10 in municipios sampled at a rate of 1 in 5, the original 

 stratum was collapsed into another stratum. Also col- 

 lapsing of stratum occurred if the stratum contained fewer 

 than 10 sample farms. 



Estimates were prepared for items in sections 21 

 through 25 of the report form by multiplying the data item 

 for each farm in the sample by the sample weight 

 assigned the farm. The weight for a certainty farm was 

 1 . Sample weights for the final strata ranged from 1 to 

 10 because all exact weights (total number of farms 

 divided by the number of sample farms in the stratum) 

 were converted to integers by a simple algorithm. 



NONSAMPLING ERRORS 



Each census or survey is subject to error. In addition 

 to sampling variability, errors arise from nonsample 

 sources such as incorrect or incomplete reporting, 

 processing, and the inability to obtain a report from each 

 eligible reporting unit. For example, an operator may report 

 the number of hogs and pigs sold but may not report the 

 value of the sale. In other cases, the respondent may 

 indicate the presence of an item but not the quantity. The 

 accuracy of a census count is determined by the joint 

 effects of sampling and nonsampling errors. Extensive 

 efforts were made to keep errors introduced during clerical 

 and electronic processing to a minimum level through the 

 use of quality control, verification, and check measures 

 on specific operations. 



CENSUS COVERAGE 



Although a complete and accurate count of farms, land 

 in farms, and farm production is the aim of each census 

 of agriculture, the complex structure of The Com- 

 monwealth of Puerto Rico's agriculture makes this difficult 

 to achieve. Among the complexities are the many places 

 to be included, the variety of arrangements under which 

 farms are operated, the continuing changes in the rela- 

 tionship of operators to the farm operated, the expiration 

 of leases and the initiation or renewal of leases, the 

 problem of obtaining a complete list of agricultural opera- 

 tions, the difficulty of locating and identifying some types 

 of farms, the operator's absence from the farm during the 

 data collection period, and the operator's opinion that part 

 or all of the operation does not qualify and should not be 

 included in the census. These complexities were 

 resolved through the use of field enumeration and quality 

 control procedures to ensure accurate reporting and 

 coverage. 



RELIABILITY OF CENSUS ESTIMATES 



The sources of possible sampling and nonsampling 

 errors have been previously discussed. Some sources 

 affected all the data; others affected only certain items 

 or geographic levels. The results of these errors, bias and 

 increased variability, are difficult to measure. 



Data items were classified as either 1 00-percent or sam- 

 ple items. The 1 00-percent items were those asked of all 



farm operators. These include land in farms, harvested 

 cropland, livestock inventory and sales, and crop acreages 

 and quantities (sections 1 to 20 of the census report 

 form). Variability in the 100-percent items is due to the 

 variation associated with response error. Sample items 

 were items asked of approximately 1 in 5 farm operators 

 and include products used for home consumption; number 

 of cuerdas on which chemicals were used; expenses; 

 number of selected machinery and equipment and the 

 value of farm machinery; and number of hired workers, 

 agregados, and sharecroppers (sections 21 to 25 of the 

 census report form). Variability in estimates of sample 

 items is the effect of the sample selection and estimation 

 procedure. The sample used is one of a large number of 

 all 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 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 (always 

 shown in 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 

 estimate 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 and the bias and 

 other types of nonsampling error not measured. 



The sample estimate and an estimate of its standard 

 error permit the Census Bureau to construct interval 

 estimates with prescribed confidence that the interval 

 include the average result of all possible samples (for a 

 given sampling rate). If all possible samples were selected, 

 and each was surveyed under essentially the same con- 

 ditions, and an estimate and its estimated standard error 

 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 

 confidence statements as related to total value of com- 

 mercial fertilizer purchased estimates, assume that an 

 estimate of total value of commercial fertilizer purchased 

 for a particular municipio is $276,741 and the relative 

 standard error of the estimate for this estimate, as given 

 in table B, is 2.8 percent, or 0.028. Multiplying $276,741 

 by 0.028 yields $7,749. Therefore, a 67-percent con- 

 fidence interval is $268,992 to $284,490 (i.e., $276,741 

 plus or minus $7,749). 



A-6 APPENDIX A 



1982 CENSUS OF AGRICULTURE 



