Randomized Complete Block Designs

Overview

Questions

• What is randomized complete block design?

Objectives

• A randomized complete block design randomizes treatments to experimental units within the block.
• Blocking increases the precision of treatment comparisons.

Design issues

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Imagine that you want to evaluate the effect of different doses of a new drug on the proliferation of cancer cell lines in vitro. You use four different cancer cell lines because you would like the results to generalize to many types of cell lines. Divide each of the cell lines into four treatment groups, each with the same number of cells. Each treatment group receives a different dose of the drug for five consecutive days.

Group 1: Control (no drug)
Group 2: Low dose (10 μM) Group 3: Medium dose (50 μM) Group 4: High dose (100 μM)

R

# create treatment levels
f <- factor(c("control", "low", "medium", "high"))

# create random orderings of the treatment levels
block1 <- sample(f, 4)
block2 <- sample(f, 4)
block3 <- sample(f, 4)
block4 <- sample(f, 4)
treatment <- c(block1, block2, block3, block4)
block <- factor(rep(c("cellLine1", "cellLine2", "cellLine3", "cellLine4"), each = 4))
dishnum <- rep(1:4, 4)
plan <- data.frame(cellLine = block, DishNumber = dishnum, treatment = treatment)
plan

OUTPUT

    cellLine DishNumber treatment
1  cellLine1          1   control
2  cellLine1          2    medium
3  cellLine1          3       low
4  cellLine1          4      high
5  cellLine2          1   control
6  cellLine2          2      high
7  cellLine2          3       low
8  cellLine2          4    medium
9  cellLine3          1    medium
10 cellLine3          2       low
11 cellLine3          3   control
12 cellLine3          4      high
13 cellLine4          1   control
14 cellLine4          2      high
15 cellLine4          3    medium
16 cellLine4          4       low

When analyzing a random complete block design, the effect of the block is included in the equation along with the effect of the treatment.

Randomized block design with a single replication

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Sizing a randomized block experiment

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True replication

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Balanced incomplete block designs

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Key Points

• Replication, randomization and blocking determine the validity and usefulness of an experiment.