On the Construction of Tables for Moving-Average Interpolation

Abstract

EXTENSIVF use of the method [1] of moving-average interpolation to estimate median-effective dose M led one of us (C.S.W.) to undertake construction of tables to give the estimate m of M and the estimated standard deviation of its logarithm for the case ni = n, a constant, using the original formulas (6) and (A9). The present purpose is to indicate some simple relations that afford great economies both in construction and in presentation of such tables. Original notations [1] will be used with D, = dosage given ni subjects, ri = the number of these that respond critically, si = ni ri , d = log (Di/Di-,) which is constant, and K = the chosen moving-average span. The interpolation is based upon results at K + 1 successive dosage levels (Da, Da+i, * *, Db) where b = a + K. For the given case (ni = n) to facilitate discussion define an f-function and a g-function of the corresponding values of ri as follows: