Overview of DS 101

1. Slides by Spiros Velianitis CSUS Overview of DS 101

2. Summary Slide • Why do I discuss the DS 101 overview with the class? • ASA Recommendations for Teaching Statistics • Our Teaching Philosophy • Introduction • Course Content • Variation, Variation, and Variation • Read Bead Experiment • Control Charts • Regression • Experimental Design and Analysis of Variance – Discovering Sources of Specific Variation • Forecasting • Software

3. Why do I discuss the DS 101 overview with the class? • The purpose of this presentation is to describe the components of DS 101 which is designed to provide business students with the necessary statistical skills to become effective managers upon graduation. • It will give us a great synopsis of all the material we will discuss in our class. • Think of it as Chapter 1, for our course. • Ideas on the content and methods of teaching DS 101 come from: • Drs. Taylor, Hopfe, and Li experience (over 15 years of experience) • The GAISE College Report

4. ASA Recommendations for Teaching Statistics The American Statistical Association (ASA) funded the Guidelines for Assessment in Statistics Education (GAISE) and offers six recommendations: • Emphasize statistical literacy and develop statistical thinking • Use real data • Stress conceptual understanding • Foster active learning in the classroom • Use technology for developing conceptual understanding and analyzing data • Use assessments to improve and evaluate student learning

5. Our Teaching Philosophy I hear and I forget I see and I remember I do and I understand Chinese proverb

6. Introduction • Prerequisite knowledge for this class are the topics of descriptive statistics, probability, confidence intervals, and hypothesis testing. • The main objective of this course is to teach statistical techniques that would support classes in the functional areas of business such as accounting, finance, marketing, operations, etc. • We explain statistical techniques using the concept of variation; in particular, common variation and specific variation.

7. Course Content • Variation, Variation, and Variation • Read Bead Experiment • Control Charts • Regression • Experimental Design and Analysis of Variance – Discovering Sources of Specific Variation • Forecasting

8. Variation, Variation, and Variation • Starting on the first day of class, we stress that this course is about studying variation. Building on the well-known phrase that the three most important things to remember about real estate are “location, location, and location,” we emphasize that the three most important things to remember about our course are “variation, variation, and variation.” • To reinforce this critical concept we frequently ask the class, “What are the three most important things to remember about this course?” By the end of the semester, the responses get louder and more enthusiastic. It is not uncommon when we encounter former students they are quick to greet us with “Variation, Variation, and Variation.” • To illustrate the idea of variation, we use the concept of volatility in finance and students usually understand that volatility (that is, variation) measures the risk of the investment. Students are asked to download some daily closing price of stocks and compute estimates of volatility (standard deviation). Students encounter time series data here and, as we discuss later, time series data are used throughout the course.

9. Read Bead Experiment • Using a paddle with 50 holes, each “factory worker” simulates a day’s output at our “factory.” This is accomplished by the “workers” taking turns inserting the paddle into a bin which contains white beads (75%) and red beads (25%). The class is told that the white beads represent successful output while the red beads represent defective output. Furthermore, the class is told that in our “factory,” in order to be cost effective, our “workers” need to average no more than eight red beads per simulated daily production. The “middle management employee” records the number of red beads (defects) drawn by each “worker.”

10. Control Charts • In order to reinforce the concepts of common variation and specific variation, we introduce control charts and discuss their applications in manufacturing, financial risk management, customer service, etc. We restrict our discussion to three types of control charts, specifically theX and R charts, the P chart, and the C chart. • The students are given assignments where they are provided scenarios describing a business application along with a snapshot of data. The objective of the assignment is to have the students determine whether the process is in statistical control; in particular they need to ascertain whether the data exhibit only common variation, or both common and specific variation.

