MEASURES OF PRECISION 
Census data obtained from the 2013 Census of 
Aquaeulture are based on the data obtained from a 
partieular set of respondents. If the entire census of 
aquaculture process was repeated over and over, it is 
not likely that the same exact mailing list would be 
constructed nor the exact same set of responding 
farm operators be obtained. The data obtained from 
each replication would undoubtedly lead to variation 
in the estimates being produced by the census. The 
question of how much these estimates might be 
expected to differ can be estimated by a statistic 
called the standard error, and also a closely related 
statistic called the relative standard error (sometimes 
referred to as the coefficient of variation). 
The relative standard error is used as an indicator of 
the precision in the estimates and is reported for 
major items in Table A. The relative standard error 
expresses the standard error of an estimate as a 
percent of the estimated value. The standard error of 
a survey estimate is a measure of the variation 
among the estimates from all possible samples. It is a 
measure of the precision with which an estimate 
from a particular sample approximates the average 
result of all possible samples. 
The relative standard errors given in Table A can be 
used to construct confidence intervals for the major 
items. Confidence intervals are another way to 
express the precision of an estimate by calculating 
the upper and lower bounds for a level of 
confidence. This confidence interval is designed to 
contain the true value being estimated. If all possible 
samples were selected, each of the samples was 
surveyed under essentially the same conditions, and 
an estimate and its standard error were calculated 
from each sample, then: 
1. Approximately 67 percent of the intervals from 
one standard error below the estimate to one 
standard error above the estimate would include the 
average value of all possible samples. 
2. Approximately 95 percent of the intervals from 
2.0 standard errors below the estimate to 2.0 
standard errors above the estimate would include the 
average value of all possible samples. 
The computations necessary to construct the 
confidence intervals associated with these statements 
are illustrated in the following example: Assume that 
the estimated number of goldfish produced in a State 
is 100,000 and the relative standard error of the 
estimate is 10.0 percent (.10). Multiplying 100,000 
by 0.10 yields 10,000, the standard error. Therefore, 
a 67-percent confidence interval is defined by the 
range (90,000 to 110,000) or equivalently 100,000 
plus or minus 10,000. If corresponding confidence 
intervals were constructed for all possible samples of 
the same size and design, approximately 2 out of 3 
(67 percent) of these intervals would contain the true 
number of goldfish produced in the State. Similarly, 
an approximate 95 -percent confidence interval is 
(80,000 to 120,000) obtained using 100,000 plus or 
minus 2.0 x 10,000. 
A- 4 APPENDIX A 
2012 Census of Agriculture 
USDA, National Agricultural Statistics Service 
