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.

Boxplots and Quartiles

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.

Random Variables


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.