Transcript Innovative Ideas for Using Statistical Software to Teach

Innovative Ideas for Using
Statistical Software to
Teach Concepts
JSM, Invited Panel Discussion
August 4, 2003
Beth Chance, Cal. Poly. St. Univ.
Robin Lock, St. Lawrence Univ.
Deborah Nolan, Univ. of Cal, Berkeley
Allan Rossman, Cal. Poly. St. Univ.
Outline
 Panelists

present activities
Fathom, Minitab, R, Self-developed
Applets
 Panelists
compare activities
 Panel discussion
 Audience questions
Some Fathom Tools for
Investigating Statistical
Concepts
Robin H. Lock
Burry Professor of Statistics
St. Lawrence University
[email protected]
Joint Statistics Meetings, San Francisco, August 2003
Three Useful Tools
•Interactive linked graphics
•Sliders
•Collections from collections
Some Minitab Tools for
Investigating Statistical Concepts
Allan J. Rossman
Cal Poly – San Luis Obispo
Minitab Activities
• Friendly Observers: Randomization test
for two-way table, significance
• Random Babies: Matching problem,
interpretation of probability
• Handedness: Simulation of coverage
probabilities of multiple confidence interval
methods
* Full versions of handouts can be found at
www.rossmanchance.com/jsm03/activities
Minitab Activity: Friendly Observers
• Psychology experiment
– Butler and Baumeister (1998) studied the
effect of observer with vested interest on
skilled performance
• Subjects played a video game ten times
• Established 70th percentile of performance score
as threshold for each subject
• Played final game for prize, aiming to beat
threshold
Minitab Activity: Friendly Observers
• 24 subjects were randomly assigned to
one of two groups:
– Group A: observer can also win prize
– Group B: observer can not win prize
• Conjecture: Those whose observer did not
have a vested interest would perform
better
– Subjects in Group B would beat threshold
more often
Minitab Activity: Friendly Observers
A (share) B (no share) Total
Win
3
8
11
Lose
9
4
13
Total
12
12
24
Minitab Activity: Friendly Observers
• 3/12 < 8/12
– Sample results support the conjecture, but by
enough?
– How often would such an extreme sample
occur by chance?
Minitab Activity: Friendly Observers
• Students investigate this question through
– Hands-on simulation
– Student-constructed computer simulation
– Mathematical model
• counting techniques
Minitab Activity: Friendly Observers
• Hands-on simulation:
– Let 11 black cards represent “win” and 13 red
cards represent “lose”
– Shuffle the 24 cards and randomly deal 12
cards to represent Group A
– How many of the winners/black cards were
assigned to Group A?
– How often do we find 3 or fewer winners in
Group A if the assignment is purely random?
Minitab Activity: Friendly Observers
6/100
Minitab Activity: Random Babies
• Four mothers give birth to baby boys on
the same night in the same hospital
• Hospital staff distributes babies to mothers
at random
• Number of mothers who get the right baby
– Students approximate probabilities through
simulation
• Hands-on
• With technology
– Enumerate sample space and determine
exact probabilities
Minitab Activity: Random Babies
Last Names
Jones
Miller
Smith
Williams
First Names
Jerry
Marvin
Sam
Willy
Minitab Activity: Handedness
• What proportion of students in class are
left-handed?
• Estimate proportion of left-handers in
population with 95% confidence
• Compare competing procedures
– Under repeated random sampling, which
succeeds in capturing population proportion
about 95% of the time
• Under what conditions on n, p?
