Paper handouts in the white folder in the box to the left of my door.
Get
Review Exercise (YouthstatsReview.doc). YouthstatsReview (SPSS) file
if you didn't Monday . This is optional, but if you hand it in by
the beginning of the InClass exam, it will count 50%; "In Class"
the other 50% of the final Exam grade. (If you take
the InClass exam early, you may have till Thursday morning IF you
tell me at your InClass time that it's coming in later.) 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! Email me with questions,
corrections; I'll email the class!
Final exam InClass: Thurs. Dec. 13, 9-12am. Come
to the classroom. Comprehensive, closed book, 2 sheets of
notes. Problem 1 : is open
book, notes, people, available NOW . BRING it (done) to the
InClass exam. If you missed class, Download it or get paper copy from
the white folder outside my door!
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 elsewhere on the exam.
Alternative time--Tueday Dec. 11 morning/afternoon (any time from 9
on, but must finish before 5 sharp!) Come to my office!
Signup for start time on attendance clipboard. Further
difficulties? Get in touch with me ASAP!Other arrangements,
please confirm with me!
Full exam schedule is at http://www.wells.edu/academic/dates.htm#exams
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.
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.
Office/Clinic hours.
Watch this space for changes.
Sievers: today to 3:45; Friday 10-3, Monday 12-2, Tuesday 9:30-5
(I may leave to eat, help other students, etc.--email for an
appointment to be sure.)
Matthew Peddle: Th 3:30-5:30, F 1-3 (usual hours this week)
Helen Penny: Monday 2-4
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 Erna in 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 .
Class was spent answering hw questions from
ch. 18: 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 an exam to decide on anything (sample vs. observational study
vs. experiment) as ambiguous as #3 or #4.
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
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 (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 computational details, and
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-Fall07/Dayf42.htm | 3pm | 12/5/07 |