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., 



■ Table B. Estimates of Reliability of Number of Farms in 

 a County Reporting a 100-Percent Item: 1982 



Farms 



Number of farms reporting: 

 25 



50 



75. . . 

 100. . 

 150. . 

 200. . 

 300. . 

 500. . 

 750. . 

 1,000 

 1,500 

 2,000 



Estimated 



relative standard 



error of estimate 



(percent) 



1.5 



1.4 

 1.4 



(NAI 

 (NA) 



$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). 



Tables B and C present the reliability of the estimates of 

 the number of farms reporting a 100-percent or sample item 

 at the county level. Both tables contain relative standard 

 errors of estimate (percent) which were weighted over all 

 counties in the State to arrive at an estimated value. In county 

 table 12, for example, in column 3 the number of farms 

 reporting hog and pig inventory is 78. From table B, an 

 approximate relative standard error of estimate (percent) for the 

 number of farms reporting hogs and pigs would be 1.4. 



Table D presents State estimates of major items for all farms 

 and for all farms with sales of $10,000 or more and measures 

 of their reliability. The estimate and the relative standard error 

 of the estimate (percent) is given for selected 100-percent and 

 sample items. The relative standard error of the estimate (percent) 

 measures the variation associated with the small whole farm 

 nonresponse adjustment. It does not measure census variability 

 associated with complete nonresponse among large farms, partial 

 or item nonresponse among all farms, response error or content 

 error. The relative standard error of estimate (percent) for 

 sample items measures both nonsampling and sampling error. It 

 measures the variation associated with selecting a sample to 

 estimate sample items as well as variability associated with 

 adjustment for small farm nonresponse. The reliability of 

 county estimates may vary substantially from each other and 

 will usually be larger than the State estimate. 



Table E presents the estimate of reliability at the county 

 level for four major 100-percent items and six sample items. The 

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

 item differs among counties in a State. Reasons for this are: 



(1) differences among counties in the total number of farms, 



(2) the number of large farms included with certainty, (3) the 

 size classifications of farms sampled, (4) the amount of non- 

 response, (5) the general agricultural characteristics, and (6) 

 the specific characteristic being measured. 



Table C. Estimates of Reliability of Number of Farms 

 in a County Reporting a Sample Item: 1982 



Farms 



Number of farms reporting: 



25 



50 



75 



100 



1 50 



200 



300 



500 



750 



1 ,000 



1,500 



2,000 



Estimated 



relative standard 



error of estimate 



(percent) 



76.2 



39.0 



26.3 



19.9 



13.5 



10.2 



6.9 



4.2 



2.8 



2.1 



(NA) 



(NA) 



Note: 100-percent items are items included in sections 1 to 

 ttie report form (appendix C). 



21 of 



Note: Sample items are items included in sections 22 to 28 of the 

 report form (appendix CI. 



1982 CENSUS OF AGRICULTURE 



APPENDIX A A-11 



