Innovative Ideas for Using Innovative Ideas for Using Statistical Software toStatistical Software toTeach ConceptsTeach Concepts

JSM, Invited Panel DiscussionJSM, Invited Panel Discussion

August 4, 2003August 4, 2003

Beth Chance, Cal. Poly. St. Univ.Beth Chance, Cal. Poly. St. Univ.

Robin Lock, St. Lawrence Univ.Robin Lock, St. Lawrence Univ.

Deborah Nolan, Univ. of Cal, BerkeleyDeborah Nolan, Univ. of Cal, Berkeley

Allan Rossman, Cal. Poly. St. Univ.Allan Rossman, Cal. Poly. St. Univ.

Outline

Panelists present activitiesPanelists present activities Fathom, Minitab, R, Self-developed Fathom, Minitab, R, Self-developed

AppletsApplets Panelists compare activities Panelists compare activities Panel discussionPanel discussion Audience questionsAudience questions

Some Fathom Tools for Investigating Statistical

Concepts

Robin H. LockBurry Professor of Statistics

St. Lawrence Universityrlock@stlawu.edu

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 First Names

Jones Jerry

Miller Marvin

Smith Sam

Williams 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

4

2 where

,4

196.1

*

***

n

xp

n

ppp

n

ppp

ˆ1ˆ96.1ˆ

Conventional method:

Alternative method:

Minitab Activity: Handedness

p\n 10 20 30 50 1000.1 64.75% 86.91% 80.12% 88.28% 93.31%

92.62% 95.81% 97.60% 97.06% 95.08%0.2 88.55% 92.29% 94.76% 93.51% 93.10%

96.50% 95.89% 96.50% 95.06% 95.15%0.5 88.58% 95.83% 95.76% 93.53% 94.01%

97.63% 95.83% 95.76% 93.53% 94.01%

Approximate coverage probabilities (10,000 repetitions):

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.  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.

92

3

5

6

4

4

105

Average = 5

2

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 conceptsCon: Limited higher level analysis tools

Pro: Easy to learn (point & click generation)Con: Dealing with multiple windows

Pro: Easy for customizable simulationsCon: Collections from collections can be tricky

Pro: Interactive, dynamic linkingCon: Danger of disturbing the dataPro: 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 learned3. Can be used in subsequent statistics

courses4. Relatively flexible and extendable5. Relatively easy-to-learn6. 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