One-Factor Experiments

One-Factor Experiments: A Comprehensive Guide for Six Sigma Black Belt

Introduction to One-Factor Experiments

One-factor experiments, also known as single-factor experiments or simple comparative experiments, are fundamental tools in the Six Sigma Improve Phase. They form the foundation of experimental design and hypothesis testing, enabling practitioners to isolate the effect of a single variable on a process outcome.

Why One-Factor Experiments Are Important

One-factor experiments hold significant importance in Six Sigma methodology for several reasons:

• Simplicity and Clarity: By isolating a single variable, these experiments provide clear, unambiguous results about how that variable affects the output.
• Cost-Effectiveness: Compared to multi-factor experiments, one-factor experiments require fewer resources and less time to conduct.
• Foundation Building: Understanding one-factor experiments is essential before moving to more complex factorial designs.
• Risk Reduction: Testing one factor at a time reduces the risk of unexpected interactions and makes results easier to interpret.
• Process Understanding: These experiments help practitioners understand cause-and-effect relationships within their processes.
• Quick Wins: One-factor experiments often lead to rapid process improvements and quick wins for organizations.

What Are One-Factor Experiments?

One-factor experiments are controlled tests where a single independent variable (factor) is deliberately changed while all other variables are held constant. The goal is to measure how changes in this single factor affect the dependent variable (response).

Key Components:

• Factor (Independent Variable): The variable being tested and manipulated (e.g., temperature, pressure, supplier, machine speed).
• Levels: The different values or settings at which the factor is tested (e.g., 100°C, 150°C, 200°C).
• Response (Dependent Variable): The outcome being measured (e.g., product quality, cycle time, defect rate).
• Replicates: Multiple runs at each factor level to account for variation and improve statistical reliability.
• Control Variables: All other factors held constant throughout the experiment.

How One-Factor Experiments Work

Step 1: Define the Problem and Objective

Clearly identify what you want to improve and which factor you suspect has the greatest impact. For example: "Does changing machine speed affect product defect rate?"

Step 2: Select the Factor and Levels

Choose the factor to test and determine the range of levels you'll test. Consider practical constraints and prior knowledge. For instance, you might test machine speed at 50 RPM, 75 RPM, and 100 RPM.

Step 3: Design the Experiment

Determine:

• How many levels of the factor to test (minimum 2, typically 2-4)
• How many replicates at each level (minimum 3-5 for statistical validity)
• The order in which tests will be conducted (randomization)
• Which variables must be controlled

Step 4: Conduct the Experiment

Execute the planned tests, recording data carefully. Maintain consistency in controlling other variables. Follow the randomized test sequence to minimize systematic bias.

Step 5: Analyze the Results

Use statistical analysis to determine if the factor has a significant effect:

• Calculate means for each factor level
• Calculate variation within and between levels
• Perform ANOVA (Analysis of Variance) to test statistical significance
• Calculate p-value to determine if differences are statistically significant (typically p < 0.05)

Step 6: Draw Conclusions

Interpret results and determine if the factor significantly affects the response. Create visualizations (main effects plots, box plots) to communicate findings.

Step 7: Implement and Verify

If the factor shows a significant positive effect, implement the optimal level in the process and monitor for sustained improvement.

Statistical Analysis of One-Factor Experiments

ANOVA (Analysis of Variance)

ANOVA is the primary statistical tool for one-factor experiments. It tests whether differences in means between factor levels are statistically significant.

ANOVA Hypothesis:

• Null Hypothesis (H₀): All factor level means are equal (the factor has no effect)
• Alternative Hypothesis (H₁): At least one factor level mean is different (the factor has an effect)

ANOVA Components:

• SST (Total Sum of Squares): Total variation in all data
• SSFactor (Sum of Squares for Factor): Variation between factor levels
• SSError (Sum of Squares for Error): Variation within factor levels
• MSFactor (Mean Square for Factor): SSFactor divided by degrees of freedom
• MSError (Mean Square for Error): SSError divided by degrees of freedom
• F-statistic: MSFactor divided by MSError

Decision Rule:

If the calculated F-statistic exceeds the critical F-value (or if p-value < 0.05), reject the null hypothesis and conclude the factor is statistically significant.

