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M 4/2/07
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Quiz on How to Lie With Statistics. You may use your personally handwritten notes if
you wish. This is a quick read, but you may want to jot some notes in your
binder as you go through the book.
Sample question: Explain and give an example to illustrate the term
“semiattached figure.”
Answer: A statistic presented as being relevant to some discussion, when the
statistic is actually only peripherally related at best. For example, a
magazine article may claim that cell phone usage is causing public health and
safety problems. Any of the following would be examples of semiattached
figures:
- “A 2000 poll showed xx% of Americans concerned
about health and safety risks from cell phones, but by 2005, that number
had increased to yy%.” This increase is semiattached because it has
nothing to do with actual health and safety risks, only people’s
opinions on the subject.
- “The number of Americans diagnosed with brain
tumors increased from xxx in 2000 to yyy in 2005.” This increase is
semiattached because it does not take into account the rates of tumor occurrence
(remember, America’s population is still growing), possible changes in
reporting, the severity of the diagnoses, the number of adverse outcomes
that occurred, or, most important of all, whether there is any reason to
suppose that a cause-and-effect relationship exists with cell phones. A
controlled experiment would be needed to prove cause and effect, but
even without a controlled experiment, the semiattached data could be
improved with some corroborating evidence, such as animal studies or
dose-response observational studies. Without those improvements, the
increase, even if expressed as a rate increase, is irrelevant to the
discussion.
- “Today, thousands more Americans die in
automobile crashes each year than in 1973, a time when only the
ultra-rich had access to mobile telephones.” True, but completely
irrelevant for many reasons. First, America’s population is much larger
than it was 34 years ago. Second, many more vehicle miles are driven
nowadays. Third, the second half of the sentence could be altered in
many absurd ways without making the sentence false: “a time before the
invention of GPS,” “a time before Donnie
Darko was released,” “a time before Styler was born,” etc., etc. In
other words, no attachment has been made between the thousands of
additional highway fatalities and the increased usage of cell phones.
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T 4/3/07
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HW due: Read pp. 658-675; write #12.13, 12.14.
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W 4/4/07
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HW due: Skim pp. 678-688; read p. 689; write #12.25, 12.26,
12.28.
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Th 4/5/07
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HW due: Read pp. 702-706 twice; write #12.35, 12.36,
12.38. Follow the full PHASTPC procedures for at least two of these.
In class: We will distribute the CSDELUXE
program. If you miss class for any reason, you are responsible for entering
this program by hand (ugh) or downloading it from someone else.
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F 4/6/07
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HW due: Skim pp. 706-709; write #13.4. You may use CSDELUXE
to do the grunt work, but a couple of warnings are needed.
Warning #1: Do not enter 78.9, 3.9, 1.4, etc. in L2.
Instead, you must enter 300(.789), 300(.039), 300(.014), etc. Do you see why?
The entries in L2 for CSDELUXE must be expected counts, not expected percentages.
Warning #2: There is a problem with the data as presented. You will
notice that the 1994 table (the second table) adds up to 300, but the first
table does not add up to 100%. I recommend that you adjust the 78.9% entry to
be 78.8%. What is my rationale?
Additional note: In addition to the
typo (78.9% versus 78.8%), there are two other typos and a large conceptual
error in #13.4 waiting to be found. Bonus points to the student with the earliest
timestamped e-mail! If you can’t find all of them, report as many as you can
find, including the answer to the question posed in Warning #2 above.
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M 4/9/07
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HW due:
1. Skim pp. 711-742.
2. Read the TI-83 STAT TESTS
Summary in detail and start memorizing it. Before you take the AP exam,
you need to have that entire handout essentially memorized, at least in your
working memory. You can get away with reading the textbook superficially,
focusing on the definitions and the summaries, but you need an absolutely
thorough knowledge of the STAT TESTS.
3. Purchase a package of M&M’s candies (plain) and bring them to class.
If you would like to purchase a large package and split the cost among 3 or 4
classmates, that is also permitted.
