7. Controlling Variability
If noise can be reduced the signal/noise ratio will go up. Sample size could be reduced, power could be increased or a smaller response could be detected. So control of variation is of fundamental importance when designing an experiment.
There are three ways in which inter-individual variation can be reduced.
1. By choosing animals of similar weight and age, eliminating clinical or sub-clinical infection and providing a non-stressful environment
2. By controlling the genetic variation using inbred strains (when using mice or rats).
3. By using randomised block experimental designs or covariance analysis so as to remove some of the variation that can not be removed in any other way during the statistical analysis.
This page gives some examples. Both genetic variation and blocking are considered in more detail later.
The plot shows that mice housed singly are more variable (SD=5.8) than those housed in pairs (SD=3.9) or groups, although they weigh slightly more on average. ( Chvedoff M et al (1980). Effects on mice of numbers of animal per cage: an 18-month study. (preliminary results). Archives of Toxicology, Supplement 4:435-438.)
Assume you want to do an experiment to see whether a specified drug treatment affects body weight in mice, with individual mice being the experimental unit.
You plan to compare treated and control means and consider that if the two means differ by 4g or more (the signal) this would be of biological interest. You plan to use a two-sided t-test with a significance level of 0.05 and a power of 0.9. Should you house your mice singly or in pairs? (you rule out having more per cage).
Assuming that the response (signal) is not affected by number per cage you would only need half the number of animals if they were to be housed in pairs
Sleeping time under barbiturate anesthetic is sometimes used to indicate whether a test drug alters drug metabolising enzymes. All mice receive the barbiturate and half of them receive the test compound while the other are used as controls. A difference in sleeping time would indicate that the test substances alters drug metabolism.
The table below shows the number, mean and standard deviation of sleeping time in five inbred strains (A/N to SWR/HeN) and two outbred stocks (CFW and Swiss) of mice under hexobarbital anesthetic.
Note the much greater variability (SD) in the outbred stocks. This substantially reduces the signal/noise ratio (assuming a signal (effect size) of 4 minutes), so much larger sample (group) sizes are needed. The last column shows the power that an experiment would have if group size were fixed at 20 mice.
Controlling the genetic variation by using inbred strains resulted in this case in either a much smaller sample size being needed or a substantial increase in power if sample size was fixed at 20/group.
This study shows the variability of kidney weight in 58 groups of rats (N=approx 30 in each group). Groups have been ranked in order of variability which is expressed as a percentage. Some groups were affected with Mycoplasma pulmonis causing chronic respiratory disease (in red), some were outbred, some F1 hybrid and some F2 hybrids.
The Mycoplasma-infected rats are clearly highly variable. Samples of outbred rats are both the most uniform and the most variable, but tend towards variability while the F1 hybrids (which are isogenic) tend to be uniform, with one exception.
Suppose the aim of an experiment is to find out whether a drug affects the weight of the kidneys in rats. We can use a power analysis to find out how many rats of each type shown on the previous page would be needed.
Assume that we want to be able to detect a 20% change in kidney weight (either way), we want a power of 80%, a significance level of 5%, and we have data on the variability of each group. The results are shown in the table below.
Note that twice as many animals (32 vs 16) would be needed to do the experiment with non-isogenic (outbred and F2 hybrid) rather than isogenic (F1 hybrid) rats, and five times more Mycoplasma-infected rats (155) than healthy rats (29, averaging across genotypes) would need to be used. If sample size is fixed at 10 animals/group then power would be 60% using the isogenic rats but only 32% using the non-isogenic ones.
All show that uncontrolled variability reduces the signal/noise ratio so larger sample sizes are needed to detect the effect of a treatment. This will cost money, time and effort, and the lives of animals.
But controlled variation can be deliberately introduced by, for example, using several inbred strains, by using both sexes, by sampling different environments or by using different diets without increasing the total number of animals, using factorial and randomised block designs (discussed later).