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.
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.
First: Perform Two Way ANOVA With Replication using QI Macros
- Click and drag over the nested data for analysis 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 and df calculations for Columns and Interaction together and eliminate the interaction:
- Then, the F value for A has to be adjusted to use the MS for B within A, not the overall Within:
- The adjusted p value for A is 0.742, not 0.034.
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