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  • DOE
    • 1. Introduction to Design of Experiments
      • 1. What is Design of Experiment
      • 2. Step 1 of DOE Introduction Hypothesis Research Question
      • 3. Step 2 of DOE Method
      • 4. Step 3 of DOE Results by Analyzing the Data
      • 5. Step 4 of DOE Contextual Conclusion
      • 6. Reference for Module 1 Intro to DOE
    • 2. Hypothesis Testing/ Inferential Statistics/ Analysis of Variance ANOVA
      • 0. All Data Module 2 Hypothesis Testing
      • 1. What is Hypothesis Testing
      • 2. Single Population Testing
      • 3. Single Sample Z-Test
      • 4. Single Sample T-Test
      • 5. Population Proportion Test Single Sample
      • 6. Comparing Two Populations Hypothesis Testing
      • 7. Two Sample Z-Test
      • 8. Two Sample T-Test Equal Variance
      • 9. Two Sample T-Test Unequal Variance
      • 10. Paired T-Test (Matched Pair/Repeated Measure)
      • 11. Two Sample Population Proportion Test
    • 3. One Way/Single Factor ANOVA
      • 0. All Data Module 3 CRD Single One-Way ANOVA
      • 1. What is One Way/Single Factor ANOVA
      • 2. Fixed Effect Model Analysis Basics for One-Way ANOVA
      • 3. Example One-Way/Single-Factor Fixed Effect Completely Randomized Design
      • 4. Diagnostic, Adequacy & Data Quality Check Fixed Effect One Way ANOVA
      • 5. Random Effect Model Analysis Bacis for One-Way ANOVA
      • 6. Example Problem Random Effect Model
      • 7. Diagnostic, Adequacy, & Data Quality Check Random Effect One Way ANOVA
      • 8. Reference
    • 4. Randomized Complete Block, Latin Square, and Graeco-Latin Design
      • 0. All Data Module 4 RCBD Graeco Latin Square Design
      • 1. What is Randomized Complete Block Design (RCBD)?
      • 2. Randomized Complete Block Design Example Problem
      • 3. Randomized Complete Block Design (RCBD) vs Completely Randomized Design
      • 4. Why Randomized Complete Block Design is so Popular?
      • 5. Latin Square Design of Experiments
      • 6. Latin Square Example Problem
      • 7. Graeco-Latin Square Design of Experiments
      • 8. Graeco-Latin Square Example Problem
      • 9. Reference
    • 5. Factorial Design of Experiments
      • 0. All Data Factorial Design of Experiment
      • 1. What is a Factorial Design of Experiment?
      • 2. Understanding Main Effects?
      • 3. Understanding Interaction Effects?
      • 4. How to Develop the Regression Equation from Effects?
      • 5. How to Fit a Response Surface?
      • 6. How to Construct the ANOVA Table from Effects?
      • 7. Practice Problem
    • 6. 2K Factorial Design of Experiments
      • 1. What is 2K Design
      • 2. Layout/Graphical Representation 22 Design
      • 3. Understanding Factor Effects
      • 4. Contrast, Effect, Estimate, Sum of Square, and ANOVA Table 22
      • 5. Practice Problem 22
      • 6. How to Design 2k Experiment
      • 7. Develop Treatment Combinations 2K Design
      • 8. Develop Generic Formulas 2K Design
      • 9. Manual Analysis Using MS Excel 2K Experiments
      • 10. MS Excel, Minitab, SPSS, and SAS
      • 11. Practice Problem 2k
      • 12. 2K Factorial Design of Experiments References
    • 7. Blocking and Confounding in 2K Design
      • 1. What is Blocking
      • 2. What is Confounding
      • 3. Confound an Effect Using -1/+1 Coding System
      • 4. How to Replicate
      • 5. Confound Two Effects Using -1/+1 Coding System
      • 6. Confound Three Effects Using -1/+1 Coding System
      • 7. Confounding and Blocking Using Linear Combination Method 0/1 Coding
      • 8. Confound Two Effects Using 0/1 Coding System
      • 9. Confound Three Effects with Eight Blocks Using the o/1 Coding System
      • 10. General Blocking and Confounding Scheme for 2k Design in 2p Blocks
      • 11. Complete versus Partial Confounding
      • 12. Reference Blocking and Confounding in 2K Design
    • 8. Fractional Factorial Design of Experiments
      • 1. What is it
      • 2. Primary Basics
      • 3. Design Resolution
      • 4. One-Quarter Fraction Design
      • 5. Alias structure
      • 6. One-Eighth Fraction Design
      • 7. Lowest Runs Design
      • 8. Analysis Example
      • 9. Plackett-Burman Design
      • 10. Reference Fractional Factorial Design of Experiments
