The Choice of a Response Metameter in Bio-Assay

U NLESS THERE ARE theoretical objections or empirical indications to the contrary, the statistician usually assumes that quantitative data which are put before him are normally distributed. If he is obliged to abandon the hypothesis of normality, he may choose some alternative specification of the distribution, or he may seek a transformation of the data (1) in terms of which the distribution is normal. The alternatives are closely related, for adoption of a transformation implies some assumption about the form of the original distribution and is an analytical convenience rather than an essentially different approach. Unless the data are very extensive, they are unlikely to discriminate satisfactorily between two or more equally plausible normalizing transformations (such as the square root and the logarithm); it is therefore natural to inquire how far conclusions drawn from a statistical analysis may be affected by the choice that is made. If the distribution is really normal in terms of one transformation, it cannot be normal for another unless the second is itself a linear transformation of the first, and in general numerical results obtained by the use of different transformations will not be identical. Similar inquiries might be made about other common assumptions, such as those of linearity and homoscedasticity of regressions, often introduced by the statistician in order to form a mathematical model (on the basis of which the data may be subjected to statistical analysis) even though no biological theory demands that particular model. Few would deny that these may represent reasonable approximations to reality, none would assert their exact and absolute truth. Must the fact that different statisticians would not always agree on the choice of a normalizing or linearizing transformation for a particular body of data be regarded as a flaw in the vaunted objectivity of statistical analysis?