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SpirosVelianiti

sCSUS

Overview of DS 101Overview of DS 101

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Summary SlideSummary Slide Why do I discuss the DS 101 overview with the class?Why do I discuss the DS 101 overview with the class? ASA Recommendations for Teaching StatisticsASA Recommendations for Teaching Statistics Our Teaching PhilosophyOur Teaching Philosophy IntroductionIntroduction Course ContentCourse Content

• Variation, Variation, and VariationVariation, Variation, and Variation

• Read Bead ExperimentRead Bead Experiment

• Control ChartsControl Charts

• RegressionRegression

• Experimental Design and Analysis of Variance – Discovering Experimental Design and Analysis of Variance – Discovering Sources of Specific VariationSources of Specific Variation

• ForecastingForecasting SoftwareSoftware

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Why do I discuss the DS 101 overview with the Why do I discuss the DS 101 overview with the class?class?

The purpose of this presentation is to describe the The purpose of this presentation is to describe the components of DS 101 which is designed to components of DS 101 which is designed to provide provide business students with the necessary statistical skills business students with the necessary statistical skills to become effective managers upon graduationto become effective managers upon graduation. .

It will give us a great synopsis of all the material we It will give us a great synopsis of all the material we will discuss in our class. will discuss in our class.

Think of it as Chapter 1, for our course.Think of it as Chapter 1, for our course. Ideas on the content and methods of teaching DS 101 Ideas on the content and methods of teaching DS 101

come from:come from:

• Drs. Taylor, Hopfe, and Li experience (over 15 years Drs. Taylor, Hopfe, and Li experience (over 15 years of experience)of experience)

• The GAISE College ReportThe GAISE College Report

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ASA Recommendations for Teaching ASA Recommendations for Teaching StatisticsStatistics

The American Statistical Association (ASA) funded the The American Statistical Association (ASA) funded the Guidelines for Assessment in Statistics Education Guidelines for Assessment in Statistics Education (GAISE) and offers six recommendations:(GAISE) and offers six recommendations:

Emphasize statistical literacy and develop statistical Emphasize statistical literacy and develop statistical thinkingthinking

Use real dataUse real data Stress conceptual understandingStress conceptual understanding Foster active learning in the classroomFoster active learning in the classroom Use technology for developing conceptual Use technology for developing conceptual

understanding and analyzing dataunderstanding and analyzing data Use assessments to improve and evaluate student Use assessments to improve and evaluate student

learninglearning

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Our Teaching PhilosophyOur Teaching Philosophy

I hear and I forgetI hear and I forget

I see and I rememberI see and I remember

I do and I understandI do and I understand

Chinese proverbChinese proverb

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IntroductionIntroduction Prerequisite knowledge for this class are the topics of Prerequisite knowledge for this class are the topics of

descriptive statistics, probability, confidence intervals, descriptive statistics, probability, confidence intervals, and hypothesis testing. and hypothesis testing.

The main objective of this course is to teach statistical The main objective of this course is to teach statistical techniques that would support classes in the functional techniques that would support classes in the functional areas of business such as accounting, finance, areas of business such as accounting, finance, marketing, operations, etc.marketing, operations, etc.

We explain statistical techniques using the concept of We explain statistical techniques using the concept of variationvariation; in particular, common variation and specific ; in particular, common variation and specific variation.variation.

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Course ContentCourse Content

Variation, Variation, and VariationVariation, Variation, and Variation Read Bead ExperimentRead Bead Experiment Control ChartsControl Charts RegressionRegression Experimental Design and Analysis of Variance – Experimental Design and Analysis of Variance –

Discovering Sources of Specific VariationDiscovering Sources of Specific Variation ForecastingForecasting

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Variation, Variation, and VariationVariation, Variation, and Variation Starting on the first day of class, we stress that this course is about Starting on the first day of class, we stress that this course is about

studying studying variation. variation. Building on the well-known phrase that the three Building on the well-known phrase that the three most important things to remember about real estate are “location, most important things to remember about real estate are “location, location, and location,” we emphasize that the three most important location, and location,” we emphasize that the three most important things to remember about our course are “things to remember about our course are “variation, variation, and variation, variation, and variationvariation.”.”

