STA643 Official Handouts

Experimental Design

What is an Experiment? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. 1 Random Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design of Experiment (DOE)
2. 1 Main Concerns in Experimental Design . . . . . . . . . . . . . . . . . . . . Objectives of an experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Application of Design of Experiments

DOE in Agriculture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Some Agriculture Related Examples . . . . . . . . . . . . . . . . . . . . . . . . . . DOE in Engineering Design

6. 1 Some Engineering Design Related Applications

Some Engineering Design Related Examples . . . . . . . . . . . . . . . . . . . . . DOE in Life Sciences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Some Life Sciences Related Examples . . . . . . . . . . . . . . . . . . . . . . . . . DOE in Environmental Sciences . . . . . . . . . . . . . . . . . . . . . . . . . . . . Some Environmental Sciences Related Examples . . . . . . . . . . . . . . . . . . . DOE in Physical Sciences

12. 1 Major Physical Sciences Related Applications

Some Physical Sciences Related Examples DOE in Management Sciences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Some Management Sciences Related Examples . . . . . . . . . . . . . . . . . . . . DOE in Social Sciences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Some Social Sciences Related Examples . . . . . . . . . . . . . . . . . . . . . . . .

Basics of Design of Experiments

Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition of Basic Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Principles of DOE: Randomization . . . . . . . . . . . . . . . . . . . . . . . Examples of Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Principles of DOE: Replication . . . . . . . . . . . . . . . . . . . . . . . . . Examples of Replication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Principles of DOE: Local Control/Blocking Examples of Local Control/ Blocking . . . . . . . . . . . . . . . . . . . . . . . . . Steps Involved in Designing of an Experiment Some Practical Advises in DOE . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Testing of Hypothesis-I

Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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28. 1 Steps Involved in Testing of Hypothesis . . . . . . . . . . . . . . . . . . . . Testing Mean of Population
29. 1 Large or Small Sample?
30. 2 Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31. 3 Z-test

Testing Mean: A Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . Testing Equality of Two Population Means . . . . . . . . . . . . . . . . . . . . . . Independent Samples When Population Variances are Equal

32. 1 Procedures of Performing the Independent Sample t-Test . . . . . . . . . . Independent Samples t-test: Numerical Example . . . . . . . . . . . . . . . . . . .

Testing of Hypothesis-II

Independent Samples When Population Variances are Unequal . . . . . . . . . . .

34. 1 Procedures of Performing the Independent Sample t-Test . . . . . . . . . . Independent Samples t-test: Numerical Example . . . . . . . . . . . . . . . . . . . Testing Equality of Two Population Means: Paired Samples

Paired Sample t-test: Numerical Example

Analysis of Variance

Analysis of variance (ANOVA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Assumptions of ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single Factor ANOVA Definition of a Model and Types of Model Fixed Effect Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fixed Effect Model: Some Examples Random Effect Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Random Effect Model: Some Examples . . . . . . . . . . . . . . . . . . . . . . . . Analysis of Fixed Effects Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Components of Analysis

Cochran’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Decomposition of Total Sum of Squares . . . . . . . . . . . . . . . . . . . . . . . .

Expected Values of Mean Square of Error and Treatment

Model Adequacy Checking Tools

Model Adequacy Checking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coefficient of Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normality Assumption: Histogram of Residuals Normality Assumption: Normal Probability Plot . . . . . . . . . . . . . . . . . . . Normality Assumption: Plot of Residuals in Time Series Normality Assumption: Plot of Residuals vs Fitted Values . . . . . . . . . . . . .

10 Barlett’s test and Nonparametric test in ANOVA

Test the Equality of Variances . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57. 1 The Bartlett’s Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Plots Based on Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . Violation of the Assumptions and Transformations
58. 1 Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page (ii)

Nonparametric Methods in ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . .

60. 1 Friedman two-way ANOVA

The Kruskal-Wallis Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ANOVA on Ranks

11 Contrasts and Post-Hoc Tests

Contrasts Inference for Contrasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthogonal Contrasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Post-Hoc Tests in ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66. 1 Omnibus tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67. 2 Common Post-Hoc Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scheffé’s Test

Scheffé’s Test Examples

12 Least Significant Difference (LSD) Test and its Examples

LSD Test LSD Test, Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13 Tukey’s Test and its Examples

Tukey’s Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tukey’s Test: Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14 Duncan’s Multiple Range (DMR) Test and its Examples

Duncan’s Multiple Range (DMR) Test DMR Test: An Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15 Dunnett’s Test and its Example

Dunnett’s Test Dunnett’s Test: an Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16 The Neuman-Keul Test and its Example

The Neuman-Keul Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Neuman-Keul: An Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . Which Post-hoc Test should we Use . . . . . . . . . . . . . . . . . . . . . . . . . .

17 One-Factor-at-a-Time Designs

Basic Experimental Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Completely Randomized Design (CRD)- Layout and ANOVA . . . . . . . . . . . . Completely randomized design (CRD)- Advantages and disadvantages . . . . . . . Application of CRD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CRD: Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Repeated Measures Designs (RMD) . . . . . . . . . . . . . . . . . . . . . . . . . . Repeated Measures Design: Model and Layout . . . . . . . . . . . . . . . . . . . . Repeated Measures Design: ANOVA Repeated Measures Design: Real Life Example . . . . . . . . . . . . . . . . . . . .

18 Randomized Complete Block Design and its Application

RCBD: Basics of Blocking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Randomized Complete Block Design - Precautions . . . . . . . . . . . . . . . . . . RCBD - Model and Assumptions

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