Making Statistics More Effective in Schools of Business: Involving Statistics Students in Activities Heather Smith and John Walker Cal Poly, San Luis Obispo Downloads: statweb.calpoly.edu/jwalker

2 Our Goal for Today Continue the conversation about engaging students Provide a few examples of how we utilize Demonstrations Activities Assignments to engage students

3 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

4 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

5 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)

6 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)

7 #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

8 #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)

9 First Model: DELL Price vs. S&P Index The regression equation is DELL = SPX Predictor Coef SE Coef T P Constant SPX S = R-Sq = 60.5% R-Sq(adj) = 58.8% Durbin-Watson statistic = 0.38

10 Tranformed Model: Return vs. Return The regression equation is DELL-r = SPX-r 24 cases used 1 cases contain missing values Predictor Coef SE Coef T P Constant SPX-r S = R-Sq = 42.8% R-Sq(adj) = 40.2% Durbin-Watson statistic = 1.86

11 #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

12 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)

13 An Example of What the Data Looks Like Jumping distance HeightFoot-to- waist Gender (m=1) AgeGood shoes Bad shoes

14 An Initial Scatterplot

15 A Second Scatterplot

16 A Typical Analysis The regression equation is: Distance = Height Foot-to-waist Gender Age Goodshoes Badshoes Predictor Coef SE Coef t pvalue Constant Height Foot-to-waist Gender Age Goodshoes Badshoes s = R-Sq = 70.0% R-Sq(adj) = 67.1%

17 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)

18 #4: The Sampling SIM Program Garfield, delMas, and Chance (NSF project) 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

19 #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

20 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.

21 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)

22 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.

23 For Even More Helicopter Variations North Carolina School of Science and Mathematics (NCSSM) Gloria Barrett and Floyd Bullard PDFS/theme_var.pdf

24 Files Available for Download 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