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Preface

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Section 1
Introduction

• Data and Measurement
• Research Questions
• Populations and Samples
• Types of Sampling
• Statistics and Variation
• Experimental Design
• Conclusions
• Summary

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Section 2
Arranging and Presenting Data

• Run Charts
• Ungrouped Frequency Distributions
• Relative Frequency Distributions
• Grouped Frequency Distributions
• Histograms and Frequency Polygons
• Histogram Patterns
• Box and Whisker Plots
• Summary

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Section 3
Descriptive Statistics

• Measures of Location
     - Mean
     - Median
     - Mode
• Measures of Position
     - Low and High
     - Percentiles
     - Quartiles
• Measures of Dispersion
     - Range
     - The Interquartile Range
     - The Semi-Interquartile Range
     - Standard Deviation
     - Variance
     - Mean Deviation
     - Pseudo-Standard Deviation
• Measures of Shape
     - Skewness
     - Kurtosis
• Summary

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Section 4
Measurement and Measurement Scales

• Nominal Scale
• Ordinal Scale
• Interval Scale
• Ratio Scale
• Absolute Scale
• Discrete and Continuous Data
• Transformations
• Determining Measurement Level
• Measurement Resolution
• Criterion Measures and Operational Definitions
• Measurement Error
• Summary

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Section 5
Introduction to Probability

• Basic Definitions
• Probabilities in the Single Performance of a Probability Experiment
     - Compound Events
     - Conditional Probabilities
• Probabilities in Multiple Performances of Probability Experiments
     - Independent Events
     - Dependent Events
• Counting Rules
• Summary

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Section 6
Probability Distributions

• Introduction
• Random Variables
• Probability Distribution for a Discrete Random Variable
• Expected Value of a Discrete Random Variable
• The Binomial Distribution
     - The Bernoulli Process
• The Poisson Distribution
• The Hypergeometric Distribution
• The Geometric Distribution
• The Normal Distribution
• Characteristics of the Normal Distribution
• Calculating Probabilities for the Normal Distribution
• The Exponential Distribution
• The Other Continuous Distributions
     - The Log-Normal Distribution
     - The Folded-Normal Distribution
     - The Rayleigh Distribution
     - The Cauchy Distribution
     - The Gamma Distribution
     - The Beta Distribution
• Summary

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Section 7
Sampling Distributions and Estimation

• Sampling Distributions and Statistical Inference
• The Central Limit Theorem
• Using the RSD of the Mean
• Finite Populations
• RSD Examples
• Types of Estimates
• Criteria for "Good" Estimators
• Point Estimates
• Various Alternative Estimates
• Estimating Standard Deviation from Multiple Samples
• Random Sampling Distribution Simulation Exercise
• Confidence Intervals
• Calculating Confidence Intervals
• Computer Generated Confidence Intervals
• Summary

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Section 8
Introduction to Statistical Hypothesis Tests

• Testing Statistical Hypotheses
• Null Hypothesis
• Alternative Hypothesis
• Directional Hypotheses
• Observations and Cautions
• Significance Level and Risk
• Test Statistics
• Rejection Regions
• Summary Observations for Statistical Hypothesis Testing
• Types I and II Error and Power and Confidence
• Calculating b and Power (for Means)
• Summary Observations
• Computer Simulation Exercise
• Summary

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Section 9
Sample Size Calculations

• Calculating Sample Size for Tests of Means
• One-sample tests of means, sigma known
• One-sample tests of means, sigma unknown
• Two-sample tests of means, sigma known
• Sample Size Calculations for Other Parameters
• Computer Example
• Summary

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Section 10
Distribution Testing and Fitting

• Distribution Testing Concepts
• Testing Normality
     - Anderson-Darling Test for Normality
     - Shapiro-Wilk Test for Normality
     - Lin-Mudholkar Test for Normality
     - Skewness and Kurtosis
     - Normality Testing Guidelines
• Testing Exponential Distributions
• Testing Poisson Distributions
• General Purpose Distribution Tests
     - The Chi-Square Goodness-of-Fit Test
     - The Kolmogorov-Smirnov One-Sample Test
• Distribution Fitting
• Transforms
• Pearson Distributions
• Johnson Distributions
• Weibull Distributions
• Summary

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Introduction

• One- and Two-Sample Statistical Tests

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Section 1
The Hypothesis Testing Procedure

• Basic Concepts
• Hypothesis Testing Procedure Report Form
• Some Observations Related to Step VII
• Summary

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Section 2
One-Sample Statistical Tests for Location, Dispersion, Rates and Counts

