Estimating livestock losses

CHARLES DRAIN, Agricultural Statistician, U.S.D.A. National Agricultural Statistics Service, Texas

Agricultural Statistics Service, P.O. Box 70, Austin, TX 78767-0070

Abstract: Most information published by the Texas Agricultural Statistics Service (TASS) is based on data gathered through a system of Sample Surveys. TASS regularly surveys sampled farms and ranches and agricultural businesses in order to make statistical inference (estimates) for a total population. The alternative to using a sample survey would be to make a complete enumeration or count of the entire population. Both cost and timely results favor the survey approach. This discussion is an attempt to explain the concepts and sampling methods TASS employs in conducting basic surveys, for both inventory and death loss data for cattle, sheep and goats. The discussion will include how estimates were developed for sheep and goat losses to predators and other causes during 1994.

Sampling frame
Every sample survey requires the availability of a sampling frame. The population to be sampled (for our discussion, cattle, sheep and goat operations in Texas) must be divided into sampling units. The sampling frame defines the population and identifies the operations that are available to be sampled. Sampling units can be names of people representing farm or ranch operations, or units of land as delineated on photographs or maps. The basic requirements of an effective sampling frame are that its sample units, when aggregated, contain the entire population and that individual sample units do not overlap.

TASS surveys use 2 kinds of frames, the “Area Frame” and the “List Frame.” The concept of area frame sampling is simple. The land area to be surveyed (in this case the state of Texas) is divided into small blocks called segments, with unique and identifiable boundaries that can be delineated on aerial photographs or maps. No segment has more than one chance of being selected. The sample is a random selection of segments.

The area frame provides a sampling vehicle for an unlimited variety of surveys. The survey population can be composed of reporting units that are farm households, farm headquarters, animals, plants, grain storage facilities, or any other identifiable units that can be associated with segments of land. The primary advantage of area frame sampling is that it provides a complete frame; that is every acre of land in the state has a known chance to be selected, so all items being surveyed have a chance of being selected by their association with a unique segment. An area frame does not grow out of date in terms of coverage of the population. With the area frame, extremely large samples are required to provide estimates for commodities that (a) appear in less than 20% of the segments, (b) are produced on less than 20% of the farms and ranches, or © if the farms and ranches vary widely in size.

The list frame is a list of farm or ranch operators or agribusinesses. The list frame contains names and addresses, along with control data that identify the relative size and type of the items of interest. The list frame has several advantages over the area frame. It permits the use of data collection by mail and telephone. It also allows the use of more efficient sampling methods, especially for items produced on a small percentage of farms and ranches or where there is extreme variability in size of operations, as for livestock. If the list frame of farm or ranch operators contains information on relative size, the extremely large operations can be selected with high probability, or certainty to minimize their impact on the sampling variability.

A basic disadvantage of a list sampling frame is that it is nearly impossible to maintain a complete list that covers the entire population of interest, and has current classification data. In addition, maintaining a complete list frame with current names, addresses and control data for sampling purposes is very costly.

Multiple frame sampling is a survey technique that uses a combination of list and area frames to gain the advantages of both. The list frame is extremely efficient for large operations and operations that produce rare items. The area frame ensures complete coverage and can be used as an independent estimator and also to estimate incompleteness of the list frame.

Sample selection
A typical multiframe sample selection procedure for a commodity requires that a “frame of interest” be established for that commodity within the overall list frame. For example, a cattle frame is established by identifying names with control data indicating the presence of cattle, or a sheep frame is established by identifying names with control data indicating the presence of sheep. Names that do not have cattle control data are not members of the cattle frame.

The same is true for the sheep frame. The classification process assigns sample units to size groups (strata) based on the relative size of previously-reported control data. For example, all extremely large units are assigned to a different stratum than extremely small units. An optimum allocation procedure distributes the list sample to the various strata. This means that strata containing operations with large numbers of cattle may be sampled much more heavily than those having small herds. The area frame segments selected are used for a measure of incompleteness.

For the January 1, 1995 cattle, sheep and goat survey, a random sample of 4,842 Texas cattle, sheep and goat producers were selected from the list frame and 5 19 tracts of land from the area frame. Survey procedures ensured that all cattle, sheep and goat producers, regardless of size, had a chance to be included in the survey. The sample was selected to provide sufficient data to estimate the items of interest at the state level only. Large operations were sampled more heavily than small operations (Table 1).

