Two Way ANOVA - Without Replication

Easy to Use Excel Add-in Makes Two Factor ANOVA a Snap

Two Way ANOVA (Analysis of variance), can help you determine if two factors have the same "mean" or average.

What Makes QI Macros Statistical Add-in for Excel Unique?

Works Right in Excel: QI Macros adds a new tab to Excel's menu making ANOVA and other statistical tests point and click simple.

Interprets the Results for You: QI Macros is the only Statistical software that tells you if you should "Reject or Not Reject the Null Hypothesis" and why that matters: "Means are Same or Different ".

Draws a chart to help you visualize the comparison between data sets. See sample results below:

interpret results of two factor anova test

Two-Way ANOVA Analysis Without Replication Example

What if you want to know if there is a difference in driving distance between three brands of golf balls for different golfers? (From Advanced Statistics Demystified by Dr. Larry J. Stephens.)

To perform a Two Way ANOVA test in Excel using QI Macros add-in, just follow these steps:

  1. Click and drag over your data in Excel to select it:
  2. Click on QI Macros and select Statistical Tools and then ANOVA Two Factor Without Replication.
  3. anova-two-factor-without-replication

  4. QI Macros will prompt you for a significance level. Default is alpha=0.05 for a 95% confidence.
  5. significance level prompt

  6. QI Macros will perform all of the calculations and interpret the results for you.

    two way anova without replication results

QI Macros built in code compares the p value to the significance level and provides this interpretation: Reject Null Hypothesis because p< .05 (Means are Different)

Further Analysis of the Results

It does look like Brand B and C are similar. We could run a paired two sample t test on Brands B and C to determine if they deliver the same average distance.

t test paired two sample for means

Since the p values are greater than alpha (0.05), we cannot reject the null hypothesis. There seems to be no difference between the two brands of golf balls, except perhaps price.

Why Choose QI Macros Statistical Software for Excel?



  • Only $249 USD - less with quantity discounts
  • No annual fees
  • Free Technical Support

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Easy to Use

  • Works Right in Excel
  • Interprets Results for You
  • Accurate Results Without Worry

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