Math 151 , Fall 2004, Monday Day 38, Nov. 29 Hit reload.....

HW assignment Day 38
Read  Moore 7.1, at least to p. 374, then rest (thru p. 382)  Next, start 7.2 .
Hand in: Moore,  Sec. 7.1
p. 364 7.1, 7.2, 7.3 "Standard error" & t-distribution family
p. 373, 7.4  CI  t*
 p. 386, 7.19 Shrimp ATP CI  A common calculational mistake is to divide the SE by
 square-root-of-n.  But square-root-of-n is already IN SE!  Don't divide by it again!  (I.e. pay
 attention to the difference between "standard deviation" and "standard error.") 
7.5, 7.6 test, one- & two-sided 
7.7 DDT  Find the mean and standard deviation by hand!(only 4 points) (or SPSS or calculator) and do the rest by
 hand.  Make a note of your results; we will do this on SPSS too, check the results. 

(SPSS) A.  Work through the handout on SPSS for Ch. 7, first page. Print and Hand in the tables shown on the handout. 
(SPSS) p. 374 7.7 DDT  do this again,  on SPSS.  Compare your results with those you got by hand. 
(SPSS) p.383 7.13 crankshafts Also, with part a,  find a 95% confidence interval for the actual mean dimension.



Exam 3 returned. 

Final exam:  Tuesday, Dec. 14, 2-5 p.m.  See me if you have a conflict.
The Final will be closed book, but bring one sheet with your notes.  Length 1 1/2 to2 times the length of the midterm exams; comprehensive but with special attention to the material covered since Exam 3.  Reading but not creating SPSS.

HW questions?
The t- distribution,  Day 37
One sample t procedures, Intro to SPSS (get Handout)Day 37

MATCHED PAIRS t procedures-- "Paired samples"(SPSS), "Paired comparisons"
   before--after, left hand--right hand, Drug A vs. Drug B on the same person or on a matched pair.
For each pair, find the difference in the observed values.  Then treat these differences as if they are "the" data set, from a normal population, and do One-sample t procedures.
Usually (always?) the null hypothesis will be " µ = 0", there is "no difference" between the treatments.

Example:  wax paper sandwich bags:  Is the wax layer the same inside and out?
25 bags:  measure (wax outside - wax inside) for each.  (pounds per square foot).
Differences:  
xbar = .093,  s = .723   n = 25    SEM = .723/5 = .1446
H0 :
µ = 0 (mean difference is 0)                  t = (.093 - 0)/SEM = .093/.1446 = .643.
Ha : µ Not = 0 (there is a difference)            t is less than .685 (d.f. = 24)
                                                                          which is right-tail t* for probability .25
       Because test is 2-sided, double the tail: .50.  P value is greater than .50.
                                           No evidence for difference.
- - - - - - - - - - - - - - - - - - - - -
ROBUST procedures:  a confidence interval or significance test is called robust if the confidence level or P-value doesn't change very much when the assumptions of the procedure are violated.  pp. 379-80.
t-procedures are quite robust against nonnormality. But sensitive to outliers. Look at data.  Need SRS!
 Details:  n <15   t ok unless data clearly not normal, or if there are outliers.
              n > 15  t ok unless there is strong skewness, or outliers.
              n > 40 or so:  t ok even if there is skewness.  (Outliers?  I suggest trying with and without them, see what changes).
     Refer to chart of possibilities, Day 37

Matched-pairs data (differences) are often more normal in shape than the separate variables ("oddness" is often the same for both items in a pair, and disappears in subtraction.  Another reason why this is a nice experimental design. )


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