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 onefactor 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

Diet A 
Diet B 

Dog 1 
Dog 4 

Dog 2 
Dog 5 

Dog 3 
Dog 6 
Randomized Block

Diet A 
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.
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.
Crossover Design (Repeated measures design)
In a crossover 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
nondestructively 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 carryover effects. It may
be that the effect of the classical music persists for days after the music is
discontinued.
Carryover 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 dont 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)
Splitplot Design
In a splitplot design we have two factors and
experimental subjects that are organized into a number of groups. For one
factor (the mainplot 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 subplot 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 subplot factor) and the interaction between
herbicide and ploughing than it is to detect
differences due to ploughing (the mainplot factor).
Example
Effects of temperature and growth medium on yeast
growth rate
Suggest the design