## Emergency Relief for the First-Time AP Statistics Teacher

As the AP Statistics course enters its second decade, there are many
teacher resources available -- so many, in fact, that the beginner
often has difficulty finding the specific resource they need for
tomorrow's class. The purpose of this page is to provide a
chronological list of the resources you may need as you need
them. The goal is to provide quick answers to pressing problems,
so there is a bias toward a small number of brief, high quality
resources that answer questions often raised by students or first-time
teachers. Hence this document does not give a list of
all the topics on the syllabus, nor the most important topics, but
simply those that have in the past generated the most questions.
It's here to be your first stop when such questions arise.

### ...Out of Tiny Acorns...

The first thing you need is
the official
course description for AP Statistics. (Old timers may refer to this
as the
"Acorn Book".) Read it!

### Join Now

AP
Central provides a wealth of resources including an electronic
discussion group (EDG) where you can ask questions (and often get
answers). You need to register for AP Central and sign up for the
EDG. Do it now! The links given here
may take non-members to different places than members, so join now.

### Course Overview

AP Central has nice overview papers by
Joan Garfield on preparing to teach statistics and by
Roxy Peck on how contemporary statistical education differs from
traditional mathematics instruction.

### Plan Ahead

The one part of this checklist that may not be obvious is that you can
often obtain software bundled with a textbook for a cost that is a tiny
fraction of what you would pay if you tried to obtain software
later. If money is tight, it might be wise to think of the
textbook and available bundled software as a package. Such
bundled software generally comes on a CD-ROM bound into each copy of
the text. You may also need to consider how to use this
disk. For example, do you want to install it on computers in your
classroom, or give students the CDs to take home? Another
alternative is a site license for a lab at your school. You may
need to
consult local resource people about what is considered acceptable or
possible.

### AP Audit

You cannot have your course designated as "AP" on a transcript you send
to colleges unless the course/teacher package has gone through the AP
audit process. ("AP" is a registered trademark.) If this is
your first time teaching AP Stats., you will almost certainly need to
do this.

### How do I pace the course?

Most of the standard texts have pacing guides, either on the text
website or in printed teacher resources available from the publisher.

### First Day of School

The course begins with descriptive statistics. Most of this will
be familiar, especially if your school has an NCTM Standards-based
curriculum.

Note: From here on you only need to read about topics that you or your
students have questions about. Many of these issues are here
because they generate questions, not because they are of major
importance.

### Descriptive Statistics

#### Why divide by n-1 in
computing a variance or standard deviation?

Actually there are many statisticians who prefer to divide by n here. The pros and cons are
beyond the scope of the course. For consistency, in AP
Statistics, everybody divides by n-1.
For slightly more detail that is within the syllabus, see "degrees of
freedom" below.

#### Do I really need to teach this stuff about transforming data?

Yes. This is item three on Jared Derksen's AP Statistics FAQ list. It is easiest
to do this for a single variable before you get to regression, and that
also avoids the mistaken impression (given also by the graphing
calculators) that transformations are a regression topic.

### Design

#### What is the difference between confounding and lurking variables?

This is item four on Jared Derksen's AP Statistics FAQ list.
### Probability

#### How much probability/combinatorics should I teach?

Very
little.

#### What's the difference
between independent and mutually exclusive?

This is item five on Jared Derksen's AP Statistics FAQ list.

### Inference

#### 10% Condition

Many texts say that when we sample from a finite population, the sample
should be less than 10% of the population. This seems paradoxical
because it seems to say we should take small samples yet everything
else suggests larger samples are better. The apparent conflict
arises because most textbooks
give formulae that are for sampling from an infinite population
or sampling with replacement. These work reasonably well for
samples that are a small fraction of a finite population.
For larger
fractions one would use a more accurate and complex formula that is not
on the AP syllabus. More details?

#### Power

Students need to understand the concept of power but do not need to know how to
calculate it. Floyd
Bullard has a nice paper about the concept and some activities for
teaching it at AP Central.

#### What is a degree of freedom?

Degrees of freedom measure the amount of information available for
estimating variability. If we sample a single observation, we
have a little information about what kind of numbers might be in the
population, but no idea about their variability. It is only
additional observations beyond the first that tell us anything about
variability. Hence, we divide by n-1 in computing variance and
standard deviation, and use n-1
degrees of freedom for a one-sample t-test.
In regression, one point does not even determine a line. That
takes two, and it is only the observations beyond the first two that
tell us about variability about the line. Hence, we divide by n-2 in computing regression s, and use n-2 degrees of freedom for the t-test of slope.

#### Pooling

When we have multiple groups and we assume they share a common variance
then it makes sense to pool the data from all the groups to estimate
that common variance. This happens throughout statistics.
The most visible instance within the AP syllabus is pooling when we
test the hypothesis that two proportions are equal. If the
proportions are equal, then the corresponding variances are as well,
and
it makes sense to pool. Charles Peltier has a paper
on this case at AP Central. In regression we have an assumption
that sigma is the same for all x's
and we pool residuals from all the x
values to compute regression s.

### I'm behind! Help!

This is item eight on Jared Derksen's AP Statistics FAQ list.