Paper handouts in the white folder in the box to the left of my door. All are linked here.
Get
Review Exercise (FinalReviewSp08.doc).
. This is optional,
but if you hand it in by the time you start the inclass final, 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, document your help! Email me with questions, corrections; I'll email the
class (and post here)!
Final exam: Tues. May 13, 7-10 pm (evening!) Start
at 6:30ish if you want. In classroom. Two sheets
of notes. I'll give you the usual tables.
Alternatives-- Tuesday afternoon, starting
any time after 1:00; finishing by 5:30. Wednesday morning, 9-12.
Choose a time (clipboard) so I know
when you're coming. Come to my office!. Email
me if you want to change your exam time. Difficulties? Get in touch with
me ASAP!
Full
exam schedule is at http://www.wells.edu/pdfs/finals.pdf
Exam 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.
In-class Final Exam problem 1:
Link active, document corrected! Correction: for p.1, A-c, "Sketch
and label the normal curve representing the
distribution of xbars from all possible SRS’s of size 6 from Joe, if H0 is true.To
label your graph, approximate sigma (the unknow
population st.dev.) by s (the standard deviation
calculated from the sample.)" Do
this page, with whatever help you need, and BRING your result to the
IN-CLASS Final. It is Problem #1 of the IN-CLASS exam.
I will not ask you to read SPSS output for CI's or significance
tests on any other part of the exam. I might ask "standard
error", hypotheses, z tests questions, reading other SPSS output
elsewhere on the exam.
HW: Better late than never! HW 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, in the box to the left
of my door. NO CAMPUS MAIL! Returned HW will be in usual red folder. Matt
says HW turned in in class today (Fri) will be graded by 4:30 today.
Office/Clinic hours.
Watch this space for changes.
Sievers: today to 4:00; Tuesday 1 to 10 pm. Gone
for dinner 5ish to 6:30
Matthew Peddle: Today F 2:30-4:30 (usual hours this week, I
trust)
Maria McLane can work with you in the times she's serving as
CLA, in the Printer room, next door to the Math Clinic.
Today 12:30-5 (before Matt comes
in.) Monday 10:30-12:30
Please fill out an evaluation,
return it to the ENVELOPE circulating
or on the table. If you missed
class, there are forms loose in the box outside my
door. Please take your form to the Dean of the Faculty's office
(Macmillan 224) It will be there till I turn in my grades..
Homework questions? Day 41 See Day 41 for notes .
Answers to Ch 19 below:
Questions from Chapter 19: answers
"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.
I would not ask
you on the In-class exam to decide on anything (sample vs.
observational study vs. experiment) as ambiguous as #3 or #4. But they
do happen!
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: describing and
exploring<<
Normal distributions and "abnormal"--graphs, summary systems
(mean/s.d., 5-number group)
Single value compared to its pack: z-score, percentile
Two related
Quantitative variables; Form. Linear: correlation, regression,
how good (r, r-squared, residuals), predicting y from x
>>Data Production: Sampling, Designing
Experiments<<
Sample
especially SRS, Observational study, Experiment
All the
ways it can go wrong (biases, placebo effect, etc.)
>>Statistical Inference: formal
Estimating and Testing--("confirming" )
quantifying
our uncertainty (which always remains!) and
satisfying the skeptic<<
Need: Language--Population/Sample, Parameter/
Statistic
Use
the Sample Statistic to infer something about the Population
Parameter.
Probability: simple. Sampling Distribution of x-bars. (Law of
Large Numbers and Central Limit Theorem)
Single mean,
sigma known (z): Normal population (or xbars), SRS!
Confidence intervals: Confidence level, margin of
error, sample size
Hypothesis tests: null and alternative (one and 2-sided),
P-value, significance and alpha
sigma unknown? Use t. Modifies z to "build in" variability that
estimating sigma brings.
Robustness of t procedures is pretty good for moderate
n
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 confidence 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.
Plan ahead!
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 18, one sample t-procedure, doing application to matched-pair
design.
--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 H.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, quantitative results
("Analysis of Variance" Ch. 25, 29online -- 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!
| Sievers home | Math151-Fall08/Days42.htm | 4pm | 5/9/08 |