Berhanie, Design Lecture notes

College of NCS Design and Analysis of Experiment Lecture Notes

Course Overview

  • Credit Hours: 4

  • Course Outline:

    • 1. Introduction (4 hr)

      • Strategy of experimentation

      • Typical Applications of Experimental Designs (ED)

      • Basic Principles of Experimental Design

      • Guidelines for Designing Experiments

      • Historical Perspective

    • 2. Simple Comparative Experiment (4 hr)

      • Basic statistical concepts

      • Sampling and sampling distribution

      • Inference about the difference in means: Randomized design and Paired Comparison designs

      • Inferences about variances of normal distribution

    • 3. Completely Randomized Design: Single Factor ANOVA (12 hr)

      • Examples

      • The analysis of variance

      • The analysis of the model: Decomposition of total sum of squares

      • Statistical analysis and estimation of model parameters

      • Model adequacy checking

      • Practical interpretation of results (e.g. treatment means comparison)

    • 4. Randomized Blocks (4 hr)

      • Why Blocking?

      • Statistical analysis

    • 5. Latin Squares and Related Designs (4 hr)

      • Latin square design

      • Graeco-Latin square design

      • Balanced incomplete block design

    • 6. Factorial Designs(20 hr)

      • Basic definitions and principles

      • The advantage of factorial designs

      • Unbalanced data in factorial designs

    • 7. Nested and Split Plot Designs (6 hr)

    • 8. Analysis of Covariance (ANCOVA) (6 hr)

    • 9. Class Project (4 hr)

Introduction to Experimental Design

  • Experiment Definition: A test to learn something or determine if a result holds true.

  • Purpose of Experiment:

    • Understand the impact of changing one variable on another

    • Compare mean differences across groups

Steps for Setting Up an Experiment

  1. Determine the goal of the experiment

  2. Select the response variable

  3. Choose factors and levels

  4. Design the experiment

  5. Perform the experiment

  6. Analyze the data

  7. Form conclusions and recommendations

Basic Principles of Experimental Design

  • Terminology:

    • Response Variable: Dependent variable of interest

    • Explanatory Variable / Factors: Factors affecting the response variable

    • Experimental Units: Subjects or objects where measurements are taken

  • Key Principles:

    • Randomization: Random assignment to treatments

    • Replication: Repeating the experiment with similar independent units

    • Blocking: Grouping similar experimental units to reduce variability

Simple Comparative Experiment

Basic Statistical Concepts

  • Random Variables:

    • Qualitative: Non-numeric attributes

    • Quantitative: Numeric attributes

      • Discrete: Countable values

      • Continuous: Infinite values within a range

  • Probability Distribution: Describes probabilities associated with possible variable values

Sampling and Sampling Distributions

  • Objective: Make inferences about a population from a sample

  • Point Estimator: Estimate based on sample data, should be unbiased with minimum variance

Analysis of Variance (ANOVA)

  • Objective: Determine whether there are any statistically significant differences between the means of three or more independent groups

  • One-Way ANOVA: Analyzes data from completely randomized designs

  • Test Statistic: The F statistic is computed based on group variances, comparing between-group variances to within-group variances

Randomized Block Design (RBD)

  • Purpose: Remove the effects of nuisance factors on statistical comparisons

  • Procedure:

    • Define blocks to reduce variability

    • Implement treatments within blocks

Factorial Designs

Overview

  • Definition: Experiments studying two or more factors simultaneously

  • Two-Factor Design: The simplest factorial design involving two factors

  • Labeling: Factors usually denoted with 1s and -1s for low and high levels

  • Effects: Main effects and interaction effects needed for analysis

Three-Factor Factorial Design

  • Extension of two-factor designs to include interactions among three factors

Nested and Split Plot Designs

  • Nested Design: Levels of one factor depend on levels of another factor

  • Split-Plot Design: Incorporates blocking with whole plots and subplots

  • Data Layout: Typically presented in matrix format according to blocks and treatments

Analysis of Covariance (ANCOVA)

  • Combines ANOVA and regression to control for the covariates

  • Adjusts response variable for the effects of nuisance variables

  • Model Utilization: Considers relationships among factors and covariates

  • Statistical Testing: Employs F-tests to evaluate significance of factors and covariates

  • Further reading: Montgomery, D.C. (1997). Design and Analysis of Experiments (4th Edition). John Wiley & Sons Inc.