Example of a One-Factor Experiment

Scenario: Improving Call Center Response Time

Problem: A call center wants to reduce average call handling time.

Factor Selected: Training intensity (Light, Moderate, Intensive)

Response Variable: Average call handling time in minutes

Experiment Setup:

• Level 1: Light training (2 hours)
• Level 2: Moderate training (5 hours)
• Level 3: Intensive training (10 hours)
• Replicates: 10 employees per training level

Hypothetical Results:

• Light: Mean = 8.5 minutes
• Moderate: Mean = 7.2 minutes
• Intensive: Mean = 6.8 minutes

ANOVA Result: F-statistic = 15.3, p-value = 0.001

Conclusion: Training intensity significantly affects call handling time. More intensive training results in shorter call times.

Advantages of One-Factor Experiments

• Simple to design and implement
• Easy to understand and communicate results
• Cost-effective compared to multi-factor designs
• Quick execution and rapid results
• Minimal statistical complexity
• Clear cause-and-effect relationships

Limitations of One-Factor Experiments

• Cannot detect interactions between factors
• Inefficient when multiple factors need investigation (requires more total experiments)
• May miss optimal combinations when multiple factors interact
• Limited insight into complex process behaviors
• Results apply only to factors and levels tested

Exam Tips: Answering Questions on One-Factor Experiments

Tip 1: Understand the Fundamentals

Know: What distinguishes one-factor experiments from other designs. Remember that the key characteristic is testing only ONE independent variable while controlling all others.

Practice: When you see an exam question, immediately identify: What is the single factor being tested? What are its levels? What is being measured?

Tip 2: Master ANOVA Concepts

Remember: ANOVA tests whether differences between group means are statistically significant. Study the ANOVA table structure thoroughly.

Key formulas to know:

• F-statistic = MSFactor / MSError
• Decision: If p < 0.05 (or F calculated > F critical), reject H₀

Practice: Work through ANOVA table calculations until they become automatic.

Tip 3: Know When to Use One-Factor Experiments

Exam questions often ask: "Which experimental design is most appropriate?"

Choose one-factor experiments when:

• You want to test the effect of a single variable
• Budget is limited
• Time is constrained
• The process is new and only preliminary understanding is needed
• You're trying to identify which factor from many possibilities has the largest effect

Tip 4: Interpret Results Correctly

When presented with results, determine:

• Is the p-value less than 0.05? If yes, the factor is significant.
• Look at the F-statistic. Is it greater than the critical value? This indicates significance.
• Examine the means. What is the direction of the relationship?
• Consider practical significance in addition to statistical significance.

Common mistake: Don't confuse statistical significance with practical significance. A factor can be statistically significant but have such a small effect that it's not practically meaningful.

Tip 5: Understand Hypothesis Testing

Always identify:

• H₀ (Null Hypothesis): The factor has no effect (all means are equal)
• H₁ (Alternative Hypothesis): The factor has an effect (at least one mean differs)
• Significance level: Usually α = 0.05
• Test statistic: F-statistic in ANOVA

Practice stating hypotheses: "H₀: μ₁ = μ₂ = μ₃ (all training levels produce the same mean call time)"

Tip 6: Watch for Red Flags in Questions

Multiple factors mentioned? This might not be a simple one-factor experiment question. Check if the question is asking about comparing different one-factor experiments or if you need factorial design.

Asking about interactions? One-factor experiments cannot detect interactions. Factorial experiments are needed for that.

Seeking optimal settings? If the question asks to optimize multiple variables simultaneously, factorial design is more appropriate than one-factor experiments.

Tip 7: Practice Graph Interpretation

Exam questions often include:

• Main Effects Plots: Show average response at each factor level. A horizontal line suggests no effect; a sloped line suggests an effect.
• Box Plots: Show distribution at each level. Well-separated boxes indicate significant differences.
• Interaction Plots: Though not used in one-factor experiments, you might see them in comparative questions.

