### Abstract

The key to the correct application of ANOVA is careful experimental design and matching the correct analysis to that design. The following points should therefore, be considered before designing any experiment:
1. In a single factor design, ensure that the factor is identified as a 'fixed' or 'random effect' factor.
2. In more complex designs, with more than one factor, there may be a mixture of fixed and random effect factors present, so ensure that each factor is clearly identified.
3. Where replicates can be grouped or blocked, the advantages of a randomised blocks design should be considered. There should be evidence, however, that blocking can sufficiently reduce the error variation to counter the loss of DF compared with a randomised design.
4. Where different treatments are applied sequentially to a patient, the advantages of a three-way design in which the different orders of the treatments are included as an 'effect' should be considered.
5. Combining different factors to make a more efficient experiment and to measure possible factor interactions should always be considered.
6. The effect of 'internal replication' should be taken into account in a factorial design in deciding the number of replications to be used. Where possible, each error term of the ANOVA should have at least 15 DF.
7. Consider carefully whether a particular factorial design can be considered to be a split-plot or a repeated measures design. If such a design is appropriate, consider how to continue the analysis bearing in mind the problem of using post hoc tests in this situation.

Original language | English |
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Pages | 48-52 |

Number of pages | 5 |

Volume | 2009 |

No. | January |

Specialist publication | Optometry Today |

Publication status | Published - Jan 2009 |

### Keywords

- ANOVA
- experimental design
- analysis

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## Cite this

Armstrong, R. A., & Eperjesi, F. (2009). Data methods in optometry Part 9: experimental design and analysis of variance.

*Optometry Today*,*2009*(January), 48-52.