# 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:

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

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

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.

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.

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• Works Right in Excel
• Interprets Results for You
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