Math 156 — Introduction to Statistics

Section 6, MWF 2-2:50 ["Traditional Statistics"]

Here is a shortcut to the course schedule/homework page.

**Lectures:** MWF in PM 103, 2-2:50pm
**Office Hours:** M-F 10-10:50am (**tentatively!**)

**Instructor:** Jonathan
Poritz **Office:** PM 248
**E-mail**
jonathan.poritz@gmail.com

**Phone:** 549-2044 (office — any time); 337-1210 (cell)
and 473-8928 (home) (both for emergencies only, please)

**Text: The Basic Practice of Statistics**

**Topics:**

- Describing data and distributions
- graphing
- measures of variation
- density curves
- Normal distributions, the 68-95-99.7 rule

- Relationships in data
- scatterplots
- correlation -- the least-squares line
- cautions: extrapolation, hidden variables, "correlation is not causation"

- producing data
- simple random samples ("independent, identically distributed")
- matched-pair and block designs
- the placebo effect, double-blind experiments

- probability
- outcome space, events, combining events, mutually exclusive events
- independent events
- the Law of Large Numbers
- distributions, cumulative distributions
- random variable
- the situation of repeated Bernoulli trials
- mean (expectation), variance, standard deviation
- sampling distributions
- the Central Limit Theorem

- confidence intervals (for means with known and unknown population
standard deviation)
- definitions
- confidence levels
- critical values on the Normal distribution
- dependence on sample size
- Student's
*T*-distribution

- hypothesis testing (tests of significance; for means with known and
unknown population standard deviation)
- null hypothesis, alternative hypothesis
- test statistic
*p*-values

**Daily procedures:** Regular attendance in class is a key to
success. I will assume students will generally be present (*e.g.*,
in terms of making announcements), although I will not take attendance
and will try to keep my HW/schedule web page up to date will all important
notices. Outside of class, you should expect to spend 2-3 hours of work
per class meeting, mostly on homework. This is not an exaggeration (or a
joke), and you should make sure you have the time and energy — but I
guarantee that if you put in the time and generally approach the class with
some seriousness you will get quite a bit out of it (certainly including the
grade you need).

In addition, there will be various worksheets we will do, individually and
in groups, during some classes. Most of these can be handed in for extra
credit.

**Homework:** Parts of this long list of topics are somewhat
intellectually challenging, but neither insightful lectures nor extensive
home study of class notes and the textbook will (alone) result in true mastery
(or even, for that matter, in passing the course): long experience shows that
*doing problems is the only way to master this material*. To this end
(and also to help keep students on track and up-to-date), there will be some
homework due every day in class. I am happy to spend time in class discussing
these problems, so don't hesitate to ask -- but don't fall behind, as it will
quickly pile up.

I get a lot of homework to grade in my various classes, so I ask your help in keeping it organized. Here are some individually trivial (some of them) but useful guidelines I would like you to follow:

- Homework is due either in class or in the box at my office door,
**no later than 3pm**. - Late homework will count, but at a reduced value — generally,
the score will be reduced by 20% for each day late... unless you
use a "
*Homework Pass*". Any unused passes may be turned in at the end of the term for extra credit on your general homework grade. - Please try to be neat (how can I give you credit for your work if I cannot read it?). In particular, don't skimp on paper. But please cut off ragged edges and please, please use staples to attach multiple pages (and not that terrible thing where you sort of chew on the corner of the pages).
- Make sure to label each assignment you hand in with your name and date, the course number, and number of the homework assignment (from the HW page).
**Make sure you define your variables and explain the steps of your work.**Similarly, if something you hand in has a graph in it, make sure the graph is clear, large enough to be legible, and has**labels**. These points are terrifically important and I will grade them more and more inflexibly as the term goes on.

**Quizzes:** Most Fridays, during weeks in which there is no hour
exam, there will be a short (10-15 minute) quiz at the end of class. These
may or may not be open book or notes, but calculators will (usually) be
allowed. The quizzes are intended to encourage reading the textbook and
classroom discussion about the "real meaning" of some technique we have
learned. Your lowest quiz score will be dropped.

**Public Awareness Analyzed Examples:** You are asked and encouraged to
hand in each week in which there is no hour exam (on Monday) a statistical
result which you find mentioned in the popular press (or in some specialized
literature in your main field of study) that pertains to the topic discussed
in the previous week. Each such example must include

- a complete citation of the source of the example;
- an interpretation of the reported result in the terminology we have used in class; and
- a (brief) critique of the reported statistic's presentation or methodology or interpretation.

1 — 2 (refers to this source) — 3 (refers to this source) — 4 — 5 — 6 — 7 — 8 — 9

You are expected to hand in at least five such examples (which will be graded on a very coarse scale along the lines of "satisfactory/missing important pieces/non-existent"), but additional examples which you hand in will be graded and will count as general course extra credit. Here are some web sites with lots of reported statistics that might make good sources:

- Textbooks or, even better, research papers you read for your other classes.
- Polling sites (particularly good in an election year!):
- A famous source of (real, hard, cutting-edge) scientific papers, many of which have statistical results in them (try the search interface): http://www.arxiv.org
- Any newspaper site, such as the following (which are some of my favorites; try the financial or scientific pages for statistical numbers or graphs):

**Exams:** We will have three in-class exams, on dates and covering
material to be announced at least a week in advance. Then we will have a
comprehensive final exam on **Thursday, December 11, from 1-3:20pm in our
usual classroom**.