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T 4/10/07
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HW due:
1. Read and work through Example 13.8 on pp. 725-727. This example shows the
detailed steps to use STAT TESTS C to perform a chi-square test on the 2-way table
given. The same technique is used for either a test of independence or a test
of homogeneity of proportions. Be sure that you understand exactly how to
reproduce the results shown in the example.
2. CSDELUXE has two modes, as you know. Mode 1 is the goodness-of-fit test,
which we used twice during yesterday’s class. Mode 2 is the chi-square 2-way
table test, which can be used for either a test of independence or a test of
homogeneity of proportions. If you put the matrix into your calculator’s [A] matrix,
the operation of CSDELUXE is exactly the same as STAT TESTS C, except that
CSDELUXE is smart enough to warn you if there are potential problems with the
assumptions. Repeat the actions of #1 using CSDELUXE.
3. Use either STAT TESTS C or CSDELUXE (your choice) to perform a complete
PHASTPC test for homogeneity of proportions concerning the data we ate
yesterday. Is there evidence based only
on the data shown below that the color mix of M & M’s plain candies
differs from M & M’s dark chocolate candies? Hint: When checking assumptions, you can save a lot of time with
CSDELUXE, because CSDELUXE stores all the expected counts in matrix [B]
automatically.
Plain: 80 brown, 66 yellow, 78 red, 77 blue, 93 orange, 109 green (503 total)
Dark chocolate: 23 brown, 25 yellow, 29 red, 16 blue, 21 orange, 35 green
(149 total)
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W 4/11/07
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HW due:
1. When I programmed Smokey, I set him up so that in our class of 15
students, each student and Mr. Hansen would be equally likely with
probability 1/18, and “true volunteer” would have a probability of 1/9. In
class, In Sung gathered data for 48 trials, and at home, I ran an additional
77 trials. Such dedication have we. Do the results shown below indicate any
systematic deviation from the designed-in probabilities? Perform a complete
PHASTPC writeup, and keep a record of how long it takes you so that we can
discuss your timing as well as the content of the problem.
13 selections: Matt
11 selections each: Julian, In Sung, true volunteer
9 Rick
8 each: Sam, James, Mr. Hansen
7 each: Peter, Michael W., Oliver
6 each: Marcus, Denny
5 Michael R.
4 Alex
2 each: Kellie, Nick
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Th 4/12/07
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HW due: Read pp. 753-767 and answer the numbered questions below.
Pay special attention to Examples 14.5 and 14.7, which demonstrate how to
read computer-produced output. (This is a skill that is tested on the AP
exam.) For instance, you need to be able to look at a printout like the one
at the top of p. 763 and ascertain that b0
= 1.0892, b1 = 0.188999,
and r = 0.9955.
1. State b0, b1, and r for the printout at the top of p.
767.
2. Showing your work, compute  for the printout at
the top of p. 763.
(Yes, I know that the answer is already shown. The question is, what if it
was not shown? Could you compute it? Show your work.)
3. Similarly, show your work and compute for the printout at
the top of p. 767.
4. Have you taken a look at the Must-Pass
Quiz? James currently has 5.675 correct and 1.325 wrong, needing 2.325
more before using up his remaining 0.675 mulligan. Good luck, James!
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F 4/13/07
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No additional HW due. Congratulations to James, who
made STAtistics history by becoming the first person ever to pass the MPQ on
the first try, before the formal beginning of review season!
In class: Nick also passes, Marcus stumbles, and Mike R. has R=2 29/48,
W=19/48. Check out last year’s tote
board if you would like to see some real drama captured on a Web page.
One student took 7 attempts to pass.
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M 4/16/07
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HW due: Read pp. 774-781 (including reading notes, as
always); write #14.15abcd. This is the last textbook reading before the AP
exam. Hooray! Note that although some of the answers are given in the back of
the book, none of the work is shown. You need to show work, including PHASTPC
for part (c) and formula, plug-ins, and answer with units for part (d).
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T 4/17/07
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No class (Diversity Day during periods D, E, and F).
