to sample-to-sample variation. Nonsampling errors 
include all other errors and can arise from many 
different sources. These sources may include 
respondent or enumerator error or incorrect data 
keying, editing, or imputing for missing data. 
Nonsampling error due to mail list incompleteness 
and duplication, as well as misclassification of 
records on the mail list, is referred to as coverage 
error. 
Undercoverage existed in the frame population to the 
extent that there were farms that either erroneously 
reported not irrigating in the 2012 census, started 
irrigating in 2013, or had succeeding irrigators in 
2013 (i.e., an operator who, since 2012, took over 
control of an irrigating farm through sales, rental, or 
other arrangements). Overcoverage existed in the 
frame because some operations were misclassified as 
irrigated and did not irrigate in 2012 or had either 
stopped farming or irrigating in 2013. Farms in these 
groups that were selected into the sample were 
identified during the survey and estimates of their 
number and acres irrigated are provided above under 
Data Comparability, items 2 and 3. 
Survey Response Rate 
The reponse rate is one indicator of the quality of a 
data collection. It is generally assumed that if a 
response rate is close to a full participation level of 
100 percent, the potential for nonresponse bias is 
small, although this has been questioned recently in 
the literature. Because the FRIS contains both farm 
and nonfarm records, the response rate is an 
indicator of replying to the FRIS data collection 
effort, but does not reflect whether those responding 
met the farm definition or had the items of interest 
for the survey. The response rate for the 2013 Farm 
and Ranch Irrigation Survey is 77.8 percent. This 
compares to 79.4 percent for the 2008 Farm and 
Ranch Irrigation Survey. 
MEASURES OF PRECISION 
The survey sample was one of a large number of 
possible samples of the same size that could have 
been selected using the same sample design. Survey 
estimates derived from the different samples will 
differ from each other. 
The relative standard error is used as an indicator of 
A - 4 Appendix A 
the precision in the survey estimates and is reported 
for major survey items in Table C and Table D. 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 C and 
Table D can be used to construct confidence 
intervals for the major survey 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 were 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 90 percent of the intervals from 
1.65 standard errors below the estimate to 1.65 
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 irrigated acres of a certain 
item is 669,813 and the relative standard error of the 
estimate is 1.6 percent (0.016). Multiplying 669,813 
by 0.016 yields 10,717, the standard error. 
Therefore, a 67-percent confidence interval is 
659,096 to 680,530 (i.e., 669,813 + 10,717). 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 figure obtained from a 
complete enumeration. Similarly, a 90-percent 
confidence interval is 652,130 to 687,496 (i.e., 
669,813 + 1.65x 10,717). 
2012 Census of Agriculture 
USDA, National Agricultural Statistics Service 
