Spring
2007
STAT 7030 – Mathematical Statistics II
|
Date |
Section |
Assignment |
|
Jan 8 |
Brief
review and discussion of problems on final. Two-sample
t-test and the F-test for comparing two variances. (sections 9.2, 9.3). Exam file. Baby
boom data file. |
Read
9.2, 9.3. Also read Chapter 8; it is short and informative and we will use it
later in the course. Hw#1 (due Jan 22): 9.2.3, 9.2.4
(plot the data and discuss normality, don’t just do the test using the given
summary descriptive statistics. Also check if it you may assume equal
variances.), 9.2.9, 9.3.1 (add to the given data: President Reagan: height
6’1”, age 93; President Ford: height 6’, age 93. If the answer in part (b) is
No, use the modified test for unequal variances.). Look
for more to come regarding statistics articles to read. |
|
Jan 22 |
Discussion
on designing experiments. See notes. Remarks
on the F distribution. Hypothesis tests and confidence intervals for two
population proportions. |
Data on gasoline taxes : an
example of a matched pairs hypothesis test. Hw#2
(due Jan 29): 8.2.2, 8.2.4, 8.2.16, 8.2.34, 8.2.36, 9.4.7, 9.5.8. Exercise 1 from notes. See article for
example of statistical study. |
|
Jan 29 |
Goodness-of-fit
tests. The multinomial distribution.(10.1-10.3) Mendel data (Minitab project file) |
Hw#2 extended: due Wednesday,
Jan. 31 See interesting
article on Goodness-of-fit tests. Hw#3: (due Feb 7)L 10.2.4, 10.3.2,
10.3.3, 10.3.6(in this problem you test for a single proportion, would it be any
different than a hypothesis test for one proportion?), 10.3.10. For the binomial data in the linked file
perform a goodness of fit test to assess normality by dividing the data into
8 frequency classes. See file for steps to
follow. |
|
Feb 5 |
Invited
talk: Dr. Brani
Vidakovic from Georgia Tech. will speak on Wavelets analysis on biomedical
data, in CL 1003. Chi-square
test for independence. |
Minitab
project worked in class: ex. 10.4.5.
fitting an exponential distribution. |
|
Feb 12 |
We will
start Ch. 11: The Method of Least Squares. Fitting data (Minitab file)
and some explanations
(word file) |
Read
10.4 and 10.5. Hw#4: (due Feb 14L) 10.4.12, 10.5.2, 10.5.6,
10.5.8. Think
about the projects you want to present: get data “generous enough” so that we
can apply all the tests that we have learned so far, and even more. Hw#5: (due Feb 21): 11.2.20, 23, 25,
30. Plot
your data, do a transformation if a linear plot does not seem appropriate, do
a residual plot for the fitted model. Write the equation of the regression
line and the fitted model. Still Hw#5: Work the exercise on the
handout given in class (12.2 “Never
the same amounts”: refer to questions 3&4, but be careful to state
the hypotheses, then run separate Chi-square tests). How does this test
compare to running separate proportion tests for each color of candy?
Consider the entire amount in all five bags. |
|
Feb 14 |
|
|
|
Feb 19 |
The
Linear Model: estimating the parameters in the regression equation and the
variance. |
Check the updates on Feb 12. Hw#6 (due Feb 26): 11.3.7, 11.3.9
(get the data and do the regression yourselves), 11.3.11. (refer to Theorem
11.3.2 for the distribution of Think about this and we will talk in class: 11.3.4. |
|
Feb 26 |
Prediction
from regression equations. Covariance
and correlation. The sample correlation coefficient. |
Minitab project file: pb. 11.2.30 Exam 1 is now posted. The exam is due Wednesday, March
14, You may
e-mail me if you have any questions. |
|
March 5 |
No
class. Spring Break! |
Although
most of you are working, have a nice and restful break! |
|
March 12 |
Estimating
the coefficients in the quadratic regression model. The Bivariate Normal
Distribution. |
Class notes on
the bivariate normal distribution. See also Maple file for some
computations and same file exported as
html file. |
|
March 19 |
Skewness and kurtosis. More on the Bivariate Normal Distribution. Tests of significance for the correlation coefficient in
the bivariate normal distribution. Discussion on why the test of significance for of the test. Simulation
(Maple file with explanations) of bivariate normal data that has a given
correlation. Same file exported in html
format. Notes to be posted soon. More to be added |
Research
skewness and kurtosis and the information they provide for normality of a
data set. See Resources page for links to texts and information online. Read article related to Galton’s
data on heights of parents and their children. Also, on the main site for Galton’s biography, you may read the
conclusions in his own words in Regression toward Mediocrity in Hereditary
Stature (make the search using the word “regression” in Search menu.
