Making Statistics More Effective in Schools of Business:

Involving Statistics Students in Activities

Heather Smith and John WalkerCal Poly, San Luis Obispo

E-mail: hsmith@calpoly.edu

Downloads: statweb.calpoly.edu/jwalker

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Our Goal for Today

Continue the conversation about engaging students

Provide a few examples of how we utilize Demonstrations Activities Assignments

to engage students

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An Outline of Topics

Our business students and business courses Activities about 6 methodology and SPC A simple regression assignment using time

series data A data collection and multiple regression

activity A demonstration simulating sampling

distributions and confidence intervals An activity to introduce DOE

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About Our Business Students/Classes Statistics requirements for all business majors

First quarter: 4 hrs./week for 10 weeks- Up to hypothesis testing for large samples

Second quarter: 5 hrs./week for 10 weeks- Small sample inference, Chi-square tests, Quality,

ANOVA, Regression, Time Series.

Most students have little business knowledge Class size ranges from 35 to 50 Emphasis on design, interpretation, computing

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Business Majors with Statistics Minors

Currently about 40 minors, most from business Four additional statistical content courses

- SAS- Regression or DOE- Two of the following:

Time Series, Categorical Data Analysis, Survey Research, S-Plus, Multivariate Analysis

“Statistical Communication and Consulting” (elective for minors beginning this year)

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Some Ways We Engage Students

1. The Cal Poly Alphabet Company (Quality)

2. Market Beta (Time Series Simple Regression)

3. The Long Jump Activity (Multiple Regression)

4. The Sampling SIM Program (Simulations)

5. The Helicopter Experiment (DOE)

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#1: The Cal Poly Alphabet Company

Introduction to 6 methodology and SPC Relationship between management practices

and statistical thinking History What is Quality? Service vs. Manufacturing Ways to Achieve Quality Focus on Process Focus on Variation Quality Progress and the ASQ

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#2: A Time Series Regression Project:The Market Beta of a Stock

Business people really do use this stuff! Each group picks a stock. (No duplicates.) Collect PRICE and INDEX data from Web. Regress PRICE vs. INDEX.

Check assumptions. Transform the Data.

Regress PRICE-RET vs. INDEX-RET Check assumptions and influential observations. Interpret the Market Beta. Test = 1 (not 0)

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First Model: DELL Price vs. S&P IndexThe regression equation is DELL = - 55.2 + 0.0667 SPX

Predictor Coef SE Coef T PConstant -55.20 15.01 -3.68 0.001SPX 0.06674 0.01125 5.93 0.000

S = 7.412 R-Sq = 60.5% R-Sq(adj) = 58.8%Durbin-Watson statistic = 0.38

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Tranformed Model: Return vs. ReturnThe regression equation is DELL-r = 2.16 + 2.58 SPX-r24 cases used 1 cases contain missing valuesPredictor Coef SE Coef T PConstant 2.157 3.253 0.66 0.514SPX-r 2.5775 0.6351 4.06 0.001

S = 15.68 R-Sq = 42.8% R-Sq(adj) = 40.2%Durbin-Watson statistic = 1.86

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#3: The Long Jump Activity Physically involves the students No need for business knowledge, in fact,

students have good intuition about the relationships that likely exist

Easy introduction to a complex area of statistics Outside activity, easily managed, < 15

minutes to collect the data Can illustrate many important issues in multiple

regression

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Team Data Collection Form Course information Team manager’s name Measurements on each variable for each team

member• Name• Jumping distance (in.)• Height (in.)• Foot to Waist (in.)• Gender (M/F)• Age (years)• Shoes (Good/Bad/None)

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An Example of What the Data Looks LikeJumping

distance

Height Foot-to-waist

Gender (m=1)

Age Good

shoes

Bad

shoes

81.0 74.0 42.0 1 22 0 1

78.0 65.0 41.0 0 20 0 0

78.0 75.0 42.0 1 20 0 1

77.0 68.0 41.0 0 21 0 0

77.0 69.0 40.0 1 19 1 0

76.0 67.0 41.0 0 19 1 0

76.0 67.0 36.0 1 21 1 0

75.5 62.0 35.5 0 21 0 0

75.0 67.0 42.0 0 22 0 0

75.0 66.0 37.0 1 22 1 0

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An Initial Scatterplot

75706560

110

100

90

80

70

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height

jum

ping

dis

tanc

eScatterplot of jumping data

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A Second Scatterplot

womenmen

75706560

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100

90

80

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height

jum

ping

dis

tanc

eScatterplot of jumping data

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A Typical AnalysisThe regression equation is:

Distance = 24.7 - 0.067 Height + 1.03 Foot-to-waist + 21.6 Gender + 0.407 Age + 0.08 Goodshoes - 3.68 Badshoes

Predictor Coef SE Coef t pvalueConstant 24.65 30.81 0.80 0.427Height -0.0673 0.6041 -0.11 0.912Foot-to-waist 1.0291 0.5747 1.79 0.078Gender 21.641 3.710 5.83 0.000Age 0.4065 0.3295 1.23 0.222Goodshoes 0.076 2.176 0.03 0.972Badshoes -3.680 3.093 -1.19 0.239

s = 7.876 R-Sq = 70.0% R-Sq(adj) = 67.1%

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Some Lessons Learned from the Long Jump Activity

Simple regression doesn’t tell the whole story Predictors may be quantitative (e.g. height, age)

or they may be categorical (e.g. gender, type of shoes)

How to create and interpret indicator variables Interactions may be present (height*gender) Multicollinearity may cause problems

(height with foot-to-waist)

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#4: The Sampling SIM Program Garfield, delMas, and Chance (NSF project) www.gen.umn.edu/faculty_staff/delmas/stat_tools

1. What is a Sampling Distribution?

2. Sampling from Non-Normal Populations Where does n = 30 come from?

3. What does “confidence” mean? “Good” intervals vs. “Bad” intervals

4. Why bother with the t-distribution? Coverage probabilities

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#5: The Cal Poly Helicopter Company

Has been successfully modified for use in many teaching environments

Introduces principles of DOE Physical activity No need for business knowledge, but easily relates

to business processes Can be an outside activity, easily managed As simple or as complex as your time, course

content, or interest allows

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My Set-Up

Customers of the Cal Poly Helicopter Company have been complaining about the limited flight time of CPHC helicopters. (Evidently, helicopters that stay in the air longer are more desirable.)

Because we are a customer-oriented company we have formed 12 teams of CPHC R&D managers, design engineers, pilots, field reps, and customers.

The mission of each team is to study how the basic CPHC design might be modified to increase flight time.

Each team will investigate their mission by utilizing experimental design methodology.

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Common Variables

Response Flight Time (quantitative) Flight Stability (categorical)

Factors Wing Length (2 levels or many levels) Body Length (2 levels or many levels) Type of Paper (2 levels or many levels) Paper Clip (Y/N) or (number of clips)

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Potential Designs/Analyses

Two sample t-test Paired t-test One-way ANOVA Multi-factor ANOVA with or without interactions Fractional factorial design and analysis Quadratic terms etc.

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For Even More Helicopter Variations

North Carolina School of Science and Mathematics (NCSSM)

Gloria Barrett and Floyd Bullard

http://courses.ncssm.edu/math/Stat_inst01/

PDFS/theme_var.pdf

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Files Available for Download

http://statweb.calpoly.edu/jwalker

1. This Presentation

2. The Cal Poly Alphabet Company handout

3. Market Beta Lab Assignment

4. Sampling SIM Lab: Sampling Distributions

5. Sampling SIM Lab: t-distribution

6. Helicopter Blueprint

7. Helicopter Experiment Variations