Feral Swine Sampling Design

Feral Pigs Sampling Frame and Sampling Design
NASS’s list frame is a roster of known farmers and ranchers and includes a profile of each
operation indicating the size of the operation and the commodities they produce. NASS
continually works to keep the list frame as complete as possible, especially for the larger
producers, by obtaining records for new or omitted operations from other USDA lists, producer
association lists, and many other sources. The list frame is an efficient method to select samples
and data can be collected using less expensive methods such as mail, telephone, or internet.
However, a list frame does not provide complete coverage of all farms since farming
arrangements are constantly changing. There will always be some farms that are out of business.
The Feral Pigs Sampling Frame (population) consist of farm operators in Alabama, Arkansas,
California, Florida, Georgia, Louisiana, Mississippi, Missouri, North Carolina, South Carolina,
and Texas with positive control data for corn, soybeans, wheat, rice or peanuts; or sorghum only
for Texas. The Multivariate Probability Proportional to Size (MPPS) sampling design1 will be
used for the Feral Pigs Survey. The MPPS design takes advantage of the efficiencies of a
Probability Proportional to Size (PPS) design, while adding the dimension of utilizing multiple
variables from partially overlapping frames in the sample allocation. The target sample size for
each commodity was derived using a simple random sample size formula that accounts for
power.
The probability of selection for an MPPS design is:
0.75
𝑥𝑖𝑗1

0.75
𝑥𝑖𝑗𝐻

𝜋𝑖𝑗 =min{ 1,max(𝑛𝑗1 × 𝑁
,…,𝑛𝑗𝐻 × 𝑁
)}
ℎ 𝑥 0.75
ℎ 𝑥 0.75
∑𝑖=1
∑
𝑖𝑗1
𝑖=1 𝑖𝑗𝐻

Where:
𝜋ij is the maximum probability of selection for farm operator i in state j.
i is the farm operator.
h is the target commodity (h=1,…,H).
j is the state.
Nh is the number of farm operators in the sampling frame for target commodity h, and
xijh is the value of target commodity h for the ith farm operator in state j.
Bailey, Jeff and Kott, Phillip (1997),”An Application of Multipurpose List Frame Sampling For MultiPurpose Surveys, Proceedings of the Section on Survey Research Methods, American Statistical
Association, pp. 496-500.
1

The target sample size for each targeted commodity is:

1

𝑛𝑗ℎ =

2

(

1
𝑍1−𝛽
1+
𝑍1−𝛼

2

(

((𝐶𝑉𝑗ℎ )𝑇𝑗ℎ )
100(𝑁𝑗ℎ 𝑠𝑗ℎ )

) +

1
𝑁𝑗ℎ

2)

Where:
njh is the sample size for target commodity h in state j,
Njh is the population for target commodity h in state j,
Sjh is the standard deviation for target commodity h in state j,
α: Type I error.
β: Type II error
CVjh is the coefficient of variation for target commodity h in state j, and
Tjh is the total for target commodity h in state j.

A CV of 15, alpha of .05 and beta of 0.20 were used derive sample sizes for all state commodity
combinations. The resulting sample sizes were used to derive the maximum probability of
selection, π. A sample is chosen by sorting the sampling frame by the sum of targeted crop
acres, generating a uniform random number (RN), calculating the cumulative probability for unit
i as Cumulativei = Cumulativei+1 + 𝜋i, and selecting unit i if
Cumulativei+1File Typeapplication/pdfAuthorQuan, Peter - NASSFile Modified2016-09-15File Created2016-09-15