**Technology:** A calculator is necessary throughout this course
(please bring it to class, we will often do group work for which you will
want it!), for all homework and during the exams. It must be capable of
performing basic scientific computations (including logarithms, exponentials and
factorials), doing simple plots, and computing standard simple statistical
functions of small data sets. Essentially any *Texas Instruments*
calculator from the *TI-83* up will suffice; the instructor will use a
*TI-84 Plus*.

**Academic integrity:** Mathematics is more effectively and easily
learned — and more fun — when you work in groups.
However, all work you turn in must be your own, and any form of cheating
is grounds for an immediate F in the course for all involved parties.

**Students with disabilities:** The University abides by the Americans
with Disabilities Act and Section 504 of the Rehabilitation Act of 1973, which
stipulate that no student shall be denied the benefits of education "solely by
reason of a handicap." If you have a documented disability that may impact your
performance in this class for which you may require accommodations, please see
me as soon as possible to arrange these accommodations. In order to receive
this assistance, you must be registered with, and provide documentation of
your disability to, the Disability Services Office, which is located in the
Psychology Building, Room 232.

**Grades:** The total homework points will be scaled to be out of 100.
Quiz total points will be scaled to 75. The Public Awareness examples will
count for 25 points, for the first five, and then as extra credit for any
others. Each hour exam during the term will be graded out of 100, while the
final will be out of 200. This means that the maximum possible course points
are then 700.
Letter grades will then be calculated in a way no more strict than:

A: |
630-700 |

B: |
560-629 |

C: |
490-559 |

D: |
420-489 |

F: |
0-419 |

**Contact outside class:** Over the years I have been teaching, I have
noticed that the students who come to see me outside class are very often the
ones who do well in my classes. Now correlation is not causation, but why not
put yourself in the right statistical group and drop in sometime? I am always
in my office, PM 248, during official office hours (to be announced
soon). If you want to talk to me privately and/or cannot make those times,
please mention it to me in class or by e-mail, and we can find another time.
Please feel free to contact me for help also by e-mail at
jonathan.poritz@gmail.com, to
which I will try to respond quite quickly (usually within the day, often
much more quickly); be aware, however, that it is hard to do complex
mathematics by e-mail, so if the issue you raise in an e-mail is too hard
for me to answer in that form, it may well be better if we meet before the
next class, or even talk on the telephone (in which case, include in your
e-mail a number where I can reach you).

**The Math Learning Center:** located in PM 132, is a fantastic resource
for CSUP math students. Use it often! (Although during my office hours,
come to my office, preferentially.) It is free and fun, staffed with friendly
and helpful tutors. One-on-one tutoring in the Gen Ed Tutoring center for
Math 156 will also be available on an appointment basis.

**A request about e-mail:** E-mail is a great way to keep in touch
with me, but since I tell all my students that, I get *a lot* of e-mail.
So to help me stay organized, please put your full name and the course name
or number in the subject line of all messages to me. Also, if you are writing
me for help on a particular problem, please do not assume I have my book, it
is often not available to me when I am answering e-mail; therefore, you should
give me enough information about the problem so that I can actually help you
solve it (*i.e.,* "How do you do problem number *n* on page *p*"
is often not a question I will be able to answer).

**Words:** One warning up front: I believe strongly that students
should learn to *think* in the way of a subject they are learning, not
merely that they become sophisticated calculators who can follow recipes.
Therefore I will **require** you to explain all your work on HWs and
tests and on the final. This doesn't mean that you have to write essay
answers to purely computational questions, but it does mean that you have
to tell me a word of two about what you are thinking as you do the
calculations. In particular, you could hand in an answer to some problem
with just a few numbers, all of which were correct — and get a **0**;
you could also hand in an answer with a few words explaining your numbers and
get full credit, even if all of the numbers were actually wrong. I will
try to give you feedback on HWs and in class on this requirement during
the term, so that it does not come as a surprise during tests.

There are three types of lies - lies, damn lies, and statistics.

*Benjamin Disraeli (1804 - 1881)*

It is easy to lie with statistics, but it is easier to lie without them.

*Frederick Mosteller (1916 - 2006 )*

The plural of anecdote is not data.

*Roger Brinner*

Forecasting is very difficult, especially about the future.

*Edgar R. Fiedler (1929 - 2003)*

Statistical thinking will one day be as necessary for efficient citizenship
as the ability to read and write!

*Samuel S. Wilks (1906 - 1964),
paraphrasing Herbert G. Wells (1866 - 1946)*

Luck is probability taken personally. It is the excitement of bad math.

*Penn F. Jillette (1955 - )*

The only statistics you can trust are those you falsified yourself.

*Sir Winston Churchill (1874 - 1965)
(Attribution to Churchill is ironically falsified)*

Thirty years ago I was diagnosed with motor neurone disease, and given two
and a half years to live. I have always wondered how they could be so precise
about the half.

*Stephen Hawking (1942 - )*

It is commonly believed that anyone who tabulates numbers is a statistician.
This is like believing that anyone who owns a scapel is a surgeon.

*Robert Hooke (1918 - )*

A statistician's wife had twins. He was delighted. He rang the minister who was also delighted. "Bring them to church on Sunday and we'll baptize them," said the minister. "No," replied the statistician. "Baptize one. We'll keep the other as a control."

A student used a digital camera to take a picture of himself. The next week he taped the photo to his statistics midterm and left the test a half hour earlier than any other student. Even though he just put down his answers without any explanations, the professor had to give him full credit for showing his work.