To reinforce this critical concept we frequently ask the class, “What To reinforce this critical concept we frequently ask the class, “What are the three most important things to remember about this course?” are the three most important things to remember about this course?” By the end of the semester, the responses get louder and more By the end of the semester, the responses get louder and more enthusiastic. It is not uncommon when we encounter former students enthusiastic. It is not uncommon when we encounter former students they are quick to greet us with “they are quick to greet us with “Variation, Variation, and Variation, Variation, and VariationVariation.”.”

To illustrate the idea of variation, we use the concept of volatility in To illustrate the idea of variation, we use the concept of volatility in finance and students usually understand that volatility (that is, finance and students usually understand that volatility (that is, variation) measures the risk of the investment. variation) measures the risk of the investment. Students are asked to Students are asked to download some daily closing price of stocks and compute estimates download some daily closing price of stocks and compute estimates of volatility (standard deviation). Students encounter time series data of volatility (standard deviation). Students encounter time series data here and, as we discuss later, time series data are used throughout here and, as we discuss later, time series data are used throughout the course.the course.

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Read Bead ExperimentRead Bead Experiment Using a paddle with 50 holes, each “factory worker” simulates a Using a paddle with 50 holes, each “factory worker” simulates a

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

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Control ChartsControl Charts

In order to reinforce the concepts of common variation In order to reinforce the concepts of common variation and specific variation, we introduce control charts and and specific variation, we introduce control charts and discuss their applications in manufacturing, financial risk discuss their applications in manufacturing, financial risk management, customer service, etc. We restrict our management, customer service, etc. We restrict our discussion to three types of control charts, specifically discussion to three types of control charts, specifically thethe X and R chartsX and R charts, , the P chartthe P chart, and , and the C chartthe C chart..

The students are given assignments where they are The students are given assignments where they are provided scenarios describing a business application provided scenarios describing a business application along with a snapshot of data. The objective of the along with a snapshot of data. The objective of the assignment is to have the students determine whether assignment is to have the students determine whether the process is in statistical control; in particular they the process is in statistical control; in particular they need to ascertain whether the data exhibit only need to ascertain whether the data exhibit only common variationcommon variation, or both common and , or both common and specific specific variationvariation..

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Regression – Modeling VariationRegression – Modeling Variation

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

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Specification PhaseSpecification Phase

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

1. What variables are involved?1. What variables are involved? 2. What is the mathematical relationship between 2. What is the mathematical relationship between

variables?variables?

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Estimation PhaseEstimation Phase

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

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Diagnostic CheckingDiagnostic Checking

We next enter the diagnostic checking phase where the adequacy of We next enter the diagnostic checking phase where the adequacy of the model is evaluated. We do so by relating each of the individual the model is evaluated. We do so by relating each of the individual diagnostics to the concepts of variation (total variation, specific diagnostics to the concepts of variation (total variation, specific variation, and common variation). variation, and common variation).

The t-test is used to test the null hypothesis H0: β1=0 or the The t-test is used to test the null hypothesis H0: β1=0 or the independent variable independent variable X is not a significant source X is not a significant source of specific variation. of specific variation. The coefficient of determinationThe coefficient of determination, or R, or R22, is explained in terms of , is explained in terms of variation (specific variation/total variation). It becomes clear to variation (specific variation/total variation). It becomes clear to students that Rstudents that R2 2 represents the proportion of total variation in the represents the proportion of total variation in the dependent variable that can be explained by this simple linear dependent variable that can be explained by this simple linear regression model. The error term is assumed to be common variation. regression model. The error term is assumed to be common variation.

The three identification tools (time series plot, the runs up and down The three identification tools (time series plot, the runs up and down test, the Shapiro-Wilk test) students learned in the Red Bead test, the Shapiro-Wilk test) students learned in the Red Bead Experiment are applied here to determine whether the residuals really Experiment are applied here to determine whether the residuals really only contain common variation. only contain common variation.

