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APPENDIX 1. Statistical Reliability

Summary Report, 1997 National Resources Inventory, Revised December 2000

Current NRI statistical procedures are a result of decades of collaborative research between NRCS and Iowa State University's Statistical Laboratory. The basic sampling procedures were established in 1977 and 1982, based upon research conducted in the 1970's. Estimation techniques have evolved with each successive survey.

The national sample is a stratified two-stage unequal-probability area sample that can be modified for specific national survey objectives and used as a frame for special studies. Stratification was developed county-by-county, utilizing the grid of sections and townships defined by the Public Land Survey System (PLSS), where possible. A section is a one-mile square segment of land, and a township is a 6-mile square area consisting of 36 sections. Each township was subdivided into three 2-mile by 6-mile strata for sampling purposes. For counties not covered by the PLSS, strata were developed by: utilizing latitude and longitude, utilizing the Universal Transverse Mercator grid system, or superimposing lines analogous to townships and sections over a county highway map.

Two-stage area samples were selected within each stratum. The first stage sample unit, or primary sampling unit (PSU), was an area of land; at the second stage of sampling, one or more sample points were selected within each sample PSU for observation. Most PSU's corresponded to quarter-sections and were half-mile squares; three sample points were selected within most PSU's. Sampling rates varied across strata, typically being between 2% and 6%. There are instances throughout the U.S. where components of the sample design deviate from these standard rules. Nusser and Goebel (1997) and Goebel (1998) provide more details on the specifics of the sampling design, and on historical perspectives.

The national framework sample has consisted of approximately 300,000 PSU's and 800,000 sample points for the 1992 and 1997 National Resources Inventories; almost all of these were also part of the 1982 NRI. Experience has shown that it is necessary to return to specific sample points that were in previous inventories in order to obtain needed data on the dynamics of change in land use and various natural resource parameters.

The statistical estimation procedure is fairly complex, because of the complexity of the data and because several requirements have been established regarding the database. The primary requirements are that the final database contains all of the information that has been gathered, that tabulations can be made easily, and that users of the database do not need to understand the complexities of the estimation procedure. Also, the database must produce estimates that agree with known data.

Most data elements (variables) are collected at the sample points; there are some items collected for the entire PSU. The other major set of inputs into the estimation process comes from a geo-statistical database. These data, called "County Base Data", are used as control totals in the statistical weighting procedures. For the 1997 NRI, the county base data include total surface area, federal land area, and large water areas. Another feature is the use of small-area estimation techniques to construct model-based estimates for urban and built-up acreages. Details of the estimation procedure are given by Fuller (1999).

Interpretation of NRI results requires an understanding of both the inventory procedures and the amount of uncertainty associated with each estimate. The precision of NRI estimates depends upon the number of samples within the region of interest, the distribution of the resource characteristics across the region, the sampling procedure, and the statistical estimation techniques.

Characteristics that are common and spread fairly uniformly over an area can be estimated more precisely than characteristics that are rare or unevenly distributed. The basic objective of the 1982 NRI was to obtain data usable for analysis at the Major Land Resource Area (MLRA) level within the state. The sample was selected so that the standard error was less than 10 percent for any estimate of a resource condition that comprised at least 10 percent of the MLRA land area. Most items could be estimated more precisely. This criterion also holds for estimates derived from the 1997 NRI database. Note that estimates of change between two points in time will be less precise (relatively) because the changes will be occurring on a smaller fraction of the landscape.

Each of the thousands of estimates found in tables 1 through 19 of this report has a different level of precision. This appendix presents estimated margins error for several sets of estimated acreages and erosion rates, in order to provide further perspective into the statistical reliability of the estimates. Note that margins of error are also presented as part of table 19 of this report.

The margin of error is approximately twice the estimated standard error, and can be used to construct a 95 percent confidence interval for the estimate. The lower bound of the interval is obtained by subtracting the margin of error from the estimate; the upper bound is obtained by adding the margin of error to the estimate.

Additional results will be made available through national and state-level Internet sites.

References

Fuller, W. A. (1999). "Estimation Procedures for the United States National Resources Inventory," Proceedings of the Survey Methods Section, SSC Annual Meeting, June 1999 [in publication].

Goebel, J. J. (1998). "The National Resources Inventory and Its Role in U.S. Agriculture," Agricultural Statistics 2000: An International Conference on Agricultural Statistics (T. E. Holland and M. P. R. Van den Broecke, editors), International Statistical Institute, Voorburg, The Netherlands, 181-192.

Nusser, S. M. and J. J. Goebel. (1997). "The National Resources Inventory: A Long-Term Multi-Resource Monitoring Programme," Environmental and Ecological Statistics, 4, 181-204.

