• 作者： 汪厥明
• 作者服務機構： 國立臺灣大學農學院
• 中文摘要： The research works in this stage may be divided into two parts:viz.,}l)The first part is chiefly devoted to comparison of three sampling methods employed in drawing variates from the experimental data.(2) In the second part, inquiry into the properties of the simple and joint fre. quency distributions of RR samples from e}'perimental data of Poisson type is emphasized.For simplicity, three sampling methods under consideration are written as (I),lA)and ( B ) respectively, i.e.,(I):The variate is drawn out randomly and discarded one by one by using ran- dam numbers such as Quenouille's Tables of Random Orderings of Numbers so that the variates remaining in the data form a smaller random sample. For instance, after random drawing and discarding 10 variates from data of 120 variates, the remaining 110 variates thus, provide a random sample of smaller size. By this process, ten kinds of random samples of different size ( ni' ) will turn out, i.e., n,' =110, 100, 90, 80, 70, 60, 50, 40, 30, and 20.(A):This method only in one point of sampling process differs from (I), that is, instead of random drawing and rejecting variates, they are randomly select- ed and saved to form a smaller random sample. Ten kinds of random sam- pies of size n;' are thus obtained, n;' ranging from 20 to 110 with a interval of IO variates. ( B ) : The manner in which the random numbers are used differs from ( I ) and (A).All random numbers which happen to appear when sampling are re-tained for sampling use no matter whether they are over large or not. It is evident that of three sampling methods above, the first (I) is most conve-nient and easy to apply for practical purposes. After statistical analyses and consi-derations, it follows that no significant difference among three sampling methodsabove is observed. Since the result from sampling with replacement and that fromsampling without replacement are identical as recently asserted by wellknown stati-sticians, the sampling method(I) is worth while recommending. In the second part, the author has, in the first place, verified theoretically thatthe sample poisson distribution of RR(SB )-that is, the Radioactivity Rate of theSoft Beta of C14 obtained by measuring experiments-is a joint distribution of twoindependent Poisson series. Therefore, the following relationship between them holdsgood; m=m1+m2 where m is the mean of joint distribution, m1 that of RR(BG), i.e., the RR ofBackground and m2 that of the net RR(SB). This joint distribution also can beregarded as that of the binomial distribution with parameter } and the Poissondistribution with parameter m, which are, of course, independent of each other.The theoretical reasoning above has been ascertained by the author with experiments.The joint frequency function with parameter } and m is as follows:where and xi (=xi-x2i)the varying counts per unit time o_f net SB plus BG.From the experimental experience in this stage and before,it follows that RR(BG ) is more fickle and unsteady than RR( SB )such that the estimated average C.V.(i.e., Coefficient of Variation) of RR(SB) is 55% as large as that of RR(BG).
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