count, expanded for nonresponse estimation, for the cell 

 containing the sample farm. This weight was approxi- 

 mately equal to the inverse of the probability of selecting a 

 farm for the census sample. 



The second step in the estimation procedure was to 

 combine, if necessary, the cells of the array (prior to the 

 repeated ratio estimation) to increase the reliability of the 

 ratio estimation procedure. Any cell within the array that 

 either contained less than 1 sample farms or had a ratio 

 of total farms to sample farms that was more than 2 times 

 the mail sample rate was collapsed with another cell (in the 

 same variable) according to a specified collapsing pattern. 

 New total farm counts and sample farm counts were 

 computed for each of the collapsed cells (final post strata) 

 and were used in the ratio estimation procedure to calcu- 

 late final sample weights. 



In the third step in the ratio estimation procedure, 

 complete counts for the three variables (TVP, SIC, acre- 

 age) were used to compute the marginals of the array 

 defined by the final post strata. Factors were then applied 

 to expanded sample totals in each cell of the array to 

 obtain agreement with the row marginal (TVP) complete 

 counts. The sample totals then had factors applied to 

 obtain agreement with the column marginal (SIC) complete 

 counts. Lastly, the sample totals had factors applied to 

 obtain agreement with the depth marginal (acreage) com- 

 plete counts. This procedure that requires the row totals, 

 then the column totals, and then the depth totals to agree 

 with the complete counts for the rows, columns, and 

 depths, respectively, is continued iteratively until the pro- 

 cess converges (the marginal totals agree with the com- 

 plete count totals). 



The ratio of the adjusted total farm count to the sample 

 farm count obtained from the second iteration of the 

 estimation procedure was the noninteger final post stratum 

 sample weight assigned to the sample farm records in that 

 post stratum. The noninteger sample weight, the product 

 of the noninteger final post stratum sample weight and the 

 nonresponse weight, was randomly rounded to an integer 

 weight for tabulation. If, for example, the final weight for the 

 farms in a particular group was 7.2, then one-fifth of the 

 sample farms in this group were randomly assigned a 

 weight of 8 and the remaining four-fifths received a weight 

 of 7. 



CENSUS SAMPLING ERROR 



Sampling error in the census data results from the 

 nonresponse sample and the census sample data collec- 

 tion. Census items were classified as either complete 

 count or sample data items. The complete count items 

 were asked of all farm operators. The complete count data 

 items included land in farms, harvested cropland, livestock 

 inventory and sales, crop acreages, quantities harvested 

 and crop sales, land use, irrigation, government loans and 

 payments, conservation acreage, type of organization, and 

 operator characteristics (sections 1 through 22 of the 



census report form). Variability in the complete count data 

 items is considerably smaller than in the sample items as 

 the variation is due only to the nonresponse sample 

 estimation procedure. The sample items were asked of 

 approximately 25 percent of the total census farm opera- 

 tors. The sample data items included farm production 

 expenditures, fertilizer and chemical usage, farm machin- 

 ery and equipment, value of land and buildings, and 

 farm-related income (sections 23 through 28 of the census 

 report form). Variability in the estimates of sample items is 

 due both to the census sample selection and estimation 

 procedure and the nonresponse sample estimation proce- 

 dure. 



The sample for the 1 987 Census of Agriculture is one of 

 a large number of possible samples of the same size that 

 could have been selected using the same sample design. 

 Estimates derived from the different samples would differ 

 from each other. The difference between a sample esti- 

 mate and the average of all possible sample estimates is 

 called the sampling deviation. The standard error or sam- 

 pling 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 aver- 

 age result of all possible samples. The percent relative 

 standard error of estimate is defined as the standard error 

 of the estimate divided by the value being estimated 

 multiplied by 100. 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 aver- 

 age value of all possible samples. 



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 inten/al 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). 



Table C presents the relative standard error of selected 

 U.S. data items for all farms and for all farms with sales of 

 $10,000 or more. The percent relative standard error of the 



1987 CENSUS OF AGRICULTURE 



APPENDIX C C-3 



