The computations involved to define the above confi- 

 dence statements are illustrated in the following example. 

 Assume that the estimate of number of farms for the State 

 is 94,382 and the relative standard error of the estimate 

 (percent) is .1 percent (0.001). Multiplying 94,382 by 0.001 

 yields 94, the standard error. Therefore, a 67-percent 

 confidence interval is 94,288 to 94,476 (i.e., 94,382 plus or 

 minus 94). 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 com- 

 plete enumeration. Similarly, a 90 percent confidence 

 interval is 94,227 to 94,538 (i.e., 94,382 plus or minus 1 .65 

 x94). 



Tables B and C provide the reliability estimates of the 

 estimated number of farms in a county reporting complete 

 count and sample items, respectively. Both tables show 

 the percent relative standard errors for selected estimated 

 number of farms in a county reporting an item.These are 

 derived from a regression equation. The parameters of the 

 regression equation were estimated using the estimated 

 number of farms in a county reporting the complete count 

 or sample item as the independent variable and the 

 standard error of that estimate as the dependent variable 

 for all counties in the State. 



Table B. Reliability Estimates for Number of Farms in 

 a County Reporting a Complete Count Item: 

 1987 



Farms 



Number of farms reporting: 



25 



50 



75 - " 



100 



150--- 

 200--- 

 300--- 

 500--- 

 750--- 

 1,000- 

 1,500- 

 2,000 ■ 



Relative standard 



error of estimate 



(percent) 



19.5 



17.5 



14.8 



13.1 



11.1 



9.9 



8.4 



6.8 



(NA) 



(NA) 



(NA) 



(NA) 



Note: Complete count items are items in sections 1 to 22 of the report 

 form. 



To illustrate the use of these tables, assume that the 

 estimate of the number of farms reporting hogs and pigs 

 for a particular county, as given in county table 12, is 89. 

 Since hogs and pigs is a complete count data item, refer to 

 table B and select the estimated relative standard error of 

 the estimate from the row whose value is equal to or just 

 less than the estimated number of farms, 89. For this 

 example, the relative standard error of the estimate comes 

 from the row for 75 farms reporting. For sample data items, 

 follow the same procedure using table C. In counties that 

 had less than 1 00 farms in the 1 982 Census of Agnculture, 

 table C does not apply because the farms in these 



C-4 APPENDIX C 



counties were sampled with certainty (1 in 1), and thus, the 

 reliability estimates for the number of farms in these 

 counties are smaller than for counties that were sampled 

 at lower rates (1 in 2 or 1 in 6). 



Table C. Reliability Estimates for Number of Farms in 

 a County Reporting a Sample Item: 1987 



Farms 



Number of farms reporting: 



25---- • 



50 



75 .-- 



100.-. - 



150-.- 

 200--- 

 300--- 

 500--- 

 750--- 

 1.000- 

 1,500- 

 2,000 - 



Relative standard 



error of estimate 



(percent) 



56.2 

 40.4 

 33.5 

 29.4 

 24.6 

 21.8 

 18.4 

 14.9 

 (NA) 

 (NA) 

 (NA) 

 (NA) 



Note: Sample items are Items in sections 23 to 28 of the report form. 



Table D presents the relative standard error of selected 

 State data items for all farms and for all farms with sales of 

 $1 0,000 or more. The percent relative standard en-or of the 

 estimate for complete count data measures the variation 

 associated with the sample-based adjustment for whole 

 farm nonresponse. The percent relative standard error of 

 the estimate for sample items measures both the sampling 

 error due to the nonresponse sample estimation procedure 

 and the census sample selection and estimation proce- 

 dure. The reliability of State estimates may vary substan- 

 tially from State to State. Generally, State estimates for a 

 given data Item are less reliable than the corresponding 

 U.S. estimate. 



Table E presents the standard error (not relative stand- 

 ard error) for percent change in State totals from 1 982 to 

 1 987. The general purpose of the percent change estimate 

 is to provide a relative measure of the difference in a 

 characteristic between censuses. The relative change for 

 a given characteristic is defined as the ratio of the differ- 

 ence of the 1 987 and the 1 982 estimate for that charac- 

 teristic to the 1982 estimate. This ratio is multiplied by 100 

 to obtain the percent change. The percent standard error 

 of a percent change estimate, then, is the standard error of 

 the ratio multiplied by 100. 



Table F presents the relative standard error for county 

 totals for 10 major complete count items and 7 sample 

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

 for the same item differs among counties in a State. 

 Reasons for this are differences among counties in (1) the 

 total number of farms, (2) the number of large farms 

 included with certainty, (3) the size classifications of the 

 farms sampled, (4) the amount of nonresponse, (5) the 

 general agricultural characteristics, and (6) the specific 

 characteristic being measured. 



1987 CENSUS OF AGRICULTURE 



