Math 151 , Day 42, Friday, May 11, 2007 .After class4pm5/11.
Hit
reload . Watch this space for updates (office hours, etc.)
In-class
Final exam: Wed. May 16,
2-5 pm. Two sheets of notes--I'll give you tables. Please bring a
calculator!: If this time is a
problem for you, please let me know soon.
You may start early (noon or later Wed.) 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.
Get
Review Exercise (Biometric).
Height-Armspan
(SPSS) file Body Temperature (SPSS)
file . 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! Email me with questions,
corrections; I'll email the class!
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, outside my door. NO CAMPUS MAIL! Returned
HW will be in usual red folder.
Office/clinic hours. Watch this space.
Sievers: Monday afternoon 2-4, Wed. 11:00 on. Possibly some time Tues.
Morning, Monday morning; not sure yet.
Jen: an hour on Monday???
Anna: ????
Please fill out an evaluation,
return it to the ENVELOPE circulating
or on the table. The envelope will be with Erna in the
Dean of the Faculty's office, if you miss doing it today.
Homework
questions? Day
41 See Day 40 for
notes .
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.
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; Form. Linear: 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 is pretty good for moderate n
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 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, and 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!
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