Such considerations apply to both in vivo and in vitro studies. If you know that the SD is the same for all values of X, this simplifies to: Those standard deviation values must be computed from lots of data. It is important to appreciate that statistical software used to analyze the data collected from such experiments assumes that these concepts have been incorporated into the design but does not provide any warning that they have not been. The chi-square is the sum of the square of the distances of the points from the curve, divided by the predicted standard deviation at that value of X. The key concepts of blocking, randomization, and replication as well as an appreciation of what the experimental unit is in the study are critical to good experimental design and subsequent statistical analysis. Experiments designed to detect such low-dose effects need careful design otherwise the results detected may be affected by artefacts. This has led to initiatives to try to detect thresholds in the responses or to identify points of departure for risk estimation of low-dose effects using approaches such as the benchmark dose methodology. There is an increasing interest in the quantification of the results of genotoxicity experiments.
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