# Need to Run Two-Way Nested ANOVA With Replication but Don't Know How?

## QI Macros can run ANOVA tests and interpret the results for you.

#### You don't have to be a statistician!

### When to Use Two-Way ANOVA for Nested Data

When there are many factors, it can be difficult to "cross" every factor with every other one, so it's possible to use a nested design with Two-Way ANOVA.

### Nested Two-Way ANOVA Analysis With Replication Example

You might have two factors with four replications, but only able to cover each combination (A1 with B1-B4, and A2 with B5-B8) without interaction. So we will need to stack the data and then adjust the results. This example comes from Conrad Carlberg.

**Example of Nested ANOVA Data **

**Example of Reorganized Data for Analysis**

#### First: Perform Two Way ANOVA With Replication using QI Macros

- Click and drag over cells A1 to E9 of the reorganized data to select it.
- Click on QI Macros Menu, Statistical Tools and then ANOVA Two Factor with Replication:
- QI Macros will prompt you for how many rows are in each sample (four) and 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.

#### Next, Adjust the Calculations to Account for the Nesting

- Copy the ANOVA calculations and paste them below the existing calculations:
- Since there can be no interactions, add the SS values for Columns and Interaction together to eliminate the interaction:

- Then, the F value for A has to be adjusted. See blue shaded cells to determine which values are used to calculate F.

- The adjusted
*p value*for A is now 0.816, not 0.034.