# Randomized Block Design

If a given variable is expected to introduce significant variation to our results, then we can control that variation by Blocking on that variable.

This involves splitting up our experimental units into blocks, such that each block is a collection of individuals that have similar values of the blocking variable.

We then take each block in turn and for each block distribute individuals randomly between treatment groups.

It is a more complicated design than completely randomized design.

Example

We are interested in whether the type of food we give to a greyhound affects its running speed. We have 80 greyhounds and a running track and we want to test the effects of four different food types.

·        Completely randomized one-factor design. Randomly allocate 20 dogs to one of the four food treatments.

If the dogs are of different ages and age affects the running speed of the dog. By using a completely randomized design we have ignored this source of variation and thus produced pseudoreplication (noise  random variation).

·        Must treat age as a blocking factor in the experiment

Method

·        Rank the dogs by age, then partition this ranking so as to divide the dogs into blocks so that those in a block have a similar age

·        Try to make the age partitions a multiple of the number of groups

·        Take each block in turn and randomly allocate those dogs to the treatment groups in exactly the way that we did in the completely randomized design

Completely Randomized

Dog 1

Dog 4

Dog 2

Dog 5

Dog 3

Dog 6

Randomized Block

## Diet B

Young

Dog 1

Dog 1`

Middle

Dog 2

Dog 2`

Old

Dog 3

Dog 3`

In the randomized experiment we will find ourselves comparing an old dog in one treatment and a young dog in another. If we compare their running speeds and find a difference, part of this may be due to food sources and part due to age.

By contrast, in the blocked design we are making comparisons within our experimental blocks, so we will only be comparing dogs of similar ages.

### Blocking on Individual characters, Space and Time

You can block in any variable that you think might be important in contributing to variations between individuals given the experimental treatment.

The only condition for a characteristic to be used as a blocking variable is that you can measure it in individuals so you can rank them

So you can block according to:

1)     Individual characters

2)     Space (greenhouses)

3)     Time (months)

Paired Designs

In paired designs, we divide the population into pairs and randomly assign the individuals in each pair one to each of two treatment groups

It is a form of blocking

Example

We want to examine the effect of an antibiotic injection soon after birth to the subsequent health of domestic cattle calves.

Use sets of twins as our experimental pairs, randomly assigning one calf from each set of twins to get the injection.

This has the same benefits as all forms of blocking, eliminating many potential confounding factors because the two twin calves in a pair will be genetically similar, will be fed by the same mother, and can easily be kept together in order to experience the same environmental conditions.

Cross-over Design (Repeated measures design)

In a cross-over design, experimental subjects experience the different experimental treatments sequentially, and comparisons are made on the same individual at different times, rather than between different individuals at the same time

Example

We want to investigate whether classical music makes chicken lay more eggs.

(One way is completely randomized design with negative and positive controls)

If we are using negative control, then we should randomly allocate houses to one of two treatment sequences. The first receives classical music fro 3 weeks, then no music for 3 weeks. The other receives no music for 3 weeks, then classical music for 3 weeks.

We then compare the number of eggs laid in the same house under the two different regimes.

(We need two groups. Why?)

This design only works if we are measuring non-destructively like measuring number of eggs. If the question was weather the classical music thickens the heart, then chicken would probably have to be killed.

There may be a problem of carry-over effects. It may be that the effect of the classical music persists for days after the music is discontinued.

Carry-over effects occur when a treatment continues to affect the subsequent behavior of experimental subjects, even after that treatment is no longer applied

What to do: either dont use this design or introduce a period of no treatment to washout the effects of the first treatment

Why this design is not considered as a pseudoreplication?

(A subject is measured more than once, but there is only one measurement made of each individual under each experimental condition, we then compare between the two measurements on the same individual)

If we are going to use three types of control (What are they) and the classical music then we will need four different groups each of which experiences the four regimes in a different order.

(Not practical  takes a long time  ethical considerations)

Split-plot Design

In a split-plot design we have two factors and experimental subjects that are organized into a number of groups. For one factor (the main-plot factor) we randomly allocate entire groups to different treatment to different treatment levels of that factor. We then randomly allocate individual experimental subjects within each of these groups to different levels of the other factor (the sub-plot factor)

Example

You want to study the effect on watermelon growth of three different methods of ploughing before planting and three different methods of applying pesticides after planting. We have six square fields of similar size.

The completely randomized design would be to divide up each field into six equal sections and then randomly allocate four of the 36 sections to each of the nine combinations of ploughing and pesticide application

The split plot design would be to allocate two fields at random to each ploughing type and then plough entire fields the same. Then take each field and randomly allocate two of the six parts to each pesticide treatment.

Completely randomized design is better

Why to do this design?

Convenience  much better able to detect differences due to pesticide use (the sub-plot factor) and the interaction between herbicide and ploughing than it is to detect differences due to ploughing (the main-plot factor).

Example

Effects of temperature and growth medium on yeast growth rate

Suggest the design