Hello! And happy Groundhog Day to you all –
Tomorrow morning (week five of the 10 week, introductory course - first course in a two
course series) brings me to the start of a required unit on probability.
One of the nice things about teaching at MHCC is that ALL math classes are taught with
students in table groups of 2-4 students, so group activities are a natural and expected
part of students’ experience.
As an introduction, I use a modification of an activity stolen from you guys, Allan and
Beth. Table groups are each given a sheet with four rectangles on it, and the names here
Hermione Hearts, Cathy Clubs, Delila Diamonds, and Sally Spades each in one of the
rectangles. Then we go through the story of the staff at a hospital handing babies back
to their mothers at random, and what is the probability that all four mothers will go home
with the correct baby.
Each table repeats the experiment 10 times, for a total “probability sample” of 90 trials.
We use this to introduce the idea of probability as long-term relative frequency - then
we go back and list all possible outcomes of the experiment as permutations of 1234 and
calculate classical probabilities as well. However we like to emphasize that relative
frequency trumps the classical model - that's how we know that the probability of a
woman having a baby boy is not exactly 50%.
From this activity, we can also develop the ideas of probability distributions based on
relative frequency histograms.
I soft pedal the algebra of probability, instead use Roxy Peck's idea of a
hypothetical sample in a two-way table. I find it helps reinforce the idea of a
categorical variable being separate from the values that variable can take – eg Dorm Type
as the variable as opposed to Co-ed.
Conditional probability and Independence can be taught as concepts springing from the
sample itself, rather than coming from algebraic definitions.
Rob Hauss
Mathematics Instructor
Mt Hood Community College
503 491 7383
From: sbi-bounces(a)causeweb.org [mailto:sbi-bounces@causeweb.org] On Behalf Of Joseph
Oechsle
Sent: Monday, February 02, 2015 8:38 AM
To: Simulation-Based Inference
Subject: Re: [SBI] Happy Groundhog Day! What happened in your introductory statistics
class today?
This is my plan for tomorrow morning's Intro Stats class: (8:10-9:50)
I put four Excel spreadsheets on Blackboard: one with data re colleges and universities,
one with a cell phone survey data, and two re automobiles. I will allow ten minutes for
groups to create numeric and graphic analyses of the data sets and present them briefly to
the class. (review of types of variables and appropriate numeric and graphic analysis)
I'll discuss the computation of standard deviation and Z scores and then do an
interactive application of these tools to four worksheets I will have put on Blackboard
and we will complete in class.
After a five minute break, I will introduce a "Friendly Observers" scenario (24
people randomly assigned to 2 groups; one group performs a skilled task and is told it
will be observed and rewarded monetarily if it exceeds its prior threshold performance;
the other group does not have observers who will also be rewarded if the performers exceed
the threshold and only the participants will receive a reward. Three persons in the first
group exceed the threshold, and eight in the second group do. The question is: do vested
observers have an effect on performance?)
One group in class will simulate the scenario using playing cards, one with a random
number table, one with a calculator random number generator, and one with Excel's
random generator. Groups will present a graphic of their results, and we will discuss
them without using the language of inference.
(We did Dolphin Therapy two weeks ago on the first day of class)
On Mon, Feb 2, 2015 at 12:34 AM, Allan Rossman
<arossman@calpoly.edu<mailto:arossman@calpoly.edu>> 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@calpoly.edu<mailto:arossman@calpoly.edu>
http://statweb.calpoly.edu/arossman/
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