    • 9. Applied Regression Analysis
      • 1. What is Regression Analysis
      • 2. Steps in Regression Analysis?
      • 3. Perform Regression Analysis
      • 4. Results Explained Regression Analysis
      • 4.1. Significance Test Regression Analysis
      • 4.2. Practical Test r-square: The Coefficient of Determination
      • 4.3. Functional Relationships Explained
      • 4.4. Diagnostics Regression Analysis
      • 4.4.1. Linearity Assumption Check
      • 4.4.2. Outlier, Leverage, and Influential Points Unusual Observations Check
      • 4.4.3. Residuals Analysis
      • 5. Lack-of-fit Test
      • 6. Practice Problem Regression
      • 7. Reference Regression
    • 10. Response Surface Methodology
      • 1. What is Response Surface Methodology
      • 2. Design Response Surface Methodology
      • 3. Analyze and Explain Response Surface Methodology
      • 4. Box-Behnken Response Surface Methodology
      • 5. Multiple Response Surface Design and Analysis
      • 6. Reference Response Surface Modeling
    • 11. Expected Mean Square EMS Basics to Advanced Design of Experiments
      • 11.1 Are You Performing the Correct ANOVA?
      • 11.2 EMS for All Fixed Factors Design
      • 11.3 EMS for All Random Factors Design
      • 11.4 Approximate or Pseudo F-Statistics/Tests
      • 11.5 EMS for Two Fixed and One Random Factors Design
      • 11.6 EMS for Fixed, Random and Nested Factors Design
      • 11.7 Expected Mean Square Using an Alternative Shortcut Method
      • 11.8 Restricted vs Unrestricted Models, Which is the Best One?
      • 11.9 References for EMS Module
    • 12. Mixed Factors Design of Experiments Nested Repeated Measure Split Plot
      • 12.1. Nested Hierarchical Design
      • 12.2. Repeated Measure Design
      • 12.3. Split-Plot Design
      • 12.4. Are Partially Nested, Repeated Measure and Split-Plot Designs differ
      • 12.5. Reference for Mixed Model Designs
    • 13. Taguchi Robust Parameter Design of Experiments
  • Econ
    • Econ Ch2
  • Ergo
    • Ergonomic Toolbox
  • Fluid
    • Fluid Power Lab Demo
  • Mechanics
  • Operations
  • Project
  • Quality
  • Statics
  • Assessment
    • Assessment of Student Learning Certificate
    • Program-Level Student Learning Assessment Certificate Training
  • CV/Resume
The Open Educator
  • Home
  • DOE
    • 1. Introduction to Design of Experiments
      • 1. What is Design of Experiment
      • 2. Step 1 of DOE Introduction Hypothesis Research Question
      • 3. Step 2 of DOE Method
      • 4. Step 3 of DOE Results by Analyzing the Data
      • 5. Step 4 of DOE Contextual Conclusion
      • 6. Reference for Module 1 Intro to DOE
    • 2. Hypothesis Testing/ Inferential Statistics/ Analysis of Variance ANOVA
      • 0. All Data Module 2 Hypothesis Testing
      • 1. What is Hypothesis Testing
      • 2. Single Population Testing
      • 3. Single Sample Z-Test
      • 4. Single Sample T-Test
      • 5. Population Proportion Test Single Sample
      • 6. Comparing Two Populations Hypothesis Testing
      • 7. Two Sample Z-Test
      • 8. Two Sample T-Test Equal Variance
      • 9. Two Sample T-Test Unequal Variance
      • 10. Paired T-Test (Matched Pair/Repeated Measure)
      • 11. Two Sample Population Proportion Test
    • 3. One Way/Single Factor ANOVA
      • 0. All Data Module 3 CRD Single One-Way ANOVA
      • 1. What is One Way/Single Factor ANOVA
      • 2. Fixed Effect Model Analysis Basics for One-Way ANOVA
      • 3. Example One-Way/Single-Factor Fixed Effect Completely Randomized Design
      • 4. Diagnostic, Adequacy & Data Quality Check Fixed Effect One Way ANOVA
      • 5. Random Effect Model Analysis Bacis for One-Way ANOVA
      • 6. Example Problem Random Effect Model
      • 7. Diagnostic, Adequacy, & Data Quality Check Random Effect One Way ANOVA
      • 8. Reference
    • 4. Randomized Complete Block, Latin Square, and Graeco-Latin Design
      • 0. All Data Module 4 RCBD Graeco Latin Square Design
      • 1. What is Randomized Complete Block Design (RCBD)?
      • 2. Randomized Complete Block Design Example Problem
      • 3. Randomized Complete Block Design (RCBD) vs Completely Randomized Design
      • 4. Why Randomized Complete Block Design is so Popular?
