AJ

Anderson SBE 15e PPT CH13 07-30-22 PC - final

Chapter 13: Experimental Design and Analysis of Variance

13.1 Introduction to Experimental Design

  • Experimental Study: Involves manipulating one or more variables to observe effects on a variable of interest.

  • Observational Study: Involves collecting data without manipulation, limiting ability to establish causation.

  • Types of experimental designs:

    • Completely randomized design

    • Randomized block design

    • Factorial experiment

Example: Chemitech, Inc.

  • Goal: Determine the best assembly method among three (A, B, C) for filtration systems.

  • Dependent Variable: Number of systems assembled per week.

  • Independent Variable: Assembly method.

13.2 Analysis of Variance (ANOVA)

Definition and Objectives

  • ANOVA tests if means of multiple populations are equal.

  • Key steps:

    • Compute ANOVA table components (e.g., SSTR, SSE).

    • Formulate hypotheses:

      • Null Hypothesis (H0): µ1 = µ2 = µ3

      • Alternative Hypothesis (Ha): Not all population means are equal.

Hypothesis Test Process

  • Collect data for different assembly methods.

  • Sample means, variances, and standard deviations computed.

  • Assumptions for ANOVA:

    • Normally distributed response variable.

    • Equal variances across populations.

    • Independent observations.

ANOVA Table Components

  1. Sum of Squares for Treatments (SSTR)

  2. Sum of Squares for Errors (SSE)

  3. Degrees of Freedom and Mean Squares for both treatments and error.

  4. F Statistic: F = MSTr/MSE, follows an F-distribution.

13.3 Fisher’s Least Significant Difference (LSD) Procedure

  • Used for pairwise comparisons of population means.

  • Test Statistic: t = (x̄i - x̄j) / MSE * √(1/ni + 1/nj)

  • Rejection rules based on p-value or critical values.

Confidence Intervals for Differences

  • Interval estimate for population means differences calculated using LSD.

13.4 Randomized Block Design

  • Accounts for extraneous variations by grouping experimental units into blocks.

  • Provides more accurate error estimates and improves test power.

Example: Air Traffic Controller Stress Test

  • Blocked by controller to assess different workstation systems.

13.5 Factorial Experiment

  • Allows analysis of multiple factors simultaneously (e.g., a preparation program and college).

  • ANOVA table partitions total variability into components for each factor and interaction effects.

Example: GMAT Preparation Programs

  • Objectives include assessing impacts of programs and instructors.

Summary

  • ANOVA tests mean differences among several populations.

  • Various designs help manage extraneous variability.

  • Procedures like Fisher’s LSD and Bonferroni adjustment guide pairwise comparisons.