Allan, et al -
Nice idea! Saw your message right after I came out of class and
should have responded then when it was fresh. This was day 9 of a 42
class semester and we're finishing up the chapter on descriptive
statistics/graphics (after initial classes on data production, sampling,
experiments). First exam is later this week and first project
(describing their own dataset) is also due at the end of the week.
Today's topic was least squares regression (after doing
scatterplots and correlation last class). Started with a Fathom demo
where students put a movable line on a scatterplot to show the trend (we
meet full time in a computer classroom), had Fathom show the "squares"
and find SSE to see whose line was best. Then let them move their lines
around to try to lower SSE until they found essentially the least
squares line.
Once they saw how to find the fit automatically in Fathom we looked
at several situations: Hgt to predict Wgt (interpreting the slope),
population of countries to predict land area (showing influential
points/outliers), presidential approval rating as a predictor of
election margin, page number in Consumer Report Guide to predict fuel
capacity of a car (no relationship). They then did another Fathom demo,
dragging a point around to see the effect on the least squares line,
especially when the the point became very influential.
We finished up by introducing r^2 as the proportion of variability
in response explained by the predictor. This involved one more Fathom
demo where they made the movable line horizontal to see that the "best"
constant is the mean, giving the total variability as its sum of squared
errors, then found the "improvement" with the least squares line to
measure the variability explained by the predictor.
Lots of Fathom today, but that changes next class (Wednesday) when
we switch to StatKey and start in on simulations to lead to bootstrap
confidence intervals - a topic more relevant to this list.
Robin Lock
St. Lawrence University
On 2/2/2015 12:34 AM, Allan Rossman wrote:
Happy Groundhog Day!
I continue to find it inexplicable that neither private colleges nor
public universities see fit to cancel classes out of respect for this
august occasion. But this year I've decided to try to make the best
of this lamentable oversight, and I need your help!
I think it might be fun to ask introductory statistics teachers to
compare notes on what's happening in their classes on one particular
day. What better day than Groundhog Day for revisiting the same
question over and over, and over and over, and over and over, from
multiple perspectives?
I'm writing this after Groundhog Day has officially begun in
Punxsutawney, Pennsylvania, but it's shortly after 9pm on Super Bowl
Sunday here in California. So, to get the ball rolling on this
whimsical idea (I strongly prefer the word "whimsical" to "silly" in
this context), I'll use future tense to anticipate what will happen in
my class on Monday. I plan to be sound asleep when Punxsutawney Phil
makes his celebrated prognostication. (Too much information: Thirty
years ago I did indeed make the trek to Gobbler's Knob with my future
bride before sunrise on February 2, but I won't be up so early or
anywhere near Punxsutawney this year!)
My introductory students and I in STAT 217-09 at Cal Poly will begin
the fifth week of our ten week term on February 2 by finishing up a
discussion of principles of well-designed experiments.We’ll discuss a
study conducted at Harvard about whether students spend $50
differently depending on whether they’re told that it’s a “tuition
rebate” or “bonus income.”Then we’ll consider one of the first studies
of the drug AZT for reducing mother-to-child transmission of HIV.We’ll
culminate this discussion by collecting some in-class data on a very
simple randomized experiment investigating whether grouping of letters
can affect memory. All students will receive the same 30 letters in
the same order, but some will find convenient, recognizable
three-letter groupings and others will see more irregular groupings of
letters.
Then I expect to have time to introduce a study about whether swimming
with dolphins is beneficial to patients who suffer from clinical
depression. We'll discuss the design of the study and do a quick
exploration of the 2x2 table of results, setting the stage for
simulating a randomization test to assess whether the difference
between success proportions in two treatment groups is statistically
significant. Carrying out this simulation in class, using cards and
then an applet, will have to wait until February 3 when the excitement
of the momentous day has passed. (Or who knows, perhaps my students
and I will find when we awake on Tuesday that we are destined to
magically relive Monday again and again...)
Please indulge me in this fanciful exercise by replying to this
Simulation-Based Inference listserv with a description of what
happened, or will happen, in your introductory statistics class on
Groundhog Day 2015. Maybe we statistics teachers will learn something
interesting by exchanging this information and reflecting on the
variety of responses.Even if not, we can honor the grand tradition of
Groundhog Day by engaging in a substantially less grand but only
marginally more silly (oops, I mean whimsical) one.
With best wishes for the special day and for an early spring (to those
of you who must endure winter),
Allan Rossman
--
Allan J. Rossman
Professor and Chair
Statistics Department
Cal Poly
San Luis Obispo, CA 93407
arossman(a)calpoly.edu
http://statweb.calpoly.edu/arossman/
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--
Robin Lock
Burry Professor of Statistics
St. Lawrence University