The article is the first hit.) Read sections
11.4 and 11.5 (see class notes above) HW#7 (due March 21): 11.4.10, 11.4.17, 11.5.8 (Be
careful here, how can you decide if the variables are independent? You can
decide if they are uncorrelated. But then does it imply they are independent?
How must they be so that we can conclude that they are independent?),
11.5.10. Here is
a treat for you: Galton’s
(slightly modified) data on heights (Excel file). Data obtained from the Jump
CD. The bivariate normal distribution (MPJ
file) |
|
March 21 |
Spring has come!
|
|
|
March 26 |
Discuss article on the sample size for Z and t confidence
intervals. Introduction to ANOVA. See article
in Minitab online resources on a complete analysis using ANOVA. Example of
ANOVA: toxins on trout. |
Hw#8Ldue March 28: 11.5.1, 11.5.4,
11.5.5, 11.5.11 Remember
the project I talked about. I would like you to have a proposal with a
description of what you plan on doing by April 4th.
See guidelines (to be posted). Here is
an article I
would like you to start reading. Please read instructions. |
|
April 4 |
Notice.
I am switching class with Dr. Lawson. I just
counted, five more classes left, I am going to miss you guys! Skewness of exponential
distribution (Maple file) and Minitab
project file. One-way
ANOVA. Comparisons
of means in ANOVA: Tuckey, Bonferroni and Scheffe’s methods. |
Read
12.1. and 12.2. Look at the ANOVA analysis example in the Minitab resources.
Here is the article
link again. Let’s
continue with the article on “How large should n be…”. Read again from the
beginning and continue to section 3. Hw#9: 1.
Devise a way of obtaining the coefficient of skewness of a standard
exponential distribution through simulations. How would you estimate it from
data? You may use Minitab, Excel or other software of choice. Give a
description of your method and report results. I do not have to see the data
worksheet. If you
adventurous enough you may try computing it with Maple or other software of
choice. 2. How would you obtain the .025 and .975
quantiles of Z_n (refer to page 5 in the article)? Try to estimate them from
the data you generate in part 1. 3. Proceed to estimate the coefficient of
skewness of the t_n statistic (see page 7). Even in the article it is
mentioned that they estimated it from 10000 samples (quite something!). o
Remember, by today you should have a clear idea of what your project
will be about. Here are some guidelines.
If there are any questions you can think of, or you feel I omitted something
of utmost importance, I will appreciate any improvements to the guidelines. |
|
April 9 |
Testing
hypotheses with contrasts. Transforming data. If you have
already done something on your project bring the questions to class. We can
start talking about your ideas. If not,
we can start Randomized
block design. Data
files: tablets; pb12.4.4 text
|
Read
12.2, 12.3. and 12.4. Scheffe’s method that I mentioned at the end of last
lecture is related to 12.4. Look at
APPENDIX 12.A.1. We obtained the Tuckey’s confidence intervals without having
stacked data! Try to answer this: in the example in class on trout toxins the
treatments did not have the same sample size. However, in the proof of
Tuckey’s method the samples are considered equal. Does it actually matter? If
it does, how would explain the confidence intervals we obtained for all the
pairwise differences between the means in that example? And, of
course, some homework, but it ain’t much! Work on your projects as well! HW#10: 12.2.3, 12.2.8, 12.3.3. Remember
to assess whether the assumptions of the model are satisfied. |
|
April 16 |
Randomized block design. More
project discussions. Notes on the
problem done in class, and the Minitab
project file. I will have the exam ready for you on Monday and it will be due on
April 30. Work on your projects this weekend. |
HW#11: 12.4.6., 12.5.1. We started in
class 12.5.3 and we decided after all we might not need to transform the
data. Run an ANOVA test but also think of a way of testing the accuracy by
conducting a Work on
your projects. Enjoy
your weekend! |
|
April 23 |
Nonparametric tests: sign test, rank test, rank-sum
test. Minitab files: rank,
Notes on Wilcoxon rank-sum test: diet_pigs (Mintab mpj file) Project presentations: Sarah Alum, Pete Stafford, Kate
Small. |
Finish
Chapter 13. You only have to cover the paired t-test, which we discussed on
the past. Pay attention to the case studies, you never know when you may need
some of the information you find in them. Hw#12: 13.2.3 (do this one using both ANOVA and paired t-test and see
how the value of the F-statistic compares to the value of the t-statistic) 13.2.5. Just “pour la bonne bouche”
which may be the equivalent of the “icing on the cake”, and extra credit, try
13.2.12. Exam 2 is now posted. The exam is due by Tuesday, May 1st,
12PM. |
|
April 30 |
This is the day of the final. We can still have
presentations, and… A party too! |
It all happened so quickly, I
did not get the chance to say good bye. I want to thank you all for two
great semesters and wish you all the best in your personal and professional
life. |
