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 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). 



Table B provides the reliability estimates of the esti- 

 mated number of farms in a county reporting an item. The 

 table shows 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 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 an 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) 



8.4 

 5.6 

 4.2 

 3.4 

 2.2 

 1.2 



To illustrate the use of this table, 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. 

 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. 



Table C 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 error of the 

 estimate measures the variation associated with the sample- 

 based adjustment for whole farm nonresponse. The reli- 

 ability of State estimates may vary substantially from State 

 to State. Generally, State estimates for a given data item 

 are less reliable than the corresponding U.S. estimate. 



Table D presents the standard error (not relative stand- 

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

 1987. 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 E presents the relative standard error for county 

 totals for 1 7 major items. The relative standard error of the 

 estimate (percent) for the same item differs among coun- 

 ties 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 amount of 

 nonresponse, (4) the general agricultural characteristics, 

 and (5) the specific characteristic being measured. 



CENSUS NONSAMPLING ERROR 



The accuracy of the census counts are affected by the 

 joint effects of the sampling errors described in the previ- 

 ous section and nonsampling errors. Extensive efforts 

 were made to compile a complete and accurate mail list for 

 the census, to design an understandable report form and 

 instructions, and to minimize processing errors through the 

 use of quality control, verification, and check measures on 

 specific operations. Nonsampling errors arise from incom- 

 pleteness of the census mail list, duplication in the mail list, 

 incorrect data reporting, errors in editing of reported data, 

 and errors in imputation for missing data. These specific 

 nonsampling errors are further discussed in this section. 

 Evaluation studies will be conducted to measure the extent 

 of nonsampling errors due to item imputation. 



Respondent and Enumerator Error 



Incorrect or incomplete responses to the mailed census 

 report form or to the questions posed by a telephone 

 enumerator introduce error into the census data. Such 



1987 CENSUS OF AGRICULTURE 



APPENDIX C C-3 