• Basic Concepts
• Testing Hypotheses for Interval or Ratio Scale Data
  • Testing Hypotheses about a Population Mean
    • The One-Sample z Test for m, with s Known
    • The One-Sample t Test for m, with s Not Known
  • Testing Hypotheses about a Population Variance
• Testing Hypotheses for Nominal Scale or Categorical Data
  • Testing for Changes in a Population Proportion (or Category Count)
  • The One-Sample Exact (Binomial) Test for Proportions
• Testing Hypotheses for Ordinal Scale Data
  • The Sign Test for Location
  • The Wilcoxon Signed-Rank Test for Location
• Testing Hypotheses for Absolute Scale or Count Data and Rates
  • Absolute Scale or Count Data that Is Not Poisson
  • The One-Sample Poisson Exact Test for Rates
  • Testing Hypotheses for Non-Poisson Count Data with Low Resolution
• Summary

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Section 3
One-Sample Statistics and Tests for Correlation and Association

• Basic Concepts
  • Introduction to Correlation for Continuous Variables
  • Computing (Product Moment) Correlation Coefficients and Pearson’s r
• The One-Sample t test for Correlation r = 0
• Fisher’s Z_F (Approximate Normal) Test for Correlation r = r₀
• Sample Size and Confidence Intervals for r
• Correlation for Ordinal Data, Spearman’s r_S
• Tests of Significance for Spearman’s r_S
• Correlation for Interval or Ratio and Two-Outcome Nominal Data
  the Point-Biserial Correlation Coefficient, r_pbi
• Association (Correlation) for Nominal Data
• Testing Hypotheses of Association for Two Nominal Scale Variables
• Concluding Comments
• Summary

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Section 4
Statistical Tests for Testing Hypotheses for Two Independent Samples

• Basic Concepts
• An Overview of Two-Sample Statistical Tests
• Testing Hypotheses for Population Means
  • The Two-Sample z test for Independent Groups
  • The Two-Sample t test for Independent Groups
• Testing Hypotheses for Variances and Dispersion
  • The F test for Variances
  • The Levene Test for Dispersion
  • The AMD_(n–1) Procedure: Extending the Levene Test
  • Testing Hypotheses for Two Independent Samples:
    Nominal, Ordinal and Absolute Scale Data
• Nominal Scale Data
  • The Two-Independent Sample Proportion Test
  • The Two-Independent Sample c² Test for Proportions
  • Ordinal Scale Data
  • The Median Test
  • The Mann-Whitney U Test
  • The Kolmogorov-Smirnov Two Independent Sample Test
• Absolute Scale Data
  • The Two-Independent Sample Poisson Test
• Summary

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Section 5
Statistical Tests for Testing Hypotheses for Two Dependent Samples

• Basic Concepts
• Testing Hypotheses for Differences in Means
  • Sampling Foundation
  • The Repeated Measures t test for Means
  • The Two Dependent Sample t Test for Means
• The Dependent Sample t Test for Variances
• Dependent Group Test Procedures for Nominal Scale Data
  • The Two Dependent Group Sign Test
  • The McNemar Test of Change for Dependent Proportions
• Dependent Sample Test Procedures for Ordinal Scale Data
  • The Wilcoxon Signed-Rank Test for Dependent Groups
  • The Sign Test for Two Dependent Groups
• Dependent Group Test Procedures for Absolute Scale Data
• Summary

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Section 6
Testing Hypotheses for Correlations in Two Samples

• Basic Concepts
• The Two Independent Sample Test for Correlations: r₁ = r₂
• Hotelling’s t Test for Two Dependent Sample Correlations: r₁₂ = r₁₃
• Concluding Comments
• Summary

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Introduction

• Perspective
• One-Way Designs
• Two-Way and Higher Level Designs

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Section 1
The Design and Analysis of a Completely Randomized Experiment

• Basic Concepts
• Comparative Experiment Example
• The General Principles of the Analysis of Variance
• The One-Way Analysis of Variance
  • The Analysis of the Soldering Method Example
  • Statistical Importance
  • Assumptions for the One-Way ANOVA
• Summary

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Section 2
Testing for Homogeneity of Dispersion in a Completely Randomized Experiment

• Basic Concepts
• Test Procedures and the Levene Test
• Extending the Levene Test: The ADM Procedure
• Summary

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Section 3
Post-Hoc Analysis of Location and Dispersion for a Completely Randomized Experiment

