Getting Down to Business: Engaging Business Majors in Statistics Class Heather Smith and John Walker Cal Poly, San Luis Obispo Downloads: statweb.calpoly.edu/jwalker

CORS-INFORMS, Banff Topics for Today Background on our students and program A few examples of how we utilize – Demonstrations – Activities – Assignments to engage business students

CORS-INFORMS, Banff 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 limited business knowledge Class size ranges from 35 to 50 Emphasis on design, interpretation, computing

CORS-INFORMS, Banff Business Majors with Statistics Minors Currently about 40 minors, most from business Four additional statistical content courses -Two of the following: Regression, DOE, or SAS software -Two of the following: Time Series, Categorical Data Analysis, Survey Research, S-Plus, Multivariate Analysis To attract new statistics minors, we invite current statistics minors to speak in introductory classes

CORS-INFORMS, Banff Activities and Assignments 1.The Cal Poly Alphabet Company (Quality) 2.Market Beta (Time Series Simple Regression) 3.The Long Jump Activity (Multiple Regression) 4.The Helicopter Experiment (DOE) 5.The Sampling SIM Program (Simulations) Introduction to sampling distributions Introduction to the t-distribution The activities above take class time, and will reduce the time available for lecture, but it’s worth it.

CORS-INFORMS, Banff #1: The Cal Poly Alphabet Company THE NECESSITY OF TRAINING HANDS FOR FIRST-CLASS FARMS IN THE FATHERLY HANDLING OF FRIENDLY FARM LIVESTOCK IS FOREMOST IN THE MINDS OF FARM OWNERS. SINCE THE FOREFATHERS OF THE FARM OWNERS TRAINED THE FARM HANDS FOR FIRST-CLASS FARMS IN THE FATHERLY HANDLING OF FARM LIVESTOCK, THE OWNERS OF THE FARMS FEEL THEY SHOULD CARRY ON WITH THE FAMILY TRADITION OF TRAINING FARM HANDS OF FIRST- CLASS FARMS IN THE FATHERLY HANDLING OF FARM LIVESTOCK BECAUSE THEY BELIEVE IT IS THE BASIS OF GOOD FUNDAMENTAL FARM EQUIPMENT. “The Cal Poly Alphabet Company doesn’t like F’s. Inspect this passage; find and count the F’s.”

CORS-INFORMS, Banff Lessons from the Alphabet Company Activity Introduction to Six-Sigma and SPC Opens the discussion about quality How can it be measured? Quality by inspection vs. Focus on process and variation Students are surprised by the amount of variation

CORS-INFORMS, Banff #2: A Time Series Regression Project: Computing the Market Beta of a Stock Each group picks a stock. (No duplicates.) Collect stock price and market index from Web. Regress Stock Price vs. Market Index –Check model assumptions. –Transform the data. Regress “Return on Stock” vs. “Return on Index” –Check model assumptions and influential observations. –Interpret the Market Beta. Test whether  = 1.

CORS-INFORMS, Banff Model 1: Dell Stock 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

CORS-INFORMS, Banff Transformed Model 2: 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

CORS-INFORMS, Banff Lessons from the Market Beta Activity Statistics really is used in business! (Business students love looking at stock data.) It’s important to check the data against the assumptions of the statistical model Time series data must be analyzed differently than cross-sectional data Data transformation is useful, not scary or wrong The most important hypothesis to test in a regression isn’t always  = 0

CORS-INFORMS, Banff #3: The Long Jump Activity Divide the class into teams and pick team leaders Equipment: a yardstick and a data collection form Teams go outside, and each person jumps For each person, record: Name Jumping distance (in.) Height (in.) Foot-to-waist height (in.) Gender (M/F) Age (years) Shoe type (Good/Bad/None)

CORS-INFORMS, Banff Sample Long Jump Data Jumping distance HeightFoot-to- waist Gender (m=1) AgeGood shoes Bad shoes

CORS-INFORMS, Banff Scatterplot: Distance vs. Height

CORS-INFORMS, Banff What about gender?

CORS-INFORMS, Banff 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%

CORS-INFORMS, Banff Benefits of 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, requires about 15 minutes to collect the data Can illustrate many important issues in multiple regression

CORS-INFORMS, Banff Lessons from the Long Jump Activity Simple regression doesn’t tell the whole story Predictors may be quantitative (e.g. height, age) or 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 is highly correlated with foot-to-waist ht.)

CORS-INFORMS, Banff #4: The Helicopter Experiment Demonstrates DOE and ANOVA Divide the class into teams Equipment: 1.paper helicopters of various designs 2.a stop watch 3.data collection form 4.a high location to drop from (window, stairs, etc.) Each team gets two different helicopters Roles within the team: randomizer, pilot, timer, and data recorder. Teams turn in data to be analyzed at next class.

CORS-INFORMS, Banff Common Variables Common Variables Response Flight Time (quantitative) What factors lead to increased flight time? 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)

CORS-INFORMS, Banff Benefits of the Helicopter Experiment Another physical activity Introduces principles of DOE Control, Randomization, Replication, and Blocking Great for demonstrating randomization and data collection! 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

CORS-INFORMS, Banff Helicopter Experiment Variations Helicopter Experiment Variations Two sample t-test Paired t-test One-way ANOVA Multi-factor ANOVA with or without interactions Fractional factorial design and analysis Quadratic terms Gloria Barrett and Floyd Bullard North Carolina School of Science and Mathematics

CORS-INFORMS, Banff #5: The Sampling SIM Program Garfield, delMas, and Chance (NSF project) FREE! Possible simulation exercises 1.What is a Sampling Distribution? 2.Sampling from Non-Normal Populations Where does the “magic” n = 30 come from? 3.What does “confidence” mean? “Good” intervals vs. “Bad” intervals 4.Why bother with the t-distribution? Coverage probabilities

CORS-INFORMS, Banff 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 Lab 7.Helicopter Blueprint 8.Helicopter Experiment Variations 9.Link to the Sampling SIM Software