720
HAWTHORNE
Students’ ¢ distribution to estimate the population standard deviations.‘
Estimates of sample size made in this way cannot take advantage of the
continuous flow of new information arriving as more specimens are
analyzed. —
Blocks of 100 specimens were assembled, each containing related
materials: soil, plants, or milk. Each specimen was assigneda random
number to separate replicate specimens of a sample. The specimens
were analyzed in numerical sequence; thus the radiochemical determinations for replicates from any given sample were acquired at Spaced
intervals in time. Sequential-analysis statistical techniques become
feasible when information on replicate specimens is obtained in this
manner. Uncompleted analyses can be terminated when standards of
precision and reliability are met.
On the average, use of sequential analysis results ina 50% reduction in sample size as comparedto the use of single fixed-sample-size
estimates.° However, the number of Specimens in a sample are not
known until the hypothesis under test is accepted or rejected. The procedure is not appropriate for estimating sample sizes. It does, however, require fewer Specimens in a sample than are estimated when
Students’ ¢ distribution is used.
Two estimates of sample size were made by using the sample sta-
tistics of means and standard deviations: assuming a normal distribution in one case and using the Students’ ¢ distribution in the other. The
ratios of the two sample-size estimates (f/normal) fell in the range of
1.5 to 1.7 for coefficients of variation from 0.05 to 0.40. Therefore the
procedure has been to make an estimate of sample size from Statistics
that are assumed to be normally distributed. In the following tables the
numbers of specimens shown for samples of soil, alfalfa, and milk
apply only to this farm and are fewer than those which were estimated
with statistical rigor. They do, however, take into account the reductions
in
analysis.
analytical
burden
which
ensue
from applying sequential
A formula is given in Table 1 for calculation of the number of
Specimens required to state the mean at some desired precision. At the
Same time the investigator may specify what risk he is willing to take
that the sample mean may actually fall outside the precision limits he
has chosen. It is apparent from Table 1 that, even though the absolute
radioactivity varied in the soil profile (Fig. 1), the required number of
specimens does not differ greatly through the plowed zone and that the
required precision can be attained. Table 2 shows how the required
number of specimens changed for the same month from year to year
and also from month to month in the same year. These changing sample
sizes reflect the changing variability in alfalfa growth rates.
The data of Table 3 show that there was less variability in "Cs
in the milk than there was in the alfalfa consumed to produce the milk