Sample size replication, experimental design

The power of the statistical test is a quantitative measure of the ability to differentiate accurately differences in populations. The usual case in toxicity testing is the comparison of a treatment group to control group. Depending on the expected variability of the data and the confidence level chosen, an enormous sample size or number of replicates may be required to achieve the necessary discrimination. If the sample size or replication is too large, then the experimental design may have to be altered. 

Appropriate design of microarray studies is critical to draw valid and useful conclusions from the large amount of data that are invariably obtained from each experiment. Criteria for design will vary depending on the type of array used— DNA, protein, and small molecule—as well as the experimental objectives, and sources of variability within the system. Issues such as selection of samples, number of replicates needed, allocation of samples to dyes for ratiometric profiling, and sample size are important considerations in these studies [127]. 

Once the process or design variables have been identified, a statistically designed experiment should be employed to collect appropriate data to fit the model. This plan includes developing the experimental objective, design matrix, and sample size (i.e., number of experimental replicates). 

One of the principal questions that arises is how to design an experiment in order to identify dispersion effects. The direct and obvious answer is to include replicate observations at the different design factor combinations used in the experiment. It is then possible to compute sample variances at each point and to use them as the basis for modeling how the dispersion depends on the experimental factors. The most immediate drawback to replication is that it increases the size and cost of the experiment. 

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