If specific variation is found to be present, we need to go back to the 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 first phase to re-specify a model to account for the source(s) of specific variation.variation.

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Experimental Design and Analysis of Experimental Design and Analysis of Variance – Discovering Sources of Specific Variance – Discovering Sources of Specific

VariationVariation In simple linear regression, we emphasize that a statistically In simple linear regression, we emphasize that a statistically

significant relationship (i.e., strong correlation) between the significant relationship (i.e., strong correlation) between the independent variable X and the dependent variable Y does not independent variable X and the dependent variable Y does not necessarily indicate X causes Y. We can only conclude that there is necessarily indicate X causes Y. We can only conclude that there is a significant relationship between X and Y or they are correlated.a significant relationship between X and Y or they are correlated.

A cause-and-effect relationship between X and Y is more easily A cause-and-effect relationship between X and Y is more easily established in a controlled experimentestablished in a controlled experiment. We then introduce . We then introduce statistical design of experiments by R. A. Fisher.statistical design of experiments by R. A. Fisher.

We illustrate the fundamental principles of statistical design of We illustrate the fundamental principles of statistical design of experiments, namely randomization, blocking, and replicationexperiments, namely randomization, blocking, and replication

To compare more than two population means, we introduce the To compare more than two population means, we introduce the Analysis of Variance (ANOVA). ANOVA is a technique that a number Analysis of Variance (ANOVA). ANOVA is a technique that a number of colleagues in the functional areas of business, especially of colleagues in the functional areas of business, especially marketing, want covered. Our approach is to again focus on marketing, want covered. Our approach is to again focus on discussing specific variation and common variation. discussing specific variation and common variation.

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ForecastingForecasting

We will mainly focus on We will mainly focus on quantitative forecasting quantitative forecasting methodsmethods which are based on an analysis of historical which are based on an analysis of historical data concerning one or more time series.data concerning one or more time series.

The three time series forecasting methods we will use The three time series forecasting methods we will use are:are:

• SmoothingSmoothing

• Trend projectionTrend projection

• Trend projection adjusted for seasonal influenceTrend projection adjusted for seasonal influence

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SoftwareSoftware

Numerous statistical packages are available for this Numerous statistical packages are available for this course. An objective for our course is that we use a course. An objective for our course is that we use a software package that supports the course but does not software package that supports the course but does not become the focus of the course. If the package is too become the focus of the course. If the package is too difficult to use, the emphasis becomes on how to use the difficult to use, the emphasis becomes on how to use the software, not statistical concepts.software, not statistical concepts.

We use StatGraphics and students have found it to be We use StatGraphics and students have found it to be easy to learn. easy to learn.

Included in StatGraphics are procedures for: basic Included in StatGraphics are procedures for: basic statistics and exploratory data analysis; analysis of statistics and exploratory data analysis; analysis of variance and regression; SPC (Capability analysis; control variance and regression; SPC (Capability analysis; control charts; measurement systems analysis); Design of charts; measurement systems analysis); Design of experiments; Six Sigma; Reliability and life data analysis; experiments; Six Sigma; Reliability and life data analysis; Multivariate and nonparametric methods; Time series Multivariate and nonparametric methods; Time series analysis and forecasting.analysis and forecasting.

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Summary SlideSummary Slide Why do I discuss the DS 101 overview with the class?Why do I discuss the DS 101 overview with the class? ASA Recommendations for Teaching StatisticsASA Recommendations for Teaching Statistics Our Teaching PhilosophyOur Teaching Philosophy IntroductionIntroduction Course ContentCourse Content

• Variation, Variation, and VariationVariation, Variation, and Variation

• Read Bead ExperimentRead Bead Experiment

• Control ChartsControl Charts

• RegressionRegression

• Experimental Design and Analysis of Variance – Discovering Experimental Design and Analysis of Variance – Discovering Sources of Specific VariationSources of Specific Variation

• ForecastingForecasting SoftwareSoftware