


Effect of sample size on distribution of x-bars:  NormalandXbar.xls

Ch. 15: "Significance tests use an elaborate vocabulary, but the basic idea is simple: an outcome that would "rarely" happen if a claim were true--is good evidence that the claim is NOT true." (p.363 top)
I'm not making it up that this idea is important:  Financial Times (influential and high-end British newspaper) this winter:
   (with formatting and pictures)  (without)   Statistical Significance: #10 of "The Ten Things Everyone Should Know About Science"

HW questions?  Day 38

Day 35 for  details..  Day 38 for Summary, comments: , continuing with Significance levels and table C


- - - - - - - More NEW STUFF- -Do HW on this:  -  - -
back to Ch. 16, cautions:  (SRS, normal pop., sigma known)
>>How small a P is convincing evidence against H0?  (What alpha, to "Reject H0?)
   --Is Ha surprising?  (Entrenched opinion is "for" H0 .  )  Need strong evidence (small P).
   --Is rejecting  H0 expensive?  Need strong evidence for Ha. 
        [May need to repeat experiment for doubters]
No sharp border between "significant" and "not"--though decisions may need to be made.

>>Statistical significance is not the same as practical significance ("clinical significance") 
      Tiny difference (from null value) can be statistically significant if sample size is large.
       Big difference may not be statistically significant if sample size is too small.
Do confidence intervals:  Estimate the size of the effect, not just yes/no of test..

Postpone the last? Yes:
>>Multiple Tests: beware! pp. 395-6
    If you do 100 tests and use the alpha = .05 significance level for each, then the structure of testing requires this:
    When all 100 null hypotheses H0 are true, out of your 100, about 5 of the 100 (.05) will give "significant" results by chance alone (falsely indicating the alternative hypothesis is to be preferred.)   (10%--1ish-- of your 10 simulations of the shoebox with mean 20 will give "significant" (P< .10) results even though the mean is the null value of 20)  (My results)
.Real shoeboxes last term, : only 1 falsely significant...   Your shoeboxes 3/16 falsely significant.
    Moral: if you use the testing mechanism as a screening instrument for many questions, a proportion will give falsely significant results.  You can't accept the results from such multiple tests as good evidence, only as indicating questions requiring further, more specific study. The game gives you one shot, not a hundred shots.    (This is becoming an important issue for developing new statistical techniques, for instance in biology, where microarrays can do a thousand tests at once.)
(not in text) You cannot legitimately test a hypothesis on the same data that first suggested that hypothesis. Every data set will turn up with some unusual pattern if you examine it hard enough. 
       (If you must explore and confirm with the same data set, one way is to (randomly) take half the data set, explore and generate hypotheses; then use the other half for confirmatory tests.  You can use P-value to describe unusualness, but be wary of making decisions with it if you didn't expect that particular unusualness.)

>>All the warnings about designing experiments and surveys still apply!

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