Math 151 , Spring 2005, Day 41 Wed. May 11 Hit reload After class

Final exam:  Tuesday, May 17, 7-10 p.m., OR Wed. May 18, starting after 10, finishing by 4.  Sign up today or Friday. See me if you have a conflict with both times.
The Final will be closed book, but bring one sheet with your notes, anything you like!
   Length 1 1/2 to 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.  Problems like the hourlies; perhaps some that cross "chapters".  If you didn't do well on Exam 3 be sure you understand those questions now.

I'll be on campus Monday midday, Tuesday afternoon and till exam time.

Day 41 (Wed. May11):  Start reviewing, making your notes for your sheet, bring questions.
Hand in 
D&V p. 491-2, # 17 and 19. Braking.  These are two different designs to investigate the same question.  Without looking at the answers, decide on what the designs are called, and decide on the appropriate method of analysis. As appropriate, use stem and leaf plots or dotplots to get a preliminary idea of what's happening, and to check assumptions (subtract numbers as needed on your calculator).  Optional:  Do the analyses.  (You'll have to type the data into SPSS.)

A.  From the group exercise on Particulates, Bring your solutions, written up to be part of a group report, and be ready to explain/discuss with your group/ the class. Data
If you were absent: read the handout (outside my door, or link here), choose one or two questions to analyze/answer.
 Some questions/analyses suggested in class:  (Or do your own! There are definitely others to look at.)
Compare means: confidence interval for differences.  Test for alternative: rural is less polluted (Method: paired samples?  [why?]
Is city/rural more variable (spread out)?  Look at side by side somethings.
Are distributions nearly normal?
Do the pollution levels "travel together"--scatterplot, correlation, regression--can one be used to predict another (which way makes sense?)
Some good questions people came up with that are not answerable from the data; that we'd like to know in understanding this situation:  What units are these?  Where is this (dry/dusty Southwest?  damp leafy Northeast)  (Those I caught; others??)

 Read,
  to 
discuss 		 Optional 

Homework questions? Day 40
Chapter 24, Comparing two means"Two-sample tests".
We use the difference of the two y-bars,  diff =  ybar1 - ybar2 = .
] 

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

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.

 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 > 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  find P-value

SPSS will do our computations when we are given raw data.  See handout.  Does same example as Optional Example by hand: twosampexample.htmDatasets
Analyze>Compare means> Independent-samples t. We use the Equal-variances-not-assumed line of the results.
  (Why?  If we don't know the means, why should we think we know the variances?  No good way to "prove" population variances are equal.  Equal-variances-assumed used to be the only method; turns out to not be very robust--if variances are not equal it can give "wrong" answers.)

Next time:Optional: Tukey's Quick test (p. 465) for two independent samples. Doesn't need Normal!!
 (Not well known;  but worth knowing!)  Put data in order (back to back Stemplot?).  One group must have the highest value and the other group the lowest to use this.  How much do they not overlap?
Count the number of items in the "Higher" set that are bigger than all the items in the "Lower" set. Plus all the items in the "Lower" set that are smaller than all the items in the "Higher" set. (A tie at the edge = 1/2.)
"7, 10, 13"  7 or more? (2-sided) Sig. at .05.  10 or more? (2-sided)Sig. at .01.  13 or more? (2-sided)Sig. at .001.
Unfortunately, text doesn't seem to have any problems this will work well on.

Group exercise --Particulates in air.  Handout   Data

Next time: What haven't we done?
--Chapter 22, comparing two proportions from independent samples.  Like comparing means, with niggling details in the SE computations.
--Chapter 26, testing whether categorical variables in two-way tables are dependent (the departures from equal proportions in all the columns are too much to attribute to sampling ("natural") variation, given independence)
--Chapter 27, testing if a correlation coefficient is really different from 0, making confidence interval-type fudge factors around our regression line.
--Experiments with more than 2 treatments, and quantitative results ("Analysis of Variance"--take Quantitative Research Methods in Psychology)
--Methods that work when our normality assumptions aren't met.  ("Nonparametric" methods)

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