Practice: Sketch main effects plots for different scenarios (strong positive effect, strong negative effect, no effect, non-linear effect).

Tip 8: Know the Assumptions

One-factor experiments assume:

• Observations are independent
• Errors are normally distributed
• Variances are equal across factor levels (homogeneity of variance)
• Factors are controllable

Exam tip: If a question mentions violations of these assumptions, know that it may affect result validity and consider transformations or non-parametric alternatives.

Tip 9: Understand Replication and Randomization

Replication: Multiple runs at each level. Provides estimates of experimental error.

• Without replication, you cannot estimate experimental error reliably.
• More replicates increase statistical power (ability to detect effects).

Randomization: Tests conducted in random order to prevent systematic bias.

• Protects against time-based trends or other sequential biases.
• Essential for valid statistical inference.

Tip 10: Study Real-World Applications

Be ready to apply concepts to scenarios like:

• Manufacturing: Temperature, pressure, machine settings
• Service: Training methods, staffing levels, process changes
• Healthcare: Different treatment protocols
• Finance: Different investment strategies

Practice: For each scenario, identify: factor, levels, response variable, and appropriate analysis.

Tip 11: Know When One-Factor Experiments Fall Short

Exam questions may test whether you know limitations:

• "Why wouldn't a one-factor experiment work here?" If multiple factors need simultaneous optimization or interactions are suspected, factorial design is better.
• "What's the next step after this one-factor experiment?" Often, follow-up with factorial experiments to investigate interactions.

Tip 12: Review Sample Size and Power

Know: The relationship between sample size, effect size, and statistical power.

• Larger sample sizes provide more power to detect true effects.
• Questions may ask: "How many replicates are needed to detect a given effect size?"
• Power analysis is used to determine adequate sample size.

Rule of thumb: Minimum 3-5 replicates per factor level, but more is generally better.

Tip 13: Practice Calculation Problems

Prepare to:

• Calculate means for each factor level
• Calculate SST, SSFactor, and SSError
• Complete ANOVA tables
• Calculate F-statistics
• Compare to critical F-values or p-values
• Make decisions about statistical significance

Don't memorize: Understand the formulas and their logic. Understanding beats memorization on exams.

Tip 14: Read Questions Carefully

Common tricks in exam questions:

• Asking about practical vs. statistical significance (both matter!)
• Presenting data with very small sample sizes (validity questionable)
• Including uncontrolled variables that could confound results
• Testing multiple factors but asking about one-factor analysis (recognize this is incomplete)

Tip 15: Prepare for Various Question Types

Multiple Choice: Focus on recognizing correct terminology, understanding when to use one-factor experiments, and identifying appropriate analyses.

Short Answer: Prepare to explain concepts in clear, concise language. Define terms like "factor," "level," "replication," and "randomization."

Problem-Solving: Practice complete scenarios from design through analysis and conclusion. Show all work.

Case Studies: Be ready to recommend one-factor experiments, propose factors to test, identify levels, and suggest appropriate analysis.

Study Strategy for Exam Success

1. Master the theory: Understand why one-factor experiments work, not just how to conduct them.
2. Work practice problems: Start simple, progress to complex scenarios.
3. Create summary charts: Make a one-page reference guide on when to use one-factor vs. other designs.
4. Review ANOVA tables: Practice creating and interpreting them until automatic.
5. Discuss with peers: Explaining concepts to others reinforces learning.
6. Take timed practice exams: Simulate exam conditions to build confidence and time management.
7. Review mistakes: Understand why you got questions wrong, not just correct answers.

Conclusion

One-factor experiments are essential tools in the Six Sigma Improve Phase. They provide a clear, cost-effective method to test how a single variable affects process outcomes. While they have limitations compared to more complex designs, their simplicity and straightforward analysis make them valuable for initial investigations and quick wins. By mastering the fundamentals, understanding ANOVA, and practicing various scenarios, you'll be well-prepared to answer exam questions confidently and apply these techniques effectively in real-world improvement projects.