How to Perform a Two-Way ANOVA in Excel 2013

Introduction

• Host: Eugene from Connection Computing at the National College of Ireland
• Purpose: Demonstrate how to perform a two-way ANOVA in Excel 2013

Experiment Setup

• Data Used: Small sample data, for illustration purposes
• Experiment: Conducted with two brands of detergent ('Super' and 'Best')
• Temperature Settings: Cold, Warm, and Hot
• Design Factors:
  • Temperature: 3 Levels
  • Brand: 2 Levels

Hypotheses in Two-Way ANOVA

1. H₁: No difference between the means of the super and best brands.
2. H₂: No difference among means of cold, warm, and hot temperatures.
3. H₃: No interaction between the factors (temperature and brand).

Setting Up Excel for Two-Way ANOVA

• Open the Data ribbon.
• Navigate to the Analysis pane and select Data Analysis Toolpak.
• If Data Analysis Toolpak is not installed, it needs to be added manually.

Performing the Analysis

1. Select "ANOVA: Two Factor with Replication"
2. Input Data:
   • Input range: Select entire data set (including labels, e.g., A1:D9)
   • Rows per sample: Must be the same for each brand (e.g., 4 rows for each brand)
   • Alpha value: Default 0.05, can be adjusted
   • Output range: Choose where to display results

Interpreting ANOVA Results

• Summary Data: Counts, sums, averages, variances for each brand at different temperatures
• ANOVA Table:
  • Source of Variation
  • Sum of Squares (SS)
  • Degrees of Freedom (df)
  • Mean Square (MS)
  • F-statistic (F)
  • P-value
  • F critical value

Results Analysis

1. Sample Row (Brand Difference):
   • F-statistic > F critical value, p-value < 0.05
   • Conclusion: Reject H₁, means differ between 'Super' and 'Best'.
2. Column Row (Temperature Difference):
   • High F-statistic, p-value < 0.05
   • Conclusion: Reject H₂, means differ among cold, warm, and hot.
3. Interaction Effect:
   • F-statistic > F critical value, p-value < 0.05
   • Conclusion: Reject H₃, interaction exists.
   • Implication: The effect of temperature on dirt removal is dependent on the detergent brand and vice versa.

Conclusion

• Successful demonstration of performing a two-way ANOVA in Excel 2013.
• Key findings involve differences between brands and temperatures and an interaction between these factors.
• Thank you for your attention.