Math 151 , Fall 2002, Wednesday Day 39,Dec. 4 Hit reload to get most current versionAfter Class

HW assignment Day 39
(Re)read 7.1. Read 7.2.  You are responsible for the material through p. 402; should read and understand the rest in order to be able to deal with the output from SPSS, and future encounters.  Up to p. 402 is the last material you're responsible for.(The horrible formula on p. 403 is the one Activstats and SPSS use to find the d.f.  You do NOT need to know it--I do not expect you to ever calculate it by hand.)
Hand in:  Moore,  Sec. 7.1
Matched pairs :  you just treat the difference/change as one variable (x). By hand.
p. 378 7.8 tomatoes.  Give two values between which P lies, from Table C. 

p.386  7.21 healing in newts You would only  need SPSS for part a, to check the mean and s.d.-- just look at the answers in the back of the book for them. Finish a, do b,c . 
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Robustness, etc. (text pp. 379-381) 
--Make a dot plot of the differences in problem 7.21
p. 386 7.20 Acculturation
7.23 Increase in CEO pay
7.25 Presidents' ages
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SPSS
A.  Work through the handout on SPSS for Ch. 7, first page. Print and Hand in the tables shown on the handout. 
p. 374 7.7 DDT  do this again on SPSS.  Compare your results with those you got by hand. 
 p.383 7.13 crankshafts Also, with part a,  find a 95% confidence interval for the actual mean dimension. . 

Matched pairs : 
B. Work through the handout on SPSS for Ch. 7, back page (matched pairs). Print and Hand in the tables shown on the handout. (Making the new variable Diff  is optional, but highly recommended!.)
 p.378, 7.9 &10 (right/left threads) Optional: make a variable for the difference  and produce a stemplot to check for outliers.  * There is an annoyance here--we expect the right thread times to be smaller than the left thread times, so it might be easier to think about (left -right) and anticipate a positive average.  But unless we exchange the order of the variables in the SPSS file, we have to do (right - left) if we do a "paired-sample test", and anticipate a  negative average.  Be clear what you do. 

 p. 382, 7.11 caffeine dependence  Again, watch out for the direction of your differences and what they mean.
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Two-sample--beginning (Not SPSS) ch 7.2
p. 391, 7.28, 7.29 which design? 

Hand in sometime....
p. 396, 7.30, 7.31 s, SE, d.f.
p. 401, 7.34 beetles in oats (test)
p. 412, 7.49 voice onset time (test and CI)
activstats at bottom of page

What is the significance to Statistics of the Guinness Stout Bottle ?
~~~~~~~~~~~~~~~
SPSS for one-sample (Handout) Day 37
Matched pairs, Robustness: Day 38
Start here Friday
Sec. 7.2, Comparing two means
"Two-sample tests".  Two SRS's, independent, from distinct  populations. (Populations are normally distributed)
Often--comparing means from an experiment with two treatments (usually control and "treatment"). Cf. p. 140.
                /--- Group 1, n1---- Treatment 1---\
              /                                    \
 Random asst.                                       Compare results
              \                                    /
               \--- Group 2, n2---- Treatment 2---/
To examine  the difference of the  two means, µ1 - µ2:
We need fairly normal populations; no extreme outliers.  Back to back stemplots are good; boxplots will do.
We use the difference of the two x-bars, (xbar1 - xbar2) = diff.
We need the Standard Error of  xbar1 - xbar2 , and then we can proceed as before, more or less.
The Standard Error is calculated like the hypotenuse of a right triangle (Pythagorean Theorem),  from the individual standard errors.
    SEdiff  = sqrt[SE(xbar1)2 + SE(xbar2)2 ]  P. 394 has another way of writing the same thing.

"t" = (xbar1 - xbar2)-0
               SEdiff
Unfortunately, this doesn't quite have an exact t-distribution, and its exact distribution is very hard to deal with.

For doing by hand:  df = smaller of (n1- 1) and (n2- 1).
Will give a "conservative" result--slightly wider C.I., slightly less significance, than a "sharper" value.  If your results hinge on the difference between this result and the computer result, they're too close for comfort anyway.

From a computer:  df = complicated formula on p. 403.  Produces non-integer degrees of freedom.  Very good approximation to the exact distribution, if both sample sizes are at least 5. Unsuitable for doing by hand.

Once we have (xbar1 - xbar2) , SEdiff ,  and the df, our formulas pattern on the earlier ones. Example
CI :  estimate + t* . SEestimate
    CI for µ1 - µ2, difference of means,  is (xbar1 - xbar2) + t* . SEdiff
Test:  H0: µ1 - µ2 = 0 same as µ1 = µ2 , "no difference"
           Ha: µ1 - µ2 > 0 same as µ1 > µ2   Be careful with these, that you know which direction you want.
      or Ha: µ1 - µ2 < 0 same as µ1 < µ2 Often we label our variables "1" and "2" so that we expect µ1 > µ2
      or Ha: µ1 - µ2 <> 0 same as µ1 <> µ2  (not equal)
        Calculate t, find P-value (approximate, conservative)

--SPSS will do our computations when we are given raw data.  Learn  SPSS next..

 Activstats 20-4 (Paired).  The 2 green stars have very good notes.
   Two-sample procedures, Activstats Ch21, pp. 1-2. 
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