# 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:**

- Click and drag over your data in Excel to select it:
- Click on the QI Macros menu > Statistical Tools > ANOVA - Analysis of Variance, and then select "ANOVA Two Factor Without Replication":
- QI Macros will prompt you for a significance level. Default is alpha=0.05 for a 95% confidence.
- 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<0.05 (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.

### Why Choose QI Macros Statistical Software for Excel?

### Affordable

- Only
**$299 USD**- less with quantity discounts - No annual fees
- Free Technical Support

### Easy to Use

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

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