Lesson 4: Blocking

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Introduction

Blocking factors and nuisance factors provide the mechanism for explaining and controlling variation among the experimental units from sources that are not of interest to you and therefore are part of the error or noise aspect of the analysis.  Block designs help maintain internal validity, by reducing the possibility that the observed effects are due to a confounding factor, while maintaining external validity by allowing the investigator to use less stringent restrictions on the sampling population.

The single design we looked at so far is the completely randomized design (CRD) where we only have a single factor. In the CRD setting we simply randomly assign the treatments to the available experimental units in our experiment.

When we have a single blocking factor available for our experiment we will try to utilize a randomized complete block design (RCBD). We also consider extensions when more than a single blocking factor exists which takes us to Latin Squares and their generalizations. When we can utilize these ideal designs, which have nice simple structure, the analysis is still very simple, and the designs are quite efficient in terms of power and reducing the error variation.

Learning outcomes & objectives

By the end of this lesson, students are supposed to know

  • Concept of Blocking in Design of Experiment
  • Dealing with missing data cases in Randomized Complete Block Design
  • Application of Latin Square Designs in presence of two nuisance factors
  • Application of Graeco-Latin Square Design in presence of three blocking factor sources of variation
  • Crossover Designs and their special clinical applications
  • Balanced Incomplete Block Designs (BIBD)

References

In this lesson specific references to material in the textbook come from Chapter 4, including:

The Hardness Testing Example, Section 4.1

Vascular Graft Example, Example 4.1

The Latin Square Design, Section 4.2