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K This follows directly from standard probability theory. This can be used to estimate the biological variation from the observed variation: √ σˆ bio = k σˆ pool √ n k = (xi − x)2 . 2) n−1 i=1 The estimate is of course only as good as the number of chips available. It does not depend on the number of biological samples in each pool. Implementation of optimal pooling in R: op. The function op is designed to calculate the optimal number of arrays and samples per arrays to minimize the costs while still maintaining a f-fold detection with a confidence level of 1-alpha.

2000) attain this result by considering only the replicability of technical replicates on a single slide. 95), but it is the reproducibility of biological replicates that is important for inference. 30. Sometimes it is suggested that with three replicates it is possible to detect one anomalous observation. Besides biasing the variance estimate, this ‘method’ cannot serve as the basis for any formal procedure. The two most obvious reasons why only a small number of replicates can be considered is the limited budget and perhaps the limited availability of mRNA from different biological replicates.

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