• Basic Concepts
• Post-Hoc Analysis of Mean Differences
  • A Brief Introduction to Comparisons and Contrasts
  • An Introduction to Test Procedures and Their Usage
  • Using the Computer for Post-Hoc Analysis
  • A Basic Discussion of Contrasts
  • Contrasts Using the Computer
• A Strategy for Performing Post-Hoc Analyses
  • Guidelines for Selecting a Post-Hoc Procedure
  • Summary Table and Recommendations
  • Concluding Comments
• Post-Hoc Analysis of Dispersion Differences
  • Testing Variances
  • Testing Dispersion
• Summary

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Section 4
The One-Way Random Effects Completely Randomized Experiment

• Basic Concepts
• The One-Way Random Effects Model
• Assumptions for the One-Way Random Effects ANOVA
• Summary

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Section 5
The One-Way Dependent Groups or Repeated Measures Experiment

• Basic Concepts
  • Design Perspective and Terminology
  • Expected Mean Squares (EMS) and Appropriate Error Terms (AET)
• Assumptions for the One-Way Dependent Groups ANOVA
• Summary

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Section 6
One-Way Experimental Designs for Ordinal and Nominal Data:
Independent and Dependent Groups

• Basic Concepts
• The Kruskal-Wallis Test (Ordinal Data, Independent Groups)
• The Friedman Test (Ordinal Data, Dependent Groups)
• The c² Test (Nominal Data, Independent Groups)
• ANOVA for Tests of Hypotheses on Proportions
• The Cochran Q Test (Nominal Data, Dependent Groups)
• Conclusions
• Summary

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Section 7
The Design and Analysis of Experimental Designs with Two Treatment Factors

• Basic Concepts
  • The One-Variable-At-A-Time Approach
  • The Design of a Complete 2x2 Factorial Experiment
• The Analysis of a 2x2 Factorial Experiment
• Two-Way Analysis of Variance (ANOVA) – Fully-Crossed Models
• Interaction Analysis
• Post-Hoc Analyses Given a Significant Interaction
• J x K Designs, Where J and/or K Are Greater Than 2
• Percent Relative Factor Contribution (%RFC)
• Summary

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Section 8
Testing for the Homogeneity of Variance and Dispersion in Factorial Models

• Basic Concepts
• The Bartlett-Kendall Procedure (Normality and Equal n >= 5)
• The ADM_(n–1) (Modified Levene) Procedure
• Summary

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Section 9
Two-Way ANOVA Models: Special Topics

• Two-Way Models for Random and Mixed Effects
• The Analysis of Random or Mixed Treatment Factor Models
• Nested Treatment Factor Designs
• Designs Involving Blocked Variables
• Designs Involving Unequal Sample Size in the Cells
• Designs with Some Cells Empty
• Two-Way Analysis: Nominal and Ordinal Data
• Analyses of Nominal Data
  • Two-Independent Sample c² Test for Proportions, More Than 2 Categories
  • Analyses of Ordinal Data
• Summary

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Section 10
Three-Way (and Higher) ANOVA Models

• Basic Concepts
• Three-Way Models for Fixed Effects
• Dispersion Analysis for Three-Way Designs
• The Analysis of Random or Mixed Treatment Factor Models
• Three-Way Designs Involving Nested Treatments
• The Analysis of Nominal and Ordinal Data
  • Nominal Data
  • Ordinal Data
• More Complex Designs
• Final Comments
• Summary

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Introduction

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Section 1
Factor and Level Selection for Effective Screening Experiments

• Select "All" Potential Factors>
• Study Independent Process Variables, Not Response Variables
• Avoid the Trap of Non-Independent Variables
• Select the Number of Levels to be Tested for Each Factor Carefully
• Level Selection
• The Consideration of Known and Non-Manipulable Independent Variables
• Studying Interaction Effects
• Summary

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Section 2
Experimental Designs for Screening Experiments

• Orthogonal Arrays
• Linear Graphs
• General Guidelines and Observations Associated with Orthogonal Array Designs
• Summary

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Section 3
Designing Screening Experiments with Orthogonal Arrays

• Introduction
• Case Study No. 1 The Case of the Plating Thickness
• Case Study No. 2 The Case of the Roll Coater
• Case Study No. 3 The Case of the Primer Seating Force
• Case Study No. 4 The Case of the Can Earing
• Case Study No. 5 The Case of the Trimmer-Chopper
• Case Study No. 6 The Case of the Dome Strength
• Case Study No. 7 The Case of the Ingot Casting
• Case Study No. 8 The Case of the Saw Chain Filing Geometry
• Summary

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Section 4
Conducting Confirming Experiments

• Summary