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W 4/18/07
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HW due: Review problems as listed below. Be sure to do at
least one of these as a full PHASTPC, but you can cut a lot of corners for
the others. If you cannot answer a question, then at a minimum you should identify the type of procedure (e.g.,
2-prop. z, 1-sample t, chi-square 2-way, or whatever). For
the problem that you do as PHASTPC, allow about 13 minutes. For all others (where
I assume you will be cutting corners), the suggested pacing times for test
proficiency are shown in parentheses. If you are taking significantly longer
than these times, then you are not sufficiently proficient yet. If you cannot
finish all of these problems during your study time, then do as many as you
can and keep a time log. We will go through as many answers in class as time
permits, provided there are no interruptions by _____ and _____ .
Note for #10.41: There is a test
that is better to use than the z
test. What is it?
p. 553 #10.41 (1½ min. unless you make this your PHASTPC, in which case allow
13 min.)
pp. 563-564 #10.59 (2 min.)
p. 564 #10.60 (2 min.)
p. 566 #10.62 (3 min.)
p. 567 #10.63 (1 min.)
p. 567 #10.64 (2 min.)
p. 567 #10.65 (4 min.) (takes longer because you must recall a previous
chapter)
p. 573 #10.68 (assume a = .05 for (b) and (c)) (2 min. for (a), 6 min. for (b) and (c))
Note: For (b) and
(c), only a sketch and an estimate are needed, not actual values.
pp. 613-614 #11.22 (3 min.)
pp. 637-638 #11.43 (5 min.)
p. 669 #12.8 (4 min.)
p. 696 #12.39 (5 min.)
p. 696 #12.40 (3 min.)
pp. 739-740 #13.27a (4 min.)
p. 742 #13.28 (skip the graph-making) (4 min.)
p. 783 #14.18c (2½ min.)
Additional material that must be studied (or crammed, if you have not studied
it already):
Answers to the review problems are available
to help you study. Although these problems are fairly comprehensive, there
are a few gaps (e.g., 2-prop. z
C.I., c2 test for indep.) that you may also wish to address
as you prepare for the test.
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Th 4/19/07
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Test (100 points) on Inferential Statistics. This test will include all types of tests,
including z and t tests, whether 1-sample, 2-sample,
or matched pairs. However, the focus will be on chi-square and LSRL t-tests.
Important: If you have grandparents
who are visiting today, please contact me immediately so that we can
structure an alternative activity for them. Unfortunately, there is really no
other suitable day for the test to be held unless you wish to take it at 7 in
the morning.
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F 4/20/07
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HW due: Re-do the entire test
from yesterday, keeping a record of your timings for each problem.
Suggested time limits for each problem are as shown below, but since I am interested
in gathering data, please simply record the true elapsed time, whatever it
may be. Also note that Wednesday’s assignment, which you should have
completed yesterday as part of your preparation for the test, may be scanned
a second time.
1. 13 minutes
2a. 7 minutes (tricky: uses formula  where s.e. =  )
2b. 3 minutes (reasonable since cutoff value of 4.286 was given in part (a))
2c. 3 minutes (note that the cutoff moves a bit to the left since s.e. has decreased)
3. 4½ minutes (rationale: similar to AP multiple choice, but with additional
answers to mark)
4. 4½ minutes (same rationale as for #3)
5. 6 minutes (requires creative use of the  formula that I gave
you)
6. 4½ minutes (same rationale as for #3)
7. 4½ minutes (same rationale as for #3)
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M 4/23/07
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Phi Beta Kappa Day (no school).
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T 4/24/07
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No additional HW due. Hooray! Please use this time to
rest, relax, recharge, and get caught up on previously assigned HW if
necessary. Starting this week, we will be relentlessly reviewing for the AP
exam. If you have not already passed the Must-Pass Quiz (or even if you
have), the MPQ makes a fairly good place to start to focus your AP review.
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W 4/25/07
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HW due: Categorize all multiple-choice problems in Practice
Exam 1 (pp. 367-375) by category,
subcategory, and difficulty level (E, M, or H). If you took written notes
during class yesterday, some of your work is already done. Try to finish all
40, but if you are a slow writer or a slow reader, you may run out of time.
Whatever. Please remember that on the real exam, you will have to answer 40 questions in 90 minutes, not
simply categorize them. You may use the abbreviations EDA, SD, Prob, and Inf.
for exploratory data analysis, study design, probability, and inferential
statistics if you wish. A few examples are shown below.