Table 1. Texas sample allocation; 1 Jan 1995 cattle, sheep and goat survey.
Survey Strata Strata Boundaries Population SampleSize Interval TotalReps SampleReps Units perRep
2 Cattle 1-49, Dairy 1-49 39,066 280 139.521 12 8 35
3 Cattle 50-99 14,348 216 66.425 12 8 27
4 Cattle 100-499 11,398 688 16.566 12 8 86
6 Dairy 50-199 1,125 104 10.817 12 8 13
7 Goats 1-499 2,901 160 18.131 20 16 10
13 Goats 500-2,499 272 128 2.125 20 16 8
15 Sheep 1-499 5,520 1,088 5.073 20 16 68
18 Cattle 500-2,999 2,411 560 43.305 12 8 70
19 Cattle on Feed 100-999 187 40 4.675 12 8 5
20 Sheep 500-2,499 814 640 1.271 20 16 40
21 Cattle 3,000-9,999 156 156 1.000 8 8 19
22 Dairy 200-499 451 64 7.046 12 8 8
30 Dairy 500-999 91 91 1.000 8 8 11
32 Goats 2,500-9,999 169 169 1.000 16 16 11
33 Sheep 2,500-4,999 135 135 1.000 16 16 9
34 Sheep on Feed 500-1,999 23 23 1.000 8 8 3
35 Cattle 10,000 22 22 1.000 1 1 22
36 Cattle on Feed 1,000+ 137 137 1.000 1 1 137
37 Dairy 1,000 41 41 1.000 1 1 41
38 Sheep 5,000+ or Goats 10,000+ 80 80 1.000 1 1 80
39 Sheep on Feed 2,000+ 20 20 1.000 1 1 20
Total List 79,367 4,842
Area Sample 519
Total Sample 5,361

The survey was conducted during December 30, 1994 -January 16, 1995 by mail, telephone, and personal interview. Livestock operators were asked to report inventory data as well as total death losses for cattle and calves, and death losses by cause for sheep, lambs and goats for the 1994 calendar year.

Estimation methods and procedures
The computations and procedures for translating survey data into estimates involve technical considerations. Usually more than one method is available, but the choices are largely dictated by survey design. There are distinct differences between the way estimates are derived from probability and nonprobability surveys.

Probability surveys. Probability surveys are de-signed on the premise that every unit in the population has a known probability of being selected. The probabilities do not have to be equal, but they must be known and used in the selection process.

Estimates can be made from probability surveys without depending on prior survey information or benchmark data. Because probabilities of selection associated with the sample units are known, data collected from them can be used to obtain unbiased estimates of current agricultural activities such as sheep and goat losses to predators. Also sampling errors can be computed for probability surveys, providing the statistician with a tool for evaluating the reliability of the estimates.

The factors involved in evaluating survey reliability are the sampling frame, survey design, and sample size. Each is important in maintaining sampling errors at acceptable levels, although constraints on sample size are frequently imposed by budget limitations. National Agricultural Statistics Service (NASS) minimizes potential nonsampling errors through survey training programs, questionnaire design and testing, simplified and uniform survey procedures, and comprehensive editing systems. The estimation model used in preparing estimates of cattle, sheep and goat death losses from the January 1, 1995 multiple frame livestock survey (area and list frame) is:

X– Xa + XL


Xa = the expanded total for the portion of the population included only in the area frame;

XL = the expanded total for the portion of the population included only in the list frame.

Analysis of data
Outlier reports can influence survey expansions considerably. Outlier reports are sampled operations that report either very small or very large answers that lie apart from the rest of the reports. In practice, only the extremely large reports are of concern. These reports present problems if not detected. Detection is primarily limited to identifying operations with answers that vary a great deal from control data.

Outliers (both list and area frame) are first identified in the machine edit. List frame outliers are identified again in a special analysis summary which excludes these reports. The summary is used to measure the outliers’ impact on the estimate. The statistician evaluates the sampling errors associated with each estimate, with and without outliers, when establishing a range for the final estimate.

Obtaining estimates of death losses
Once the survey has been conducted, data edited, summarized, and analyzed, the estimates are prepared for the items of interest, i.e., death losses by all causes for various kinds of livestock. Only total death losses were estimated for cattle and calves from the January 1, 1995 survey. The survey questionnaire was not designed to obtain losses of cattle and calves by cause.

Total sheep (1-year old and older) losses from all causes were estimated first using the multiple frame direct expansion and ratio to all sheep 1-year old and older inventory. The survey ratio of losses by all predators was then applied to total sheep losses to arrive at an estimate for losses by all predators. The survey ratio of sheep losses by type of predator was applied to the estimate of losses by all predators to arrive at estimates by type of predator. Estimates of nonpredatory losses were prepared using the same procedure (Table 2)

