Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning 11-1 Business Statistics, 3e by Ken Black Chapter 11 Analysis of Variance & Design of Experiments

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning 11-2 Learning Objectives Understand the differences between various experimental designs and when to use them. Compute and interpret the results of a one-way ANOVA. Compute and interpret the results of a random block design. Compute and interpret the results of a two-way ANOVA. Understand and interpret interaction. Know when and how to use multiple comparison techniques.

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning 11-3 Introduction to Design of Experiments, #1 Experimental Design - a plan and a structure to test hypotheses in which the researcher controls or manipulates one or more variables.

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning 11-4 Introduction to Design of Experiments, #2 Independent Variable Treatment variable is one that the experimenter controls or modifies in the experiment. Classification variable is a characteristic of the experimental subjects that was present prior to the experiment, and is not a result of the experimenter’s manipulations or control. Levels or Classifications are the subcategories of the independent variable used by the researcher in the experimental design.

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning 11-5 Introduction to Design of Experiments, #3 Dependent Variable - the response to the different levels of the independent variables.

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning 11-6 Three Types of Experimental Designs Completely Randomized Design Randomized Block Design Factorial Experiments

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning 11-7 Completely Randomized Design Machine Operator Valve Opening Measurements

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning 11-8 Example: Number of Foreign Freighters Docking in each Port per Day Long Beach Houston New York New Orleans

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning 11-9 Analysis of Variance: Assumptions Observations are drawn from normally distributed populations. Observations represent random samples from the populations. Variances of the populations are equal.

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning One-Way ANOVA: Procedural Overview

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning One-Way ANOVA: Sums of Squares Definitions

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Partitioning Total Sum of Squares of Variation SST (Total Sum of Squares) SSC (Treatment Sum of Squares) SSE (Error Sum of Squares)

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning One-Way ANOVA: Computational Formulas

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning One-Way ANOVA: Preliminary Calculations Long Beach T 1 = 18 n 1 = 4 Houston T 2 = 20 n 2 = 5 New York T 3 = 42 n 3 = 6 New Orleans T 4 = 17 n 4 = 5 T = 97 N = 20

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning One-Way ANOVA: Sum of Squares Calculations

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning One-Way ANOVA: Sum of Squares Calculations

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning One-Way ANOVA: Mean Square and F Calculations

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Analysis of Variance for the Freighter Example Source of VariancedfSSMSF Factor Error Total

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning A Portion of the F Table for  = Denominator Degrees of Freedom Numerator Degrees of Freedom

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning One-Way ANOVA: Procedural Summary Rejection Region  Critical Value Non rejection Region

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning MINITAB Output for the Freighter Example ANALYSIS OF VARIANCE SourcedfSSMSFp Factor Error Total LEVELNMeanStDev Long B Houston New York NewOrlns Pooled StDev = 1.662

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Excel Output for the Freighter Example Anova: Single Factor SUMMARY GroupsCountSumAverageVariance Long Beach Houston New York New Orleans ANOVA Source of VariationSSdfMSFP-valueF crit Between Groups Within Groups Total

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Multiple Comparison Tests An analysis of variance (ANOVA) test is an overall test of differences among groups. Multiple Comparison techniques are used to identify which pairs of means are significantly different given that the ANOVA test reveals overall significance. Tukey’s honestly significant difference (HSD) test requires equal sample sizes Tukey-Kramer Procedure is used when sample sizes are unequal.

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Tukey’s Honestly Significant Difference (HSD) Test

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Data for Demonstration Problem 11.1 PLANT (Employee Age) Group Means n j 555 C = 3 df E = N - C = 12MSE = 1.63

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning q Values for  =.01 Degrees of Freedom Number of Populations

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Tukey’s HSD Test for the Employee Age Data

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Tukey-Kramer Procedure: The Case of Unequal Sample Sizes

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Freighter Example: Means and Sample Sizes for the Four Ports PortSample SizeMean Long Beach44.50 Houston54.00 New York67.00 New Orleans53.40

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Tukey- Kramer Results for the Freighter Example Pair Critical Difference |Actual Differences| 1 and (Long Beach and Houston) 1 and (Long Beach and New York) 1 and (Long Beach and New Orleans) 2 and * (Houston and New York) 2 and (Houston and New Orleans) 3 and * (New York and New Orleans) *denotes significant at .05

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Partitioning the Total Sum of Squares in the Randomized Block Design SST (Total Sum of Squares) SSC (Treatment Sum of Squares) SSE (Error Sum of Squares) SSR (Sum of Squares Blocks) SSE’ (Sum of Squares Error)

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning A Randomized Block Design Individual observations Single Independent Variable Blocking Variable.....

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Randomized Block Design Treatment Effects: Procedural Overview

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Randomized Block Design: Computational Formulas

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Randomized Block Design: Tread-Wear Example Supplier SlowMediumFast Block Means ( ) Treatment Means( ) Speed C = 3 n = 5 N = 15

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Randomized Block Design: Sum of Squares Calculations (Part 1)

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Randomized Block Design: Sum of Squares Calculations (Part 2)

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Randomized Block Design: Mean Square Calculations

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Analysis of Variance for the Tread-Wear Example Source of VarianceSSdfMSF Treatment Block Error Total

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Randomized Block Design Treatment Effects: Procedural Summary

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Randomized Block Design Blocking Effects: Procedural Overview

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Excel Output for Tread-Wear Example: Randomized Block Design Anova: Two-Factor Without Replication SUMMARYCountSumAverageVariance Suplier Suplier Suplier Suplier Suplier Slow Medium Fast ANOVA Source of VariationSSdfMSFP-valueF crit Rows Columns E Error Total

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Two-Way Factorial Design Cells Column Treatment Row Treatment.....

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Two-Way ANOVA: Hypotheses

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Formulas for Computing a Two-Way ANOVA

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning A 2  3 Factorial Design with Interaction Cell Means C1C1 C2C2 C3C3 Row effects R1R1 R2R2 Column

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning A 2  3 Factorial Design with Some Interaction Cell Means C1C1 C2C2 C3C3 Row effects R1R1 R2R2 Column

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning A 2  3 Factorial Design with No Interaction Cell Means C1C1 C2C2 C3C3 Row effects R1R1 R2R2 Column

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning A 2  3 Factorial Design: Data and Measurements for CEO Dividend Example N = 24 n = 4 X= Location Where Company Stock is Traded How Stockholders are Informed of Dividends NYSEAMEXOTC Annual/Quarterly Reports Presentations to Analysts XjXj XiXi X 11 =1.5 X 23 =3.75X 22 =3.0X 21 =2.0 X 13 =3.5X 12 =2.5

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning A 2  3 Factorial Design: Calculations for the CEO Dividend Example (Part 1)

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning A 2  3 Factorial Design: Calculations for the CEO Dividend Example (Part 2)

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning A 2  3 Factorial Design: Calculations for the CEO Dividend Example (Part 3)

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Analysis of Variance for the CEO Dividend Problem Source of VarianceSSdfMSF Row Column * Interaction Error Total * Denotes significance at  =.01.

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Excel Output for the CEO Dividend Example (Part 1) Anova: Two-Factor With Replication SUMMARYNYSEASEOTCTotal AQReport Count44412 Sum Average Variance Presentation Count44412 Sum Average Variance Total Count888 Sum Average Variance

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning Excel Output for the CEO Dividend Example (Part 2) ANOVA Source of VariationSSdfMSFP-valueF crit Sample Columns E Interaction Within Total