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 State 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 

 2x $7,749). 



Table C presents U.S. 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 

 State estimates may vary substantially from each other and 

 will usually be larger than the U.S. estimate. 



Table D presents the estimate of reliability at the State 

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

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

 item differs among States. Reasons for this are: (1) differences 

 among States 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 nonresponse, (5) the 

 general agricultural characteristics, and (6) the specific charac- 

 teristic being measured. 



1982 CENSUS OF AGRICULTURE 



APPENDIX A A-13 



