the extent of the undercount and overcount of farms in the 

 census. A description of this evaluation will be in a separate 

 Coverage Evaluation report. This report includes estimates of the 

 net percentage of all farms, acres, and sales missed in the census. 



Classification Problems 



In 1978, the proportion of farms missed due to misclassifica- 

 tion (1.8 percent) was higher for farms with small values of 

 sales. The rate of misclassification was higher on (1) crop farms 

 than livestock farms, (2) farms with a small number of acres 

 than larger farms, or (3) tenant farms than full or part-owner 

 farms. Full owners were misclassified more often than part 

 owners. Farm operators over 55 years of age were misclassi- 

 fied more often than younger operators. 



An evaluation study of classification errors was conducted 

 in the 1982 Census of Agriculture and will be reported in 

 Coverage Evaluation. A sample of mail list respondents was 

 selected, and these addresses reenumerated to determine 

 whether they were a farm or nonfarm. Two types of errors were 

 identified; missed farms and overcounted farms. Missed farms 

 were farm operations included on the mail list but classified in 

 the census as nonfarms. Overcounted operations were non- 

 farm operations classified in the census as farms. 



Mail List Problems 



A major problem with the use of a mail list is the failure to 

 include all farms on the list. In 1978, approximately 10.8 per- 

 cent of all farms were not included on the census mail list. 

 There were several reasons for the farm operator's names not 

 being included on the mail list— the operation may have been 

 started after the mail list source was developed; the operation 

 may not have been included on any source list used to con- 

 struct the mail list; or the operation may have been removed 

 from the list because of incorrectly identifying duplicates or 

 falsely classifying it as a nonfarm prior to mailout. 



A great many of the farms not included on the mail list were 

 small in both acres and sales. The operator in many cases had 

 a full time off-farm job and farmed part time. In 1978, the 

 average size of farms and sales for all farms and farms not on 

 mail list is given below. 



All farms 



Average size 



Farms not on 

 mail list 



Land (acres) . 

 Sales (dollars) 



415 

 $43,618 



68 

 $4,709 



RELIABILITY OF CENSUS ESTIMATES 



The sources of possible sampling and nonsampling errors 

 have been previously discussed. Some sources affected all the 

 data; others affected only certain items or geographic levels. The 

 results of these errors, bias and increased variability, are difficult 

 to measure. 



Census items were classified as either 100-percent or sample 

 items. The 100-percent items were those asked of all farm 

 operators. These included land in farms, harvested cropland, 

 livestock inventory and sales, and crop acreages and quantities 

 (sections 1 to 21 of the census report form). Variability in the 



100-percent items is due to the variation associated with non- 

 response imputation and response error. Estimation of this 

 variation results in a standard error of an estimate originating 

 in the selection of the sample of small nonrespondents at the 

 State level. Sample items were items asked of approximately 



1 in 4 farm operators and include value of land and building, 

 value of farm machinery, energy expenses, and selected farm 

 production expenses, such as hired farm labor and interest 

 expense (sections 22 to 28 of the census report form). Varia- 

 bility in estimates of sample items is the effect of the sample 

 selection and estimation procedure and all the factors affecting 

 the variability of 100-percent items. 



In the 1982 Census of Agriculture, the sample used is one of 

 a large number of all possible samples of the same size that 

 could have been selected using the same sample design. Esti- 

 mates derived from the different samples would differ from 

 each other. The difference between a sample estimate and the 

 average of all possible samples is called the sampling deviation. 

 The standard or sampling error of a survey estimate is a measure 

 of the variation among the estimates from all possible samples, 

 and thus 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 error of estimate 

 (percent) is defined as the standard error of the estimate divided 

 by the value being estimated. 



As calculated for this report, the standard error of the esti- 

 mate (percent) partially measures the effect of certain non- 

 sampling errors but does not measure any systematic biases 

 in the data. Bias is the difference, averaged over all possible 

 samples, between the estimate and the desired value. The 

 accuracy of a survey result depends on both the sampling and 

 nonsampling errors measured by the relative standard error of 

 the estimate (percent) and the bias and other types of non- 

 sampling error not measured. 



If all possible samples were selected, each of those surveyed 

 under essentially the same conditions, and an estimate and its 

 estimated standard error were calculated from each sample 

 then: 



a. 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. 



b. Approximately 95 percent of the intervals from two 

 standard errors below the estimate to two standard 

 errors above the estimate would include the average 

 value of all possible samples. 



To illustrate the computations involved in the above confi- 

 dence statements as related to average value of land and build- 

 ing estimates, assume that an estimate of a average value of land 

 and buildings published for a particular county is $276,741 and 

 the relative standard error of the estimate (percent) for this 

 estimate, as given in table D, is 2.8 percent, or 0.028. Multi- 

 plying $276,741 by 0.028 yields $7,749. Therefore, a 67- 

 percent confidence interval is $268,992 to $284,490 (i.e., 

 $276,741 plus or minus $7,749). 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 95-percent confidence interval is 

 $261,243 to $292,239 (i.e., $276,741 plus or minus 



2 X $7,749). 



A-10 APPENDIX A 



1982 CENSUS OF AGRICULTURE 



