Displaying Factor Relationships in Experiments

Wendy A. Bergerud
1996 American Statistician  
Displaying Factor Relationships in Experiments Determining the proper description of a study requires identifying the independent variables in the study, how they are related to each other, and how they are replicated. The Factor Relationship Diagram (FRD) described here is a useful aid for doing this and for generating the list of sources of variation for an ANOVA table. Once developed for a study, the diagram can be used to discuss replication issues and the effects of any proposed changes.
more » ... proposed changes. Furthermore, it clarifies the structure of various experimental designs, particularly the often confusing split-plot, and allows the determination of the experimental design for studies that do not follow the traditional patterns presented in most textbooks. The FRD has been used within the B.C. Research Program for many years where it has been commonly called the 'stick diagram'. This pamphlet will describe how to use the diagram by using a randomized block study example, and then modifying the example to illustrate the factor relations within a split-plot design. Features of these designs, including common pitfalls, are discussed throughout. A review of the basic concepts and terminology used is in Appendix 1 while a formalized description of the steps for diagram construction are presented in Appendix 2. R R Ra a an n nd d do o om m mi i iz z ze e ed d d B B Bl l lo o oc c ck k k D D De e es s si i ig g gn n n w w wi i it t th h h S S Su u ub b bs s sa a am m mp p pl l li i in n ng g g The construction of a factor relationship diagram will be illustrated with a randomized block design. Suppose that data from the following experiment are to be analyzed. Three blocks of land were each divided into two plots, each of which was randomly assigned one of two levels of a fertilizer treatment, called treatment A. Ten similar nursery seedlings were then planted in each plot and the treatment applied. A year later, the height of each seedling was recorded. This study has three unit factors 1 : block, plot, and seedling and one treatment factor, A. Each factor is identified by a letter, B, P, S, or A, respectively, and each level of each factor is given a unique number. For example, B has three levels, 1, 2, and 3. The study includes six unique plots, therefore P is assigned numbers 1 through 6. Similarly, the 60 seedlings are uniquely numbered from 1 to 60.
doi:10.1080/00031305.1996.10474385 fatcat:dwsv3rx3bjc77bf6zsw2fzvbdm