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All these formulas from Equations 9 are independent of the special type of distribution function—If the basic hypothesis and the few very general presuppositions are acceptable. Therefore, it makes sense to use them for calculations and for the compression of data regardless of the type of distriIt must not be forgotten that bution. the statistical independence of the variables Zi (or of the repeated measurements) is an essential presupposition, except tor Equation 10. to 14a
ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
Correction of Misconceptions
This is the moment to set up a warning signal: mistake to (1) It is a common use the formally calculated values for s and x to make predictions, to state statistical significance, confidence limits, etc. Very often this is close to nonsense, because the description of an unknown distribution by estimates of its first two At moments may be too coarse. this stage of our investigation, s and x must be regarded as purely descriptive parameters used for the compression of many data. (Only in the case of a normal distribution would they be sufficient.) (2) The two parameters x and s are, in general, independent of each other, s is not attached to x. Therefore all shorthand expressions of the form x =b a are meaningless without detailed explanation. a has been used to indicate the observed range, or the standard deviation or confidence intervals of different significance. There is so much confusion and diversity, and this notation is so much spoiled, that no new convention of how this should be understood will help. This type of shorthand expression must be banned (2), at least for the next two generations until the present confusion will have been completely forgotten. (3) If the reported values {x, x s, etc.) allow further interpretation —beyond the descriptive compression of data—such interpretation should be given in sentence form and, if necessary, its presuppositions should be thoroughly discussed. There is such a variety of possible cases that no formal simple rules will cover them all. Where the experts to keep them in are mind ? (4) If not more than a descrip-