      • 5. Latin Square Design of Experiments
      • 6. Latin Square Example Problem
      • 7. Graeco-Latin Square Design of Experiments
      • 8. Graeco-Latin Square Example Problem
      • 9. Reference
    • 5. Factorial Design of Experiments
      • 0. All Data Factorial Design of Experiment
      • 1. What is a Factorial Design of Experiment?
      • 2. Understanding Main Effects?
      • 3. Understanding Interaction Effects?
      • 4. How to Develop the Regression Equation from Effects?
      • 5. How to Fit a Response Surface?
      • 6. How to Construct the ANOVA Table from Effects?
      • 7. Practice Problem
    • 6. 2K Factorial Design of Experiments
      • 1. What is 2K Design
      • 2. Layout/Graphical Representation 22 Design
      • 3. Understanding Factor Effects
      • 4. Contrast, Effect, Estimate, Sum of Square, and ANOVA Table 22
      • 5. Practice Problem 22
      • 6. How to Design 2k Experiment
      • 7. Develop Treatment Combinations 2K Design
      • 8. Develop Generic Formulas 2K Design
      • 9. Manual Analysis Using MS Excel 2K Experiments
      • 10. MS Excel, Minitab, SPSS, and SAS
      • 11. Practice Problem 2k
      • 12. 2K Factorial Design of Experiments References
    • 7. Blocking and Confounding in 2K Design
      • 1. What is Blocking
      • 2. What is Confounding
      • 3. Confound an Effect Using -1/+1 Coding System
      • 4. How to Replicate
      • 5. Confound Two Effects Using -1/+1 Coding System
      • 6. Confound Three Effects Using -1/+1 Coding System
      • 7. Confounding and Blocking Using Linear Combination Method 0/1 Coding
      • 8. Confound Two Effects Using 0/1 Coding System
      • 9. Confound Three Effects with Eight Blocks Using the o/1 Coding System
      • 10. General Blocking and Confounding Scheme for 2k Design in 2p Blocks
      • 11. Complete versus Partial Confounding
      • 12. Reference Blocking and Confounding in 2K Design
    • 8. Fractional Factorial Design of Experiments
      • 1. What is it
      • 2. Primary Basics
      • 3. Design Resolution
      • 4. One-Quarter Fraction Design
      • 5. Alias structure
      • 6. One-Eighth Fraction Design
      • 7. Lowest Runs Design
      • 8. Analysis Example
      • 9. Plackett-Burman Design
      • 10. Reference Fractional Factorial Design of Experiments
    • 9. Applied Regression Analysis
      • 1. What is Regression Analysis
      • 2. Steps in Regression Analysis?
      • 3. Perform Regression Analysis
      • 4. Results Explained Regression Analysis
      • 4.1. Significance Test Regression Analysis
      • 4.2. Practical Test r-square: The Coefficient of Determination
      • 4.3. Functional Relationships Explained
      • 4.4. Diagnostics Regression Analysis
      • 4.4.1. Linearity Assumption Check
      • 4.4.2. Outlier, Leverage, and Influential Points Unusual Observations Check
      • 4.4.3. Residuals Analysis
      • 5. Lack-of-fit Test
      • 6. Practice Problem Regression
      • 7. Reference Regression
    • 10. Response Surface Methodology
      • 1. What is Response Surface Methodology
      • 2. Design Response Surface Methodology
      • 3. Analyze and Explain Response Surface Methodology
      • 4. Box-Behnken Response Surface Methodology
      • 5. Multiple Response Surface Design and Analysis
      • 6. Reference Response Surface Modeling
    • 11. Expected Mean Square EMS Basics to Advanced Design of Experiments
      • 11.1 Are You Performing the Correct ANOVA?
      • 11.2 EMS for All Fixed Factors Design
      • 11.3 EMS for All Random Factors Design
      • 11.4 Approximate or Pseudo F-Statistics/Tests
      • 11.5 EMS for Two Fixed and One Random Factors Design
      • 11.6 EMS for Fixed, Random and Nested Factors Design
      • 11.7 Expected Mean Square Using an Alternative Shortcut Method
      • 11.8 Restricted vs Unrestricted Models, Which is the Best One?
      • 11.9 References for EMS Module
    • 12. Mixed Factors Design of Experiments Nested Repeated Measure Split Plot
      • 12.1. Nested Hierarchical Design
      • 12.2. Repeated Measure Design
      • 12.3. Split-Plot Design
      • 12.4. Are Partially Nested, Repeated Measure and Split-Plot Designs differ
      • 12.5. Reference for Mixed Model Designs
    • 13. Taguchi Robust Parameter Design of Experiments
