Two-Way Nested ANOVA With Replication for Non-Statisticians

Using 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 ANOVA Two-Way Nested Data

Example of Reorganized Data for Analysis

how to organize anova nested data for analysis

First: Perform Two Way ANOVA With Replication using QI Macros

  1. Click and drag over cells A1 to E9 of the reorganized data to select it.
  2. Click on QI Macros Menu, Statistical Tools and then ANOVA Two Factor with Replication:
  3. anova-two-way-menu

  4. 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.

ANOVA Two-Way with replication results

Next, Adjust the Calculations to Account for the Nesting

  1. Copy the ANOVA calculations and paste them below the existing calculations:
  2. Since there can be no interactions, add the SS values for Columns and Interaction together to eliminate the interaction:
    ANOVA Two-Way Nested Summarization
  3. Then, the F value for A has to be adjusted. See blue shaded cells to determine which values are used to calculate F.
    ANOVA Two-Way Nested F Calc Adjustment
  4. The adjusted p value for A is now 0.816, not 0.034.

Why Choose QI Macros Statistical Software for Excel?

easy to use

Easy to Use

  • Works Right in Excel
  • Interprets p-values for You
  • Accurate No-Worry Results
  • Free Training Anytime

proven and trusted

Proven and Trusted

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



  • Only $349 USD
    Quantity Discounts Available
  • No annual fees
  • Free Technical Support