Two-Way ANOVA

Authors

Affiliations

Nate Yomogida, B.S., SPT

Doctor of Physical Therapy

B.S. in Kinesiology

Chloë Kerstein, B.S., SPT

Doctor of Physical Therapy

B.A. in Neuroscience

Purpose

A two-way analysis of variance is designed to address three main questions:

1. Does the additive model hold?¹
2. If so, is the mean outcome the same for all levels of the row factor?¹
3. If so, is the mean outcome the same for all levels of the column factor?¹

Assumptions

The standard two-way ANOVA hypothesis tests are valid under the following conditions:

1. The design must be complete¹.
2. The design must be balanced¹.
3. The number of replicates per treatment, K , must be at least 2¹.
4. Within any treatment, the observations Xij1,…,XijK are a simple random sample from a normal population¹.
5. The population variance is the same for all treatments. We denote this variance by \(\sigma^2\)¹.

References

1.

Navidi WC. Statistics for Engineers and Scientists. 4th ed. McGraw-Hill Education; 2015.