Math 151 , Day 42, Wednesday, December 6, 2006   Hit reload . Watch this space for updates (office hours, etc.)

Final Exam* Tuesday evening, Dec. 12 7-10. Alternate exam time?  Tues. afternoon 2-5, Th. morning 10-1. 
     Sign in sheet today! -your Choice.  Email me if you change your mind.

Get  Review Exercise (Precipitates).  SPSS file. This is optional, but if you hand it in, it 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!

In-class final exam:  Closed book, one sheet of notes (& calculator!).  1 1/2 to 2 times as long as hourlies. Comprehensive but with special attention to the material covered since Exam 4. Reading but not creating SPSS.  Will certainly be broader in range than the Review Exercise; but most problems will be similar to the types on hour exams and HW. 
Jenn has emailed everyone with a list of your missing HW's.  Better late than never! HW accepted & read thru 9 am this Friday.  Accepted, marked "in" but not read, up to the time you take the inclass final. Put it into the yellow folder,
but not inside the red folder, outside my door. NO CAMPUS MAIL!  Returned HW will be in usual red folder.
Jenn's review times:  
Tuesday 5th 3:30-5:30pm
Wednesday 6th 6:30-8pm
Thursday 7th 6:30-8pm
Sunday 10th 7-8:30pm
Monday 11th 11-noon
I'll be on campus Friday morning 10:30-1, and Tuesday 12th from 12:30 on.  (And Thursday 10 am)

Please fill out an evaluation,
return it to the ENVELOPE circulating or on the projection cart.  The envelope will be with Erna in the
Dean of the Faculty's office, if you miss doing it today.
Handout for SPSS Ch. 18

Homework questions? Day 41   See Day 40 for notes .
Another situation which uses t-statistics is the one in Chapter 19
"Two-sample problems".  Two random samples,  independent of each other, from distinct  populations. (Populations are normally distributed)
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 look at the difference of the xbars. 
We need the Standard Error of the difference  xbar1 - xbar2 , and then we can proceed as before, more or less (with some adjustments.)

 p. 461, 19.1, 2, 3, 4.  For each, after deciding which design it is, tell if  the data comes from a sample, an observational study, or an experiment. 
#1: Design = matched pairs (a pair is the couple). Not clear if they've been chosen as a random sample from some group, or if it's observational study.
#2: Design = two-sample (volunteers, non-volunteers).  Random sample.
#3: Design = single-sample (comparing these measurements with the "known" value).  What are we getting information about here?  Not the reference specimen really, but the accuracy of the new method.  Could regard data as a sample (20 of all possible measurements which could be made on such a reference specimen by this method).  Could this be an "experiment"? A chemist might call it that.  We're seeing what the  "treatment" of the new measuring method does.  But there's no "control".  And we don't usually think of  "treatments" as being the actual "measuring".  How to do the math  is straightforward, but the situation doesn't fall perfectly into our old categories.
#4: Design = two-sample (new method, old method)  It's set up like our experimental design for treatment/control, and the "old analysis method" looks like the control.  But again,  usually an "experiment" means doing something to the subjects which you then measure the results of.  Here we're assessing the effectiveness of the measuring method, and specifically not doing anything else to the specimen.  Doesn't fall clearly into our sample/observational study/experiment categories.

BUT, Remember, when we're doing the math, our assumption is always that our data can be regarded as a SRS from some population.  So whether it's sample, observational study, or experiment, it's important to look for potential biases, and state clearly any limitations on what "population" it's reasonable to infer to.  (People willing to volunteer for the experiment?) 
(If the new analytical method does fine at one concentration, does it do equally well at 1/10 that concentration?)

What we studied: (Overall: always questioning the source, context of data)
>>Data Analysis: description and exploration<<
          Normal distributions and "abnormal"--graphs, summary systems (mean/s.d., 5-number group)
          Two related Quantitative variables; correlation, regression, how good (r, r-squared, residuals), predicting y from x
>>Data Production: Sampling, Designing Experiments<<
           Sample, Observational study, Experiment
           All the ways it can go wrong (biases, placebo effect, etc.)
 >>Statistical Inference: formal Estimating and Testing--
         quantifying our uncertainty (which always remains!) and satisfying the skeptic<<
            Need: Language--Population/Sample, Parameter/ Statistic
                       Probability:  simple. Sampling Distribution of x-bars. (Law of Large Numbers and Central Limit Theorem)
           Single mean, sigma known (z), and unknown (t) .  Matched pairs (t).  (Difference of means for two independent samples.)
                          Robustness of t procedures
            Confidence intervals:  Confidence level, margin of error, sample size
            Hypothesis tests:  null and alternative (one and 2-sided), P-value, significance  and alpha
        
Anything you'll meet will fall into one of those big categories--
   --Fancy ways of torturing a data set to make it give up its secrets--"data mining," subtle and complex summary methods
   --Sophisticated experimental and sample designs
   --Estimations (usually intervals) , tests (P-values, "significant at") based on other parameters

 "If your only tool is a hammer, every problem looks like a nail."  Studies are often set up so that they can be analyzed using certain techniques.
  Conversely--if you want to do statistical inference, you'd better know what statistical processes you want to use, and design your study so those processes are appropriate.  Don't expect to just gather data and then figure out how to do statistics on it (not that this isn't done--all too often!)  If you've got nails, you need a hammer, if you have screws, you need a screwdriver.  It's not too hard to create data sets for which good inferential techniques don't exist!

What haven't we done?
--Chapter 19, comparing two means from independent samples.  CI and test, based on difference of sample means.
--Chapters 20 and 21 Inference (CI and tests) about a proportion from one sample (voters for Clinton), and  comparing two proportions from independent samples.  Like  means, with niggling details in the SE computations.
--Chapter 23, (& Ch. 6) two categorical variables (are Clinton voters disproportionately Female?) (Quantitative Research methods in Sociology)
--Chapter 24, testing if a correlation coefficient is really different from 0, making confidence interval-type fudge factors around our regression line. Chapter 28 on CD, Multiple Regression--relationships when there are more than 2 variables (Econometrics)
--Experiments with more than 2 treatments, and quantitative results ("Analysis of Variance" Ch. 25 on CD--take Quantitative Research Methods in Psychology)
--Methods that work when our normality assumptions aren't met.  ("Nonparametric" methods--Ch. 26 on CD)

Thank you for a very interesting semester! 


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