11. Regression – Modeling Variation • With an understanding of variation, we next move into the arena of modeling variation. The statistical technique we initially utilize is linear regression analysis, restricting our data to time series data. This restriction is contrary to what one usually sees in textbooks, where it is customary to introduce cross sectional data, before time series data. The reason we choose to focus on time series data at the outset is that we want to build on our previous work and explain the technique in terms of total variation, specific variation, and common variation. Later on, we are able to generalize our discussion to include cross sectional data.

12. Specification Phase • We introduce our students to the realistic concept that sales for a firm are not constant from one time period to the next. When asked what explains the variation in sales, a number of responses surface, but the most common is advertising. We tend to focus on the response mentioning advertising. At this point students are comfortable substituting in the equation SALES for Y and ADVERTISING for X. With a scatter plot of SALES versus ADVERTISING drawn, we then emphasize to the students that a model is an approximation of a process and that when developing a model in the specification phase one should use economic theory to answer two questions: • 1. What variables are involved? • 2. What is the mathematical relationship between variables?

13. Estimation Phase • The mathematical model contains parameters (β’s) that are unknown to the practitioner. These parameters need to be estimated from the data and we hence enter the estimation phase. This phase is mostly accomplished using a statistical software package. However, we have found that students can gain better understanding of regression by learning the ordinary least squares (OLS) method for estimating the β’s in simple linear regression.

14. Diagnostic Checking • We next enter the diagnostic checking phase where the adequacy of the model is evaluated. We do so by relating each of the individual diagnostics to the concepts of variation (total variation, specific variation, and common variation). • The t-test is used to test the null hypothesis H0: β1=0 or the independent variable X is not a significant source of specific variation. The coefficient of determination, or R2, is explained in terms of variation (specific variation/total variation). It becomes clear to students that R2 represents the proportion of total variation in the dependent variable that can be explained by this simple linear regression model. The error term is assumed to be common variation. • The three identification tools (time series plot, the runs up and down test, the Shapiro-Wilk test) students learned in the Red Bead Experiment are applied here to determine whether the residuals really only contain common variation. • If specific variation is found to be present, we need to go back to the first phase to re-specify a model to account for the source(s) of specific variation.

15. Experimental Design and Analysis of Variance – Discovering Sources of Specific Variation • In simple linear regression, we emphasize that a statistically significant relationship (i.e., strong correlation) between the independent variable X and the dependent variable Y does not necessarily indicate X causes Y. We can only conclude that there is a significant relationship between X and Y or they are correlated. • A cause-and-effect relationship between X and Y is more easily established in a controlled experiment. We then introduce statistical design of experiments by R. A. Fisher. • We illustrate the fundamental principles of statistical design of experiments, namely randomization, blocking, and replication • To compare more than two population means, we introduce the Analysis of Variance (ANOVA). ANOVA is a technique that a number of colleagues in the functional areas of business, especially marketing, want covered. Our approach is to again focus on discussing specific variation and common variation.

16. Forecasting • We will mainly focus on quantitative forecasting methods which are based on an analysis of historical data concerning one or more time series. • The three time series forecasting methods we will use are: • Smoothing • Trend projection • Trend projection adjusted for seasonal influence

17. Software • Numerous statistical packages are available for this course. An objective for our course is that we use a software package that supports the course but does not become the focus of the course. If the package is too difficult to use, the emphasis becomes on how to use the software, not statistical concepts. • We use StatGraphics and students have found it to be easy to learn. • Included in StatGraphics are procedures for: basic statistics and exploratory data analysis; analysis of variance and regression; SPC (Capability analysis; control charts; measurement systems analysis); Design of experiments; Six Sigma; Reliability and life data analysis; Multivariate and nonparametric methods; Time series analysis and forecasting.

18. Summary Slide • Why do I discuss the DS 101 overview with the class? • ASA Recommendations for Teaching Statistics • Our Teaching Philosophy • Introduction • Course Content • Variation, Variation, and Variation • Read Bead Experiment • Control Charts • Regression • Experimental Design and Analysis of Variance – Discovering Sources of Specific Variation • Forecasting • Software