Principles

A powerful experiment will have a high Signal/Noise ratio. Signal is the response to the treatment, noise is the within-group variation. Use of isogenic strains controls the noise by eliminating genetic variation. On average it does not alter the signal. In the simplest possible experiment two  individuals which are as alike as possible are assigned at random either to a “treated” or a “control” group. Any difference between them is attributed to the effect of the treatment.

However no two individuals are exactly alike so it is necessary to use several animals in each group to average out any slight differences. The four experiments below explain the situation, assuming a measurement outcome

	Experiment 1 This shows such a simple experiment where all individuals are genetically identical, using an isogenic strain. Any difference in the  outcome is assumed to be due to the effect of the treatment. The required number of replications (group or sample size) will be small if the variation between individuals, due only to non-genetic effects, is slight. Group means will be compared using a two-sample t-test.
	Experiment 2 This shows the situation using a genetically heterogeneous stock, where each individual is different. Now any difference in outcome is due both to genetic differences and the effect of the treatment. These can not be separated so the experiment gives no information on the extent of genetic variation in response. Sample sizes must be increased to average out both the genetic and non-genetic differences between the two groups otherwise the experiment will fail to detect a treatment effect unless it is substantial.  Alternatively if group size is fixed the experiment will lack power to distinguish between the groups. Group means will be compared using a two sample t-test.
	Experiment 3 This shows one strategy if the aim is to take account of genetic variation without having to increase sample size. This experiment involves two animals of five isogenic strains. Treated and control groups are genetically identical so any difference between the means is due to the effect of the treatment. But genetic variation is detected as the difference in response between the pairs.  This experiment is very like a human study using monozygous twins. Group means  will be compared using a paired t-test, and the experiment is likely to be much more powerful than experiment 2.
	Experiment 4 It may not be practical to use just two animals from each of six strains, as shown in Experiment 3. This experiment illustrates an alternative using just two isogenic strains. Treated and control groups are still genetically identical so the experiment is powerful and it also gives an estimate of any intrinsic strain differences and any differences in response. It will need to be analysed using a two-way analysis of variance. It does not require more animals than Experiments 1 and 3, but will require fewer than Experiment 2.