Information Pertaining to the Final Exam
The final exam is an open book(s) / open notes exam --- you can use
whatever books and other printed or written material that you want to bring
with you. I recommend that you also bring a basic scientific
calculator. You will not be allowed to use a computer.
The final exam is on Thursday, Dec. 12.
Extra Office Hours
I'll be at GMU and potentially free to meet with you on
Monday night from 8 PM to midnight, and on Tuesday from 5 PM to
midnight. On Wednesday, I'm giving my other class an exam, but it still
may be possible for me to meet with you. Since part of the time when
I'll be at GMU I'll be in the Consulting Center room
where I hold office
hours (Room 25 of the Central Module), and part of the time I'll be in my office (or perhaps Dr. Gantz's
office) in Science & Technology 2, it'll be best for us to firm up
specific appointments using e-mail --- just let me know when you want to
see me, and I'll reply back with where to find me.
However, prior to about 7:30 PM on Monday, I won't have access to e-mail.
But, for most of the time from 7:30 PM to 10:30 PM on Monday, I
think I'll be in or near my office in Sci-Tech 2. So if you want to see
me Monday night, just come on over to GMU and find me --- don't wait for
me to respond back with a specific time and place.
Study Guide
The exam will be worth 40 points, since it accounts for 40% of your
grade for the course. The exam will have three parts to it.
- Part I will be worth 14 points (so 35% of
the exam, and 14% of the course grade). It will consist of 3 problems
worth 7 points each, and I'll count your best 2 of the 3. These will be
problems that you have to work out and show some work for. I'll give
some specific hints about them below.
- Part II will be worth 20 points (so 50% of
the exam, and 20% of the course grade). It will consist of 5 problems
worth 5 points each, and I'll count your best 4 of the 5. These will be
matching exercises: for each of the problems, you are to do a one-to-one
matching of two lists of 5 "items". I'll give
some specific hints about them below.
- Part III will be worth 6 points (so 15% of
the exam, and 6% of the course grade). It will consist of 7 questions
worth 1 point each. You are to answer exactly 6 of these questions
(eliminating 1 of them from consideration). These will be
true/false or multiple choice questions (with each multiple choice
question having only 4 or 5 choices for the answer (and I won't use the
none of the above as a choice)).
I'll give
some specific hints about them below, but here I'll state that there
will be exactly one such question from each of the following chapters of
H&W (or material that I presented in class related to these chapters): Ch.
3, Ch. 4, Ch. 5, Ch. 6, Ch. 7, Ch. 8, and Ch. 9.
further information about Part I
In class, I made some comments about what the three "big" problems would
be, but since one of them was to be based on Ch. 11, and I wasn't able
to present any of Ch. 11 to you because our last class meeting was
cancelled due to snow, I had to make some adjustments. What I have done
is make what was to be parts (a) and (b) of one problem into two
separate problems. (I've also reduced how much the big problems will
count, since before I wanted to put more weight on them since one of
them was to pertain to Ch. 11, which I wasn't assigning any HW exercises
on. Also, since two of the 3 problems will now be somewhat similar, I
don't want to have too much weight concentrated on such a small part of
the course.)
- One problem will be about finding an exact p-value using a
nonparametric test for the general two-sample problem (and so the data
is to come from two independent samples). The test will be one which
isn't presented in H&W, and isn't on StatXact's menu. But it is
a two-sample linear rank test, and it's exact null sampling
distribution can be determined by considering N choose n
equally-likely outcomes, where N is the combined sample size,
m + n, and n is the sample size of one of the two
samples. I'll give you very small samples to deal with, and so it may
well be that you'll find it easiest to just use a "brute force"
approach. I'll make the data such that there are no tie
situations.
- One problem will be about finding an approximate p-value using a
nonparametric test for the general two-sample problem (and so the data
is to come from two independent samples). The test will be one which
isn't presented in H&W, and isn't on StatXact's menu. But it is
a two-sample linear rank test, and you will be instructed to use
a normal approximation to obtain an approximate p-value.
I'll make the data such that there are no tie
situations.
- One problem will be about determining an expected value for a part
of a test statistic. For example, consider Friedman's test, and
consider the sum of the ranks for one of the treatments. (So, if there
are n blocks, the sum will be comprised of the sum of n
ranks, with each block contributing a rank for the treatment under
consideration.) If you know how to derive the null expectation of such a
sum (as opposed to merely finding it in a book or your notes), then you
should be able to produce what is expected for this
problem.
further information about Part II
Some of the matching problems may take appreciably more time than the others.
