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Mathematical Statistics
- Homework:
-
Should there be a lack
of attendance accompanied by an increasing number of homework
assignments showing up in the grader's box during class time,
assignments will no longer be posted. Come to class to find
out what is due and when.
- Handouts:
- The following were handed out in
class.
-
Class Syllabus
-
R
Graphics
-
R
Numerical Descriptives
-
R
Empirical Rule Plots
- AppleJacks box
front and
back.
- Rao-Blackwell:
PDF
file of the theorem, proof, and example. Yes,
the proof does include a bit of hand waving.
- Neyman-Pearson Most Powerful
Test:
PDF
file of plot showing the effects of sample size and
alpha on the power of a test of H0: lambda=1/2 vs.
Ha: lambda>1/2 when Xi iid Exponential(lambda),
n=10. We reject for large Xbar. Note:
joint pdf is f(x)=lambda^n * exp(-lambda*sum(xi)).
- R/S-Plus Code:
-
Tanks
programs for simulating the collection of data.
The functions tanks.ests can be modified to allow for your
own estimators.
- Tank data collection form in
Excel
format.
- The following can be "source"d into R or
"restore"d into S-Plus.
- Data Files:
- NCSS "Sample"
data in Excel format.
- R/S-Plus "Singer"
data in Excel format.
- "Hospital
Survival" data in Excel format.
- Anscombe's Data:
Excel
file with data and graphs. NCSS data only in
.S0
and .S1
files (you will need both).
- Olympic Skaters:
Data from the
2002 Pairs competition wherein a judging controversy occurred. The data as
presented by NBC is given in an
Excel
file. A description of the judging process is in a
PDF file.
- El-Far'ah 12/98 Surface Data:
Excel
file containing data. The first two rows of data should be
discarded since the data from the two circles were mixed when a cat spilled one
box in which the sherds were drying into the other.
Demos: The following demonstrations were used in
class.
- Penny Flop
Calculator:
Excel file to help look at the power of a test as demonstrated
in testing the "fairness" of coins.
Java Applets:
- Pass the Oinkers:
A fun way to get a feel for
probabilities and expected values.
Play
the game here or download
everything you need to play it on your Java enabled machine.
-
Histogram - check the effect of bin size on Old Faithful data
(Webster West - S. Carolina).
-
N=111
Exams Histogram - apply Webster's sliding bin size to our
class example.
-
Calculating normal probabilities - just click or slide the
boundaries to find the probability of the shaded region - or try
the more
Accurate Normal Calculator where you enter the endpoints
numerically. Both applets are demos from Gary McClelland's
Seeing Statistics
project.
-
Guessing Correlations - a neat "game" to show the relationship
between correlations and scatterplots Part of the CUWU
Statistical Program at Illinois-Champaign-Urbana.
-
Drawing a Regression Line by "Eye" Click the "Begin" box to
bring up a scatterplot. Use your mouse to draw a line on the
scatterplot. The MSE error is computed (i.e. "average" squared
error). Check the minimum MSE and see how close you can get.
Click the box to see the least squares line. You can also guess
and check the correlation. This applet is part of the Rice
Virtual Lab in Statistics. (Note: Netscape 4.06 or better is
required for Java 1.1)
-
Influence in Regression - see the effects of adding an outlier
to a least squares line. (Webster West - S. Carolina).
-
Normal Approximation to Count data - see how the distribution
of counts(binomial) in a sample relate to the sample size (n) and
proportion (p). Note: The sample proportion is just count/n so
this helps see how well the normal curve fits the sampling
distribution of a sample proportion. Try it for n=12 and p=0.1,
0.2, 0.4, 0.5, 0.6, 0.8, and 0.9. (Rice Virtual Lab in Statistics)
-
Confidence Interval Simulator - (CUWU Statistical Program)
You will first need to define your "population" by specifying the
values and their probabilities.
- For a quick demo, choose the "Die" option and a number of
sides. Click on "Accept Box" to see the population model.
- To simulate CI's for a proportion, choose the "Coin" option
and specify the population p. Again click on the "Accept Box" to
see the population model.
- Click on the "Confidence Intervals" button, then specify n,
CI level and the number of intervals to simulate.
-
Confidence Interval Simulator - (Rice Virtual lab in Statistics).
Simulates samples of size n=10, 15, or 20 from a population with
mean 50 and std. dev. 10. Window shows confidence intervals for
100 samples, highlighting those that miss 50 at a 95% or 99%
level.
Utilities:
- R
is a freeware "statistical package". It has been
compiled to run under Windows, Mac OSX, and Linux --
other versions are probably around. R is actually
a vectorized, object oriented programming language with
a large library of statistical functions already written
for it. It is used in a number of graduate
programs and companies. R is known for its
flexibility and its presentation quality graphics. Not-
guaranteed-to-be-most-recent versions for
Windows
and Mac OSX
as well as the
Windows installation notes are available locally by
clicking on the appropriate version. If possible,
you should download the executables directly from the
CRAN.
Some documentation can be found
here,
here, and
here.
You will probably want to install and load the "lattice"
and "Rcmdr" libraries.
- The very much not free version of R
is S-Plus
which has a somewhat nicer front end and about a $2000
street price. Academics get a discount, and
students can get a
free version
(alternate
site). For those who care, S came first
(Bell Labs), then S-Plus showed up (work at UW and then
Insightful), and then the S people came back with R.
- NCSS
(Number Cruncher Statistical Software) is not free.
However, there is a trial version that works for 7 days. NCSS is available on
campus.
- SAS
(Statistical Analysis System) is used by many Fortune
500 companies. It contains both analytical and
data management tools. However, its graphics are
weak. It is also very expensive -- particularly to
small liberal arts colleges. A working knowledge
of this package can definitely get you a job.
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