APPENDIX C. 

 Statistical l\/lethodology 



Page 



MAIL LIST MODEL C-1 



CENSUS SAMPLE DESIGN C-1 



CENSUS ESTIMATION C-1 



CENSUS SAMPLING ERROR C-3 



CENSUS NONSAMPLING ERROR C-5 



EDITING DATA AND IMPUTATION FOR ITEM 



NONRESPONSE C-6 



TABLES: 



A. PERCENT OF STATE TOTALS CONTRIBUTED BY 

 WHOLE FARM NONRESPONSE ESTIMATION: 1987 



B. RELIABILITY ESTIMATES FOR NUMBER OF FARMS IN 

 A COUNTY REPORTING A COMPLETE COUNT ITEM: 

 1987 



C. RELIABILITY ESTIMATES FOR NUMBER OF FARMS IN 

 A COUNTY REPORTING A SAMPLE ITEM: 1987 



D. RELIABILITY ESTIMATES OF STATE TOTALS: 1987 



E. RELIABILITY ESTIMATES OF PERCENT CHANGE IN 

 STATE TOTALS: 1982 TO 1987 



F. RELIABILITY ESTIMATES OF COUNTY TOTALS: 1987 



G. STATE COVERAGE EVALUATION ESTIMATES OF 

 FARMS NOT ON THE MAIL LIST: 1987 



MAIL LIST MODEL 



A statistical discriminant model was developed to pre- 

 dict the probability that a mail list addressee operated a 

 farm. The model was used to identify the 4.1 million 

 records from the preliminary census mail list of 6.0 million 

 records that would receive a census of agriculture report 

 form. Records from the 1982 census mail list were used to 

 build the model. Record characteristics such as the source 

 of the mail list record (see appendix A for a description of 

 record sources), number of source lists on which the 

 record appeared, expected value of agricultural sales, and 

 geographic location were used to separate mail list records 

 into model groups. The proportion of 1982 census farm 

 records in each group was calculated to provide an 

 estimate of the probability that an addressee in the group 

 operated a farm. 



Using these same group definitions, the 1987 census 

 mail list records were separated into groups, each with an 

 associated estimate of farm probability from the model. 

 The 4.1 million mail list records in groups with the largest 

 estimate of farm probability were selected to receive the 

 census report form. A large percentage of the 1 .9 million 

 records that were dropped from the 6.0 million preliminary 

 census mail list were nonfarm records from the previous 

 census. This procedure was used to obtain a more com- 

 plete census enumeration without excessive respondent 

 burden and data collection cost. 



CENSUS SAMPLE DESIGN 



Each of the 4.1 million name and address records on 

 the census mail list was designated to receive one of three 

 different types of census report forms. The three forms 

 were the nonsample census form (a four-page form), the 

 sample form (a six-page form), and the short form (a 

 two-page form). Sections 1 through 22 of the sample form 

 were identical to sections on the nonsample census form. 

 However, the sample form contained additional sections 

 on farm production expenditures, usage of fertilizers and 

 insecticides, value of machinery and equipment, value of 

 land and buildings, and farm-related income. The short 

 form contained abbreviated versions of the sections on the 

 nonsample census form. These three different forms were 

 used to reduce the response burden of the census, while 

 providing quality information on a large number of data 

 items at the county level. 



The sample form was mailed to all mail list records in 

 Alaska and Hawaii and to a sample of records in other 

 States identified when the mail list was constructed. Addresses 

 were selected into the sample with certainty if they were 

 expected to have large total values of agricultural products 

 sold or large acreage, if they were firms with two or more 

 farms, or if they had other special characteristics. When a 

 nonsample large farm was identified during processing, a 

 supplemental form that contained the additional data 

 inquiries was mailed. All farms in counties with less than 

 100 farms in 1982 were included in the sample with 

 certainty; counties containing 100 to 199 farms in 1982 

 were systematically sampled at a rate of 1 in 2; and 

 counties containing 200 or more farms in 1982 were 

 systematically sampled at a rate of 1 in 6. This differential 

 sample scheme was used to provide reliable data for 

 sections 23 through 28 of the report form for all counties. 



To determine which mail list records would receive the 

 short form, all mail list records not designated for the 

 sample were sorted into model groups according to farm 

 probability as specified by the mail list model. The 906,000 

 mail list records in the model groups with the lowest 

 probability of being farms and with an expected total value 

 of agricultural product sales less than $20,000 were des- 

 ignated to receive the short form. The remaining mail list 

 records were selected to receive the nonsample census 

 form. 



CENSUS ESTIMATION 



The 1987 Census of Agriculture used two types of 

 statistical estimation procedures. These estimation 



1987 CENSUS OF AGRICULTURE 



APPENDIX C C-1 