- One will be matching 5 tests (one from each of 5 different chapters
of H&W (from among Chapters 3 through 9)) to numbers of equally-likely
outcomes that underlie the exact null sampling distributions of the
tests. (For example, if you have samples of sizes m and n
and you're considering the Wilcoxon rank sum test, then the null
hypothesis sampling distribution can be obtained from a consideration of
m+n choose n equally-likely outcomes.)
- One will be matching 5 different values (representing p-values) to
5 different tests
(one from each of 5 different chapters
of H&W (from among Chapters 3 through 9)).
The tests will be among the more commonly used
nonparametric tests. The sample sizes will all be very small. (While
one could do all of these tests using StatXact, you won't be
allowed to use StatXact. I think you should know how to do "hand
computations" of p-values for some of the more commonly used
nonparametric tests --- knowing how to compute the value of the test
statistic should give you a better understanding of how the tests work.)
In each case, you can use the tables in the Appendix of H&W to get the
p-value.
It will suffice to know how to obtain exact p-values
from the tables in H&W for the following tests:
Wilcoxon signed-rank test,
Wilcoxon rank sum test,
Kruskal-Wallis test,
Jonckheere-Terpstra test,
Friedman's test,
and Kendall's test (for association (Sec. 8.1)).
The numbers of observations will be very small, and there will be no
ties to deal with. (Suggestion: Use a good strategy --- for this
matching problem, do the 4 tests you can do the quickest first, and if
you match 4 of the 5 values in the p-value list, then you can perhaps skip
doing the fifth test.)
- One will be matching 5 different values (representing p-values) to
5 different tests
(from among Chapters 5 through 8 of H&W).
The tests will be ones that are not on the menus of
StatXact, and so it's good to know how to do these tests by hand
(and brain).
The sample sizes will all be very small.
In each case, you can use the tables in the Appendix of H&W to get the
p-value. (Note: Even though I plan to make the sample sizes
small, this matching exercise may take a bit of time. So perhaps you
should work on other problems first, and do this one only if you have
time.)
It will suffice to know how to obtain exact p-values
from the tables in H&W for the following tests:
Lepage's test (Sec. 5.3),
Mack-Wolfe test (the one covered in Sec. 6.3.A),
Fligner-Wolfe test (Sec. 6.4),
Durbin's test (Sec. 7.6),
and Hoeffding's test (Sec. 8.6).
The numbers of observations will be very small, and there will be no
ties to deal with. (Suggestion: Use a good strategy --- for this
matching problem, do the 4 tests you can do the quickest first, and if
you match 4 of the 5 values in the p-value list, then you can perhaps skip
doing the fifth test.)
- One will be matching
5 different tests
(from among Chapters 3 through 9 of H&W) to 5 different situations /
hypotheses / experimental designs.
- One will be matching
5 different tests
(from among Chapters 3 through 9 of H&W)
to 5 other tests
(from among Chapters 3 through 9 of H&W and/or StatXact),
with the tests in each pair being ones that are generally used
for the same situations /
hypotheses / experimental designs.
For the two last matching problems referred to above, in addition to
knowing about the tests listed for the 2nd and 3rd
matching problems described above, also know what type of situations are
appropriate for
the following tests:
Ansari-Bradley test,
two-sample Kolmogorov-Smirnov test,
Spearman's test,
Siegel-Tukey test,
Wald-Wolfowitz test,
and Quade's test.
further information about Part III
I won't make a comment about each of the questions, because I haven't
firmed them up enough yet. However, I'll indicate that
- the Ch. 6 question will deal with Monte Carlo estimatimation of the
exact p-value (since it wasn't until we got to Ch. 6 procedures that we
needed to use the Monte Carlo option of StatXact);
- the Ch. 7 question pertains to adequate situations for the
tabluated null sampling distribution for Friedman's test to hold (i.e.,
relaxation of the additive model with iid
error terms);
- the Ch. 8 question deals with the "motivations" of Kendall's,
Spearman's, and Hoeffding's tests;
- the Ch. 9 question deals with the interpretation of a small p-value
from Theil's test.
I'll go to my web page comments about H&W to get inspiration for the
questions pertaining to Ch. 3, Ch. 4, and Ch. 5.