# 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 the Null Hypothesis or Cannot Reject the Null Hypothesis (Accept the Null Hypothesis)" and why that matters: "Means are Different/Means are not the Same" or "Means are not Different/Means are the Same."

**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/Means are not the Same).

### 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 (Accept 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
**$329 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

### Proven and Trusted

- 100,000 Users in 80 Countries
- Celebrating 20th Anniversary
- Five Star CNET Rating - Virus Free