Math 151 , Spring2006, Day 41 Wednesday May 10 Hit reload After class

Day 41  (Re)reading Ch. 23, reading Ch. 25 (for Matched pairs), Reading: D&V Ch. 24 (two independent samples) first 2 pages, then lightly for ideas rather than formulas, thru p. 462 top, then 465-9.  You will not need to compute a two-sample t procedure by hand, but you will need to know how to identify the situation, (possibly) to use SPSS, and understand the results. This is the end of the course material.
Work on Review Exercise (50% of final exam grade) due 9 am Fri. May 19.

Hand in Friday
Using SPSS: ( Handout,one sample t)
A.  Use SPSS. Redo the example on the handout (Cola sweetness loss). Type in the 10 data values.
B. Use SPSS. Redo the example on Day 38 page (Milk bacteria) Data is on the lab computers, in  Math151 D&V\SPSS for Class 05\MilkBacteria_t.sav.  Or You can copy and paste the data from Datasets page.
C.  Use SPSS. Redo the computations from p. 448, #9 (Normal body temperature). The data is not where it's supposed to be.  You can copy and paste the data from Datasets page.
p. 451 #27 Chips Ahoy Use SPSS. You can copy and paste the data from Datasets page.  For c,  Do the test with SPSS, and get the P-value.

Paired samples:
p. 491 #13 a-d (e optional) Sleep (by hand)  Use Table T to get a benchmark significance level, instead of P-value. (Optional, find the P-value using Activstats:  The table tool (23-1, activity 3) or T the Density tool  (Ch. 23--"normal dist" looking button on menu bar does t distribution))
D. Redo the Mileage example on the SPSS handout (back side).  The data is at   SPSS file, or in columns in Datasets page. 
p. 489 # 7 City Temperatures Use SPSS.  Data is on the lab computers, in  Math151 D&V\spss data files  D&V\dv01_25_07.sav
p. 493 # 22 Uninsured Use SPSS.  Data is on the lab computers, in  Math151 D&V\spss data files  D&V\uninsure.sav
p. 491 #12 Summer school Use SPSS. Type in the data.  Choose the columns so the Paired Data procedure subtracts the way you want it to.

Two independent samples 
Optional E.  Repeat the analysis on the SPSS handout for the Polyester in landfill data.
p. 471, #1, 3 CPMP
6 a,b only Pulse rates
17 Job satisfaction (What should you do? (Don't do it...))
12 a,b Memory
11 Hurricanes. Do a back-to-back tally of the two sets. Don't do the test, just think about appropriateness.  The answer in the back was a little misled by the inappropriate boxplot into thinking there are outliers, tho there aren't really, there's just "granularity" (small whole numbers here). 

 Read,
  to 
discuss 		 Optional
E. (Two-sample)  Repeat the analysis on the SPSS handout for the Polyester in landfill data.
Final exam:   "In-class" Friday May 19, 9am-12m.  Wells Exam schedule. Contact me ASAP me if you have a problem with this time.
The "in-class" Final will be closed book, but bring one sheet with your notes, anything you like!  And a calculator! Length 1 to 1 1/2 times the length of the midterm exams; comprehensive but with special attention to the material covered since Exam 3. Reading but not creating SPSS.
Review exercise (get handout) will count 50%, "in class" the other 50% of the final exam grade.  Get all the help you can find on the Review Exercise but make sure you understand and write the final result yourself.  Show your work!

Fay has promised lots of help times during study & exam week.  I'm on jury duty but will try to be available some time.
Late homework is accepted up until the time of the final exam.  Will not be commented on after Fay quits doing so.  Will be returned outside my door, in the orange folder.

Homework questions? Day 40
Add your 80% CI for the shoebox to the circulating  yellow pad.
One-sample t procedures,
  Conditions of "near-normality", random-sample-like, Day 39
  Start here today.
SPSS Handout One sample and Matched Pairs,
  And Matched Pairs designs Day 39

Last thing: lightly
Chapter 24, Comparing two means"Two-sample tests". Chapter 24  Two random samples,  independent of each other, from distinct  populations. (Populations are normally distributed)  p. 454-5
Often--comparing means from an experiment with two treatments (usually control and "treatment").
                 /--- Group 1, n1---- Treatment 1---\
               /                                    \
 Random asst.(?)                                       Compare results --"means"
               \                                    /
                \--- 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.
(Above 40, Central Limit Th. helps:  15 to 40, a little skewness ok.  p. 455)
We use the difference of the two y-bars,  diff =  ybar1 - ybar2 = .
We need the Standard Error of the difference  ybar1 - ybar2 , and then we can proceed as before, more or less.

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)

Beyond here is optional to know:
 The Standard Error is calculated like the hypotenuse of a right triangle (Pythagorean Theorem),  from the individual standard errors.
 SE(diff) = SE( ybar1 - ybar2 )= sqrt[SE(ybar1)2 + SE(ybar2)2 ] 
P. 453 has another way of writing the same thing:

This almost fits the  t-model. Degrees of freedom are weird.(p. 454)

(For doing by hand, if you must: 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. 494 bottom.  Produces non-integer degrees of freedom.  Very good approximation to the exact distribution, if both sample sizes are at least 5.   Always between "smaller of (n1- 1) and (n2- 1)" and [(n1- 1) + (n2- 1)].   Unsuitable for doing by hand.

Once we have (ybar1 - ybar2) , SE(diff) ,  and the df, our formulas pattern on the earlier ones. Optional Example by hand
CI :  estimate + t* . SE(estimate)
    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  find P-value

SPSS will do our computations when we are given raw data.  See handout.  Datasets
Analyze>Compare means> Independent-samples t. We use the Equal-variances-not-assumed line of the results.
  (Does same example as Optional Example by hand: twosampexample.htm)

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