Minitab Activity: Handedness
Conventional
ˆ 1  pˆ 
p
method:
pˆ  1.96
n
Alternative
*
*


p
1

p
*
p  1.96
,
method:
n4
x2
*
where p 
n4
Minitab Activity: Handedness
Approximate coverage probabilities
(10,000 repetitions):
p\n
0.1
0.2
0.5
10
64.75%
92.62%
88.55%
96.50%
88.58%
97.63%
20
86.91%
95.81%
92.29%
95.89%
95.83%
95.83%
30
80.12%
97.60%
94.76%
96.50%
95.76%
95.76%
50
88.28%
97.06%
93.51%
95.06%
93.53%
93.53%
100
93.31%
95.08%
93.10%
95.15%
94.01%
94.01%
Some Self-developed Applets for
Investigating Statistical Concepts
Beth L. Chance
Cal Poly – San Luis Obispo
Self-developed Java Applets
• Sampling words: Simulation of sampling
distributions
• Sampling regression lines: Simulation of
sampling distributions of regression slope,
intercept
* Full versions of handouts can be found at
www.rossmanchance.com/jsm03/activities
Self-developed Java Applets
• Activity: Sampling words
– Is the sample representative of the larger
population?
– How do results vary from sample to sample?
Four score and seven years ago, our fathers brought forth upon this continent a
new nation: conceived in liberty, and dedicated to the proposition that all men are
created equal.
Now we are engaged in a great civil war, testing whether that nation, or any
nation so conceived and so dedicated, can long endure. We are met on a great
battlefield of that war.
We have come to dedicate a portion of that field as a final resting place for those
who here gave their lives that that nation might live. It is altogether fitting and
proper that we should do this.
But, in a larger sense, we cannot dedicate, we cannot consecrate, we cannot hallow
this ground. The brave men, living and dead, who struggled here have consecrated
it, far above our poor power to add or detract. The world will little note, nor long
remember, what we say here, but it can never forget what they did here.
It is for us the living, rather, to be dedicated here to the unfinished work which
they who fought here have thus far so nobly advanced. It is rather for us to be here
dedicated to the great task remaining before us, that from these honored dead we
take increased devotion to that cause for which they gave the last full measure of
devotion, that we here highly resolve that these dead shall not have died in vain,
that this nation, under God, shall have a new birth of freedom, and that
government of the people, by the people, for the people, shall not perish from the
earth.
Four score and seven years ago, our fathers brought forth upon this continent a
new nation: conceived in liberty, and dedicated to the proposition that all men are
created equal.
Now we are engaged in a great civil war, testing whether that nation, or any
nation so conceived and so dedicated, can long endure. We are met on a great
battlefield of that war.
We have come to dedicate a portion of that field as a final resting place for those
who here gave their lives that that nation might live. It is altogether fitting and
proper that we should do this.
But, in a larger sense, we cannot dedicate, we cannot consecrate, we cannot hallow
this ground. The brave men, living and dead, who struggled here have consecrated
it, far above our poor power to add or detract. The world will little note, nor long
remember, what we say here, but it can never forget what they did here.
It is for us the living, rather, to be dedicated here to the unfinished work which
they who fought here have thus far so nobly advanced. It is rather for us to be here
dedicated to the great task remaining before us, that from these honored dead we
take increased devotion to that cause for which they gave the last full measure of
devotion, that we here highly resolve that these dead shall not have died in vain,
that this nation, under God, shall have a new birth of freedom, and that
government of the people, by the people, for the people, shall not perish from the
earth.
Four score and seven years ago, our fathers brought forth upon this continent a
new nation: conceived in liberty, and dedicated to the proposition that all men are
created equal. 9
2
Now we are engaged in a great civil war, testing whether that nation, or any
nation so conceived and so dedicated, can long endure. We are met on a great
battlefield of that war.
5
We have come to dedicate a portion of that field as a final resting place for those
3 who here gave their lives that that nation might live. It is altogether fitting and
proper that we should do this.
6
But, in a larger sense, we cannot dedicate, we cannot consecrate, we cannot hallow
this ground. The brave men, living and dead, who struggled here have consecrated
it, far above our poor power to add or detract. The world will
4 little note, nor long
remember, what we say here, but it can never forget what they did here.