  • Econ
    • Econ Ch2
  • Ergo
    • Ergonomic Toolbox
  • Fluid
    • Fluid Power Lab Demo
  • Mechanics
  • Operations
  • Project
  • Quality
  • Statics
  • Assessment
    • Assessment of Student Learning Certificate
    • Program-Level Student Learning Assessment Certificate Training
  • CV/Resume
  • More
    • Home
    • DOE
      • 1. Introduction to Design of Experiments
        • 1. What is Design of Experiment
        • 2. Step 1 of DOE Introduction Hypothesis Research Question
        • 3. Step 2 of DOE Method
        • 4. Step 3 of DOE Results by Analyzing the Data
        • 5. Step 4 of DOE Contextual Conclusion
        • 6. Reference for Module 1 Intro to DOE
      • 2. Hypothesis Testing/ Inferential Statistics/ Analysis of Variance ANOVA
        • 0. All Data Module 2 Hypothesis Testing
        • 1. What is Hypothesis Testing
        • 2. Single Population Testing
        • 3. Single Sample Z-Test
        • 4. Single Sample T-Test
        • 5. Population Proportion Test Single Sample
        • 6. Comparing Two Populations Hypothesis Testing
        • 7. Two Sample Z-Test
        • 8. Two Sample T-Test Equal Variance
        • 9. Two Sample T-Test Unequal Variance
        • 10. Paired T-Test (Matched Pair/Repeated Measure)
        • 11. Two Sample Population Proportion Test
      • 3. One Way/Single Factor ANOVA
        • 0. All Data Module 3 CRD Single One-Way ANOVA
        • 1. What is One Way/Single Factor ANOVA
        • 2. Fixed Effect Model Analysis Basics for One-Way ANOVA
        • 3. Example One-Way/Single-Factor Fixed Effect Completely Randomized Design
        • 4. Diagnostic, Adequacy & Data Quality Check Fixed Effect One Way ANOVA
        • 5. Random Effect Model Analysis Bacis for One-Way ANOVA
        • 6. Example Problem Random Effect Model
        • 7. Diagnostic, Adequacy, & Data Quality Check Random Effect One Way ANOVA
        • 8. Reference
      • 4. Randomized Complete Block, Latin Square, and Graeco-Latin Design
        • 0. All Data Module 4 RCBD Graeco Latin Square Design
        • 1. What is Randomized Complete Block Design (RCBD)?
        • 2. Randomized Complete Block Design Example Problem
        • 3. Randomized Complete Block Design (RCBD) vs Completely Randomized Design
        • 4. Why Randomized Complete Block Design is so Popular?
        • 5. Latin Square Design of Experiments
        • 6. Latin Square Example Problem
        • 7. Graeco-Latin Square Design of Experiments
        • 8. Graeco-Latin Square Example Problem
        • 9. Reference
      • 5. Factorial Design of Experiments
        • 0. All Data Factorial Design of Experiment
        • 1. What is a Factorial Design of Experiment?
        • 2. Understanding Main Effects?
        • 3. Understanding Interaction Effects?
        • 4. How to Develop the Regression Equation from Effects?
        • 5. How to Fit a Response Surface?
        • 6. How to Construct the ANOVA Table from Effects?
        • 7. Practice Problem
      • 6. 2K Factorial Design of Experiments
        • 1. What is 2K Design
        • 2. Layout/Graphical Representation 22 Design
        • 3. Understanding Factor Effects
        • 4. Contrast, Effect, Estimate, Sum of Square, and ANOVA Table 22
        • 5. Practice Problem 22
        • 6. How to Design 2k Experiment
        • 7. Develop Treatment Combinations 2K Design
        • 8. Develop Generic Formulas 2K Design
        • 9. Manual Analysis Using MS Excel 2K Experiments
        • 10. MS Excel, Minitab, SPSS, and SAS
        • 11. Practice Problem 2k
        • 12. 2K Factorial Design of Experiments References
      • 7. Blocking and Confounding in 2K Design
        • 1. What is Blocking
        • 2. What is Confounding
        • 3. Confound an Effect Using -1/+1 Coding System
        • 4. How to Replicate
        • 5. Confound Two Effects Using -1/+1 Coding System
        • 6. Confound Three Effects Using -1/+1 Coding System
        • 7. Confounding and Blocking Using Linear Combination Method 0/1 Coding
        • 8. Confound Two Effects Using 0/1 Coding System
        • 9. Confound Three Effects with Eight Blocks Using the o/1 Coding System
        • 10. General Blocking and Confounding Scheme for 2k Design in 2p Blocks
        • 11. Complete versus Partial Confounding
