Math 151 , Spring 2004, Monday Day 40, May 10 Hit reload ...After class

HW assignment Day 40
Read 7.2.  You are responsible for the concepts material through p. 402; should read and understand the rest enough 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.
Hand in Wednesday:  p.423,  7.68 bus conductor's alcohol parts a and d only! (Reviews today's review)
Bring questions: this or earlier work.
Hand in Wednesday: FRIDAY
Two-sample-- (SPSS problems are marked.  Other long computations by hand are optional.)
p. 391, 7.28, 7.29 which design? 

p. 396, 7.30, 7.31 s, SE, d.f.  (In 7.31: the null hypothesis is that there is no difference in the CA/CL, the alternative is that failed companies will have had a lower CA/CL than healthy--assets is what you own, liabilities is what you owe.  Duh.)

 A.  (SPSS) (Mimicking the handout.)  Examples 7.7, 7.8, 7.10 in Moore, p.393 ff.  Produce (& Hand IN) the output shown in the handout. Write down the p-value for the test, & the 90% confidence interval for the difference of means.   We'll "always" use the "equal variances not assumed" option. 
 Note--If you bring in the data from the Excel or text file, the "groups" column will have 2's and 16's so you use 2 and 16 as the labels for group 1 and 2.  If you use "2" for group 1 and "16" for group 2, it will do (2-week-mean) - (16-week-mean).  It will also allow you to use "16" for group 1 and "2" for group 2--then it will do (16-week-mean) - (2-week-mean).  So (unlike the matched-pairs situation) you can choose which way to subtract. 

 (SPSS) p.399 7.32 logging  If you type in the data , remember you need all the tree species numbers in one column, and  a "groups" column for logged or unlogged.  (You can use strings or numbers for your logged/unlogged labels) 

 7.35 (a) chicks.   You can do this efficiently by hand with a back-to-back stemplot, or use SPSS.  SPSS won't do back-to-back stemplots, but you can get separate stemplots and side-by-side boxplots, using Analyze>Descriptive Statistics>Explore,  using the plots there.  Your response variable goes in the  Dependent list, your groups variable goes in the Factor list. 
 (SPSS) 7.35 b,c chicks 

Reading other output: 
 p.404, 7.37 (DDT), (read page 404 about SAS output, compare with our SPSS handout.)
 p.406, 7.39 self concept 

By hand: All Optional!
p. 401, 7.34 beetles in oats (test) 
 p. 412, 7.49 voice onset time (test and CI) 
 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 Due Friday:  Try SPSS now?  More complicated problems: putting together everything... 
     Read them over, do what you can,  bring questions ? These are all 2-sample questions; so I don't expect any hand computations (7.45, 67, 72).  But they are worth reading for the style of presentation of data, what are the hypotheses, CI's of what.
(SPSS) p. 400, 7.33 Math sublimina. This is a complicated design:  matched pairs, then 2-sample on the differences!  But notice chicks (7.35 ) was also  matchedpairs--weight gain =after-before--but they gave us the pre-subtracted numbers. 
 p.410, 7.45 fitness  Do b.  Then Look in the back at the answers for a and b.  (Don't bother to do the computations yourself)
 (SPSS) p.422, 7.63  pasture fertilization 
 p.423 7.67 London bus people Do (a) for sure.
 p.425 7.72 reading biology 

Final exam   Tuesday, May 18, 9 a.m.  Optional later time:  Thurs. May 20 any period of time after 9:15, finishing by 4:30, by signup.  Notify me ASAP if neither of these work for you!

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.  Please contact me ASAP if you have a problem/conflict.
Exam is closed book and notes, except bring One sheet of notes (both sides if you want) with anything you want on it.
Get handout of info, and review problems.
~~~~~~~~~~~~~~~
Questions on HW: Matched Pairs: Day 39
Exam 3 comments
Start here Wednesday
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.
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 > µ2Be 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.
Handout for SPSS two-sample, section 7.2  Last side of "Statistical inference" handout.(p.3 is optional: tables built in to SPSS).  Go through text example, other HW examples.
Analyze>Compare means> Independent-samples t. We use the Not-equal-variances line of the results.
Example of hand computation--Optional!

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