Generalized randomized block design
In statistical experiments, generalized randomized block designs (GRBDs) are used to study the interaction between blocks and treatments. For a GRBD, each treatment is replicated at least two times in each block; this replication allows the estimation and testing of an interaction term in the linear model.
Like a randomized complete block design (RCBD), a GRBD has randomization. Within each block, treatments are randomly assigned to experimental units and this randomization is independent between blocks. In a (classic) RCBD, there is no replication of treatments within blocks. Without replication, the (classic) RCBD has no interaction-term that may be estimated and tested using the randomization distribution.[1]
Many authors do not distinguish between RCBDs and GRBDs. GRBD has the advantage that replication allows block-treatment interaction to be studied. However, if block-treatment interaction known to be negligible, the experimental protocol may specify that the interaction terms be assumed to be zero and that their degrees of freedom be used for the error term: Many textbooks on the analysis of variance and on the analysis of experimental data ignore the possibility of testing for block-treatment interaction and instead present only the RCBD analysis with extra degrees of freedom for error.[2]
See also
- Analysis of variance
- Block design
- Blocking (statistics)
- Complete block design
- Incomplete block design
- Interaction (statistics)
- Random assignment
- Randomized block design
- Randomization
- Randomized experiment
Notes
References
- Hinkelmann, Klaus and Kempthorne, Oscar (2008). Design and Analysis of Experiments. Vol. I and II (Second ed.). Wiley. ISBN 978-0-470-38551-7.
{{cite book}}: External link in|publisher=- Hinkelmann, Klaus and Kempthorne, Oscar (2008). Design and Analysis of Experiments, Volume I: Introduction to Experimental Design (Second ed.). Wiley. ISBN 978-0-471-72756-9.
{{cite book}}: External link in|publisher=and|title= - Hinkelmann, Klaus and Kempthorne, Oscar (2005). Design and Analysis of Experiments, Volume 2: Advanced Experimental Design (First ed.). Wiley. ISBN 978-0-471-55177-5.
{{cite book}}: External link in|publisher=and|title=
- Hinkelmann, Klaus and Kempthorne, Oscar (2008). Design and Analysis of Experiments, Volume I: Introduction to Experimental Design (Second ed.). Wiley. ISBN 978-0-471-72756-9.
- Lentner, Marvin (1993). "The Generalized RCB Design (Chapter 6.13)". Experimental design and analysis (Second ed.). P.O. Box 884, Blacksburg, VA 24063: Valley Book Company. pp. 225–226. ISBN 0-9616255-2-X.
{{cite book}}: Unknown parameter|coauthor=ignored (|author=suggested) (help)CS1 maint: location (link)