        • 12. Reference Blocking and Confounding in 2K Design
      • 8. Fractional Factorial Design of Experiments
        • 1. What is it
        • 2. Primary Basics
        • 3. Design Resolution
        • 4. One-Quarter Fraction Design
        • 5. Alias structure
        • 6. One-Eighth Fraction Design
        • 7. Lowest Runs Design
        • 8. Analysis Example
        • 9. Plackett-Burman Design
        • 10. Reference Fractional Factorial Design of Experiments
      • 9. Applied Regression Analysis
        • 1. What is Regression Analysis
        • 2. Steps in Regression Analysis?
        • 3. Perform Regression Analysis
        • 4. Results Explained Regression Analysis
        • 4.1. Significance Test Regression Analysis
        • 4.2. Practical Test r-square: The Coefficient of Determination
        • 4.3. Functional Relationships Explained
        • 4.4. Diagnostics Regression Analysis
        • 4.4.1. Linearity Assumption Check
        • 4.4.2. Outlier, Leverage, and Influential Points Unusual Observations Check
        • 4.4.3. Residuals Analysis
        • 5. Lack-of-fit Test
        • 6. Practice Problem Regression
        • 7. Reference Regression
      • 10. Response Surface Methodology
        • 1. What is Response Surface Methodology
        • 2. Design Response Surface Methodology
        • 3. Analyze and Explain Response Surface Methodology
        • 4. Box-Behnken Response Surface Methodology
        • 5. Multiple Response Surface Design and Analysis
        • 6. Reference Response Surface Modeling
      • 11. Expected Mean Square EMS Basics to Advanced Design of Experiments
        • 11.1 Are You Performing the Correct ANOVA?
        • 11.2 EMS for All Fixed Factors Design
        • 11.3 EMS for All Random Factors Design
        • 11.4 Approximate or Pseudo F-Statistics/Tests
        • 11.5 EMS for Two Fixed and One Random Factors Design
        • 11.6 EMS for Fixed, Random and Nested Factors Design
        • 11.7 Expected Mean Square Using an Alternative Shortcut Method
        • 11.8 Restricted vs Unrestricted Models, Which is the Best One?
        • 11.9 References for EMS Module
      • 12. Mixed Factors Design of Experiments Nested Repeated Measure Split Plot
        • 12.1. Nested Hierarchical Design
        • 12.2. Repeated Measure Design
        • 12.3. Split-Plot Design
        • 12.4. Are Partially Nested, Repeated Measure and Split-Plot Designs differ
        • 12.5. Reference for Mixed Model Designs
      • 13. Taguchi Robust Parameter Design of Experiments
    • Econ
      • Econ Ch2
    • Ergo
      • Ergonomic Toolbox
    • Fluid
      • Fluid Power Lab Demo
    • Mechanics
    • Operations
    • Project
    • Quality
    • Statics
    • Assessment
      • Assessment of Student Learning Certificate
      • Program-Level Student Learning Assessment Certificate Training
    • CV/Resume

Systematically Flawlessly Develop Treatment Combinations

Originally, this method of writing the treatment combination was shown in the one of the most popular classic texts in DOE (Kempthorne 1952) (Table 5). However, with the invention of the great MS Excel, writing the treatment combination can be performed even more easily and flawlessly. The step by step process of writing the treatment combinations is described in the Video 5. 

Video 5. Write Treatment Combinations Systematically and Flawlessly in Design and Analysis of Experiments DOE 

Table 5 shows the step by step process of writing the treatment combinations.

  1. Write the treatment combinations for the basic 22 design. 

  2. Add a column next to it and type c to add the factor C with it. 

  3. Now use the treatment combinations for the three variables A, B, and C to develop the treatment combinations for four variables A, B, C, and D. 

  4. And so on. 

Table 5. Flowless system for writing the treatment combinations 

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Develop Generic-Formulas for 2K Design

The Open Educator is Created by Shaheen AhmedThe Open Educator is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.Feel free to contact us at email@theopeneducator.com if you have any questions or concerns.Copyright © Shaheen Ahmed
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