By F. X. Schumaher, R. A. Chapman
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12. A popuhttion of 200 cellR, divided into 10 blocks of 20 (Jells euch. 2 Comparison of Representative with Unrestricted Random Sampling. The efficiency of representative sampling as compared to unrestricted random sampling of stratified populations may, perhaps, be most convincingly demonstrated by graphic comparison of estimates of the popUlation mean as based upon repeated sampling trials. In Figure 13A are plotted 11 estimates of the mean of the population of the 200 numbers of Figure 12. Each estimate is the mean of 20 cell 63 STRATIFIED RANDOM SAMPLING TABLE 10.
9 ............ 10 ............ l0 90 74 120 76 125 94 98 137 101 150 65 113 149 Sum ............................. 1,904 1--------------------Mean ............................ 2 values, drawn at random from the populntion as a whole according to the single plot method used in Sec. 3. Figure 13B shows 11 estimates of the mean of the same population according to the representative sampling design of the preceding section. Each mean is again based upon 20 cell values, but the drawing was made with the restriction that two cells be taken independently and at random from eltch of the 10 blocks.
3) The sampling variance of a sum of n single variates is therefore n times the variance of single variates. The s:1mpling variance of a mean follows at once. n of n values of y is 1 n y= S (y), n and the variance of this mean is the average over all samples of 1 E [ -n (fl+ 2+ .... _1 n (1:). _ n (J2 . . . . • • • • • . . . • • • • • • (4), that is, the sampling variance of mean y is the variance of y divided by the number of observations upon which the mean is based. ple. ANGE MANAGEMEN'l' tion mean was a known parameter; hence, we were ennblcd to make unbiased estimates of population variances directly from the known errors.