4
2
It is for us the living, rather, to be dedicated here to the unfinished work which
they who fought here have thus far so nobly advanced. It is rather for us to be here
dedicated to the great task remaining before us, that from these honored dead we
take increased devotion to that cause for which they gave the last full measure of
devotion, that we here highly resolve that these dead shall not have died in vain,
that this nation, under God, shall5 have a new birth of freedom, and that
government of the people, by the people, for the people, shall not perish from the
10
earth.
Average = 5
Applet Activity: Sampling Words
• Students examine results for evidence of
bias
The population mean of all 268 words is
4.295 letters
Applet Activity: Sampling Words
• Comparing biased to random sampling
Applet Activity: Sampling Words
• What is the long-term behavior of this
random sampling method?
• What happens if we change the sample
size? Population size?
Self-developed Java Applets
• Activity: Sampling regression lines
– Sample of 80 students
– Cumulative GPA and hours/week studying
Applet Activity: Sampling
Regression Lines
• If no relationship
– GPA = 3.24 + 0(hrs/wk)
• How often do we see a sample slope at
least this extreme?
Some Fathom Pros & Cons
Pro: Designed for teaching concepts
Con: Limited higher level analysis tools
Pro: Easy to learn (point & click generation)
Con: Dealing with multiple windows
Pro: Easy for customizable simulations
Con: Collections from collections can be tricky
Pro: Interactive, dynamic linking
Con: Danger of disturbing the data
Pro: Infinite undo
More about Fathom?
www.keypress.com/fathom
Fathom User Group Meeting – Tonight
5:30 pm Nikko Carmel
Advantages of Minitab
1. Widely used and powerful data analysis
tool
2. Not separate software tool to be learned
3. Can be used in subsequent statistics
courses
4. Relatively flexible and extendable
5. Relatively easy-to-learn
6. Students can learn/apply some
programming skills
Disadvantages of Minitab
1. More tempting for students to focus on
software/programming and not concepts
2. Not as clear a link to context/activity
3. Not as interactive or dynamic
4. Not as visually appealing or effective
Other Applet Features
• Dragging, shading, color-coding
• Data analysis, probability calculations,
inference calculations
• Predict and test
Advantages of Self-developed
Applets
• Portability!
• Very visual and interactive, see effects
immediately
• Appeals to students’ sense of “play,” easy
to begin use
• Can make clear connection to tactile
simulation, reducing level of abstraction
• Collaboration between statistics teacher
and programmer
– Ability to modify based on classroom use
Disadvantages of Applets
• Can be more difficult to match existing course
materials
– May not give a consistent look and feel
• Can be more difficult to extend exploration
– More instructor-led investigations, no “help” button
• Will probably also need a stand alone statistical
package
– Can separate exploration and analysis
• Can appear more “black-box” to students
– Coding vs. specifying values
• Set-up Cost
Implementation Suggestions
• Consider learning curve of students and
course goals
– How familiar should they be with this package
– How much do you have to step them through
the exploration
• Minimize distractions
– Consistency
– Preserve contextual link
Implementation Suggestions
• Carefully design activities to achieve
learning goals (the hard part!)
– Guide student interaction
– Always start with tactile simulations
– Ease students to natural next step
– Utilize instant feedback capabilities
– Require student prediction in advance
Implementation Suggestions
• Provide follow-up instruction
– Allow debriefing opportunities
– After student exploration
– Promote constructive, collaborative learning
– Simultaneously design assessments
• Pick and choose your spots
– Address most prevalent misconceptions
– Emphasize power of simulation as general
problem solving tool
Hopes for the Future
• More visual, interactive, dynamic and
user-friendly
• More user control of settings
• More collaboration among programmers,
statisticians, users
Take-Home Message
• Technology can be effective for helping
students to learn statistical concepts
• Standard software packages can be useful
– Start with the concept you want to address
and the learning activity to guide student
interaction
• Specifically designed software can be very
useful
– Minimize transition time and learning curve,
maximize accessibility