1. EDA, terminology of 1-var. stats., M
2. EDA, terminology of 1-var. stats./stemplots, E to M
3. EDA, use of invNorm, M
4. Inf., def. of C.I., M
5. SD, basic defs., E
6. Prob., cond. prob., M
7. Inf., def. of Type I/II, H since unfair question (no basis to est. Type
I/II value for towels)
Note for #7: You really can answer this if you get inside the
head of the question writer. Clearly there is a subtext that towels are
fundamentally different from dialysis patients. Therefore, after we have
determined that Type II error is the more serious error type in a dialysis
center, we should be able to infer that the question writer wants us to see
that the situation is different in a towel factory. My claim is that this is
“testmanship” and has nothing to do with the subject of statistics. After
all, in the real world, there is going to be a tradeoff between the cost of
shutting down the towel production line and the cost of throwing out
defective towels. It all depends on how long the machines have to be shut
down and how expensive it is to start them back up. Only the plant manager
could provide that information.
Will flaky questions like this occur from time on the real exam? Certainly.
Is there anything you can do to guarantee that you come up with the “correct”
answer that the authors were looking for? No. Is that a problem? Only if you
get so stuck on one question that you fail to finish the rest of the exam. In
a sense, #7 is training for the real world, in which the answers are not
always cut-and-dried, and a good deal of unfairness may be part of the
environment.
In class: AP review and Must-Pass
Quiz.
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Th 4/26/07
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HW due: Write (from Barron’s book) pp. 378-379 #5, 6. Use
standard HW format. This should take you 38 minutes. If it takes longer, I
want to know.
Note: If you are lazy, you can
obviously copy the solutions from the book. In fact, you need to do this if
you have no clue about how to proceed. However, it will obviously be much
more educational for you to attempt to perform the problems without such
assistance.
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F 4/27/07
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HW due: Write (from Barron’s book) any 3 of free-response
problems #1-4 from Practice Exam 1. These are your choice, and I recommend that
you choose 3 problems that will help you. My suggestion is that you omit the
one that you think is the easiest. Time target is 39 minutes, and again, if
it takes you longer than that, I want to know.
Class today will be conducted by Mr. Andreoli. He will take attendance and
will collect homework from Thursday and today (total of 2 problems on
Thursday plus 3 problems for today). He may then leave the classroom. At that
point, you may (if you wish) pursue Marcus’s suggestion of mini-projects to
replace some of the points that were lost on the April 19 test.
On Monday, if I am presented with a joint proposal that covers 5
mini-projects meeting the requirements below, I will implement that plan.
1. Projects must be supported by all students. In other words, each project
concept must be one that students who were randomly assigned to it would not
reject.
2. Each project must be something that could be implemented in a day of data
gathering and a second day for data processing and writeups, for a total of
two days of work.
3. One of the projects must involve a t
test (1-sample, 2-sample, or 1-sample matched pairs).
4. One of the projects must involve a LSRL t test.
5. One of the projects must involve a chi-square 2-way test. (Remember, we
already did two full in-class mini-projects on chi-square g.o.f.)
6. One of the projects must involve a 1-proportion z test (or matched pairs).
7. One of the projects must involve a 2-proportion z test.
8. Each project must be simple enough that it can be efficiently implemented
by 3 students with very little time outside class. Projects that involve
experiments on other class members or data gathered from the library or
on-line sources are ideal.
9. Research question (phrased as a question) and methodology must be outlined
for each mini-project so that the feasibility will be self-evident.
I hope that all of you can stay long enough to put together a joint proposal.
If you can’t finish, you can work on it via IM and e-mail over the weekend.
If you can finish before the end of the class period, then you will have a
weekend free of required homework.
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M 4/30/07
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HW due: One joint proposal for 5 mini-projects (see above).
No other HW is required, although I would strongly recommend that those
planning to take the AP set aside approximately 30-40 minutes per day for
working problems in the Barron’s review book.
In class, courtesy of Nicholas: Gauss birthday celebration.
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