Value of Losses From Predators

Table 2: Texas Losses of Sheep and Lambs From Predators and Other Causes, 1990 and 1994
Causes Sheep Lambs
Before marking, docking or branding After marking, docking or branding
1990 1994 1990 1994 1990 1994
Number % of Total Number % of Total Number % of Total Number % of Total Number % of Total Number % of Total
Head Percent Head Percent Head Percent Head Percent Head Percent Head Percent
Total losses from predators 27,000 29.3 16,400 35.7 NA 57,000 63.1 80,000 66.7 31,000 58.4
Coyotes 16,000 59.2 7,400 45.1 NA 22,750 39.9 40,000 50 19,700 63.5
Dogs 4,000 14.8 2,300 14 NA 1,225 2.2 4,000 5 1,100 3.5
Mountain lions 1,500 5.5 3,300 20 NA 1,975 3.5 1,000 1.2 1,600 5.2
Bears 0 0 NA 75 0.1 0 100 0.3
Foxes 500 1.9 500 3.0 NA 4,175 7.3 6,000 7.5 2,000 6.5
Eagles 500 1.9 200 1.2 NA 13,525 23.7 8,000 10 3,200 10.3
Bobcats 500 1.9 1,400 8.5 NA 9,775 17.2 8,000 10 2,300 7.4
All other animals 1/ 4,000 14.8 1,300 7.9 NA 3,500 6.1 13,000 16.3 1,000 3.2
Losses from other causes 65,000 70.7 29,600 64.3 NA 21,000 26.9 40,000 33.3 22,125 44.6
Digestive problems 2/ NA 4,575 15.5 NA 1,375 6.6 NA 2,700 12.2
Respiratory problems 3/ NA 325 1.1 NA 1,800 8.6 NA 800 3.6
Metabolic problems 4/ NA 375 1.3 NA 400 1.9 NA 200 0.9
Weather related causes 5/ NA 1,200 4.1 NA 4,250 20.2 NA 1,600 7.2
Theft NA 500 1.7 NA 0 NA 700 3.2
Poisoning 6/ NA 925 3.1 NA 125 0.6 NA 400 1.8
Lambing problems 7/ NA 1,475 5.0 NA NA 3,125 14.1
Other causes 8/ NA 9,700 32.8 NA 2,000 9.5 NA 3,300 14.9
Unknown causes NA 10,525 35.6 NA 7,925 37.7 NA 9,300 42.1
Losses from all causes 92,000 100 46,000 100 NA 78,000 100 120,000 100 53,125 100
Value per head 9/ 59.00 55.00 35.00 39.00
Value 1.6 mil 0.9 mil 2.8 mil 1.2 mil

1/ Includes wolves, ravens, crows, pigs, etc.

2/ Incudes bloat, scours, parasites, enterotoxemia, acidosis, etc.

3/ Includes pneumonia, shipping fever, etc.

4/ Include milk fever, twin lambs disease, pregnancy toxemia, etc.

5/ Includes chilling, drowning, lighting.

6/ Includes nitrate poisoning, noxious feed, noxious weeds, etc.

7/ Includes all lambs before and after marking, docking and branding.

8/ Include lameness, old age, on back, diseases not reported earlier, etc.

9/ Sheep value per head based on a two-year straight average of the value of ewes one year old and older from the 1 Jan 94, and 1 Jan 95, NASS surveys. Lamb value/head based on the USDA annual average price received by farmers and ranchers for 60-pound lambs.

Total estimates of lamb (under 1 year old) losses from all causes before and after marking, docking, or branding were prepared utilizing the multiple frame direct expansion and ratio to the 1994 lamb crop. The survey ratio of predator losses to all losses of lambs before marking, docking, or branding, and after marking, docking, or branding was applied to their respective estimate of losses from all causes to arrive at estimates of losses from predators and nonpredators. The survey ratio of losses by species of predator was applied to the estimate for each of the parts to arrive at estimates by predator species, and by cause for nonpredatory losses (Table 2).

Estimates of goat losses were not made at the state level by predator species. However estimates were prepared at the state level for all losses to predators, losses to other causes and total losses (Table 4). Combined estimates of losses by predator species were prepared for 5 states (Arizona, Michigan, New Mexico, Oklahoma and Texas) by our headquarters office in Washington, D.C. (Table 3).

Table 3: Losses of All Goats by Specific Predators and Total Value, Five States, 199O and 19941
Year Coyotes Dogs Mountain lions Bears Foxes Eagles Bobcats All otherpredators Totalpredators Value 2/
— Head — Dollars
1990 64,900 9,700 2,900 0 4,100 16,300 20,600 10,900 129,400 5,661,250
1994 41,000 15,000 5,000 1,000 7,000 25,000 21,000 25,000 140,000 5,481,000

1 Includes Arizona, Michigan, New Mexico, Oklahoma and Texas. 2/ Goat value is based on a straight average of the value per head of all goats from 1990-91 and 1994-95 NASS surveys.

Table 4. Texas losses of all goats by cause, 1990 and 1994.

Year Lost to Predators Other causes1 Total losses
1990 1994 No. head 121,000 45,000 166,000 137,000 73,000 210,000

1Includes diseases, weather, theft and unknown.

Literature Cited

NASS Staff Report. 1995. Sheep and Lambs Death Losses 1994.

Scope and Methods of the Statistical Reporting

Service of the United States Department of Agriculture. Misc. Publ. No. 1308.