Math 151 , Fall 2004, Wednesday Day 39, Dec. 1 Hit reloadAfter 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 SPSS uses 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 . 
- - - - - - - - - - - - - - - - - - 
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
= = = = = = = = = = = = = = = = =
SPSS, Matched pairs 
(SPSS) 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!.) 
(SPSS) 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. 

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

Postpone the rest:  Read now for context.
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)  

Get your exam if you didn't Monday.  Comments link, Day 38.
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.
The exam will be closed book, but one sheet of 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.

What is the significance to Statistics of the Guinness Stout Bottle ?
~~~~~~~~~~~~~~~

HW questions on t-procedures?  SPSS?
Matched pairs, Robustness: Day 38
SPSS for Matched pairs:  See Handout from Monday, backside of one-sample t. 
--You can use the built-in Analyze>Compare Means>Paired-Samples T-Test. 
   Disadvantages:  It always subtracts the rightmost variable from the leftmost.  You don't get a list of the differences.
--Create a new variable of the Differences:  Transform>Compute: 
       Target variable: Difference, Numeric Expression: firstVariable - secondVariable. 
       Do One Sample on Difference.

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,  diff =  xbar1 - xbar2 = .
We need the Standard Error of the difference  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:

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 
Test:  H0: µ1 - µ2 = 0 same as µ1 = µ2 , "no difference" always
        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.
Back page of t- handout.

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