Appendix Table 1. Estimated acres of cultivated cropland and developed land (per 1,000 acres), with estimated margins of error in parentheses
State Cultivated cropland, 1997 Change in cultivated cropland, 1992 to 1997 Developed land, 1997 Change in developed land, 1992 to 1997
Alabama 2,614.1 (155.6) -189.8 (64.3) 2,252.3 (139.7) 315.3 (31.6)
Arizona 982.2 (123.7) -34.5 (37.2) 1,491.4 (286.4) 113.8 (35.9)
Arkansas 7,362.4 (257.0) -74.1 (58.0) 1,409.1 (130.7) 168.9 (34.7)
California 6,219.7 (558.8) -337.5 (183.3) 5,456.1 (303.0) 553.4 (76.6)
Colorado 7,567.4 (443.7) -107.6 (128.0) 1,651.7 (149.7) 112.5 (28.2)
Connecticut 81.0 (20.2) -12.9 (13.3) 873.9 (46.6) 39.4 (7.3)
Delaware 478.4 (35.5) -14.7 (9.0) 225.5 (22.7) 23.1 (7.4)
Florida 1,480.3 (184.8) -213.4 (87.2) 5,184.8 (224.8) 825.2 (91.3)
Georgia 4,174.8 (186.8) -539.4 (91.1) 3,957.3 (145.4) 851.9 (58.4)
Hawaii 198.0 (35.7) -30.6 (16.9) 179.7 (35.3) 6.8 (2.9)
Idaho 4,541.3 (254.8) -113.9 (145.0) 754.9 (64.3) 91.9 (21.6)
Illinois 23,563.4 (266.4) 60.6 (95.6) 3,180.9 (125.8) 246.5 (37.8)
Indiana 12,761.4 (214.6) -162.4 (85.1) 2,260.4 (97.0) 195.3 (31.9)
Iowa 24,216.5 (283.8) 239.4 (124.7) 1,702.1 (86.8) 69.1 (17.1)
Kansas 24,793.6 (421.6) -293.2 (123.9) 1,939.9 (97.4) 96.5 (20.0)
Kentucky 3,514.0 (130.5) -109.6 (103.9) 1,737.5 (94.5) 237.1 (24.5)
Louisiana 5,470.1 (172.7) -323.1 (67.0) 1,623.8 (61.5) 133.6 (16.9)
Maine 154.7 (43.5) -5.6 (29.8) 712.0 (76.2) 111.1 (17.8)
Maryland 1,412.8 (70.6) -85.8 (28.4) 1,235.7 (52.7) 177.6 (19.0)
Massachusetts 64.7 (20.4) -11.7 (14.5) 1,479.2 (79.2) 211.8 (19.2)
Michigan 6,558.8 (200.9) -558.1 (109.4) 3,545.5 (134.1) 364.1 (36.8)
Minnesota 19,731.2 395.3) 111.8 (173.9) 2,185.5 (112.9) 231.8 (39.8)
Mississippi 4,931.5 (161.5) -550.2 (79.4) 1,474.0 (101.5) 206.4 (26.5)
Missouri 10,517.2 (236.0) -477.8 (114.5) 2,517.4 (115.1) 224.2 (25.9)
Montana 12,526.7 (789.5) 44.4 (248.1) 1,032.3 (107.8) 76.3 (20.8)
Nebraska 17,983.5 (357.3) 173.1 (127.8) 1,205.9 (90.7) 55.1 (12.7)
Nevada 121.2 (75.5) -89.9 (48.6) 381.4 (65.7) 26.7 (9.6)
New Hampshire 20.7 (10.4) 0.0 (4.5) 588.6 (47.6) 62.6 (9.4)
New Jersey 426.7 (48.4) -60.9 (21.0) 1,778.2 (60.8) 213.6 (19.2)
New Mexico 1,388.1 (125.8) -72.9 (59.4) 1,152.7 (114.7) 217.2 (74.5)
New York 2,751.6 (146.2) -123.7 (97.2) 3,183.6 (117.6) 317.6 (27.2)
North Carolina 5,065.5 (206.2) -483.6 (85.5) 3,856.4 (178.2) 506.6 (60.6)
North Dakota 22,820.7 (378.7) -36.0 (142.1) 991.8 (72.1) 32.8 (10.6)
Ohio 10,254.6 (193.3) -598.6 (103.5) 3,611.3 (136.0) 364.8 (34.3)
Oklahoma 9,345.4 (288.7) -289.9 (107.4) 1,926.3 (110.2) 176.7 (31.4)
Oregon 2,676.8 (178.6) -104.4 (55.7) 1,222.3 (112.7) 103.9 (22.7)
Pennsylvania 3,629.1 (156.4) -104.4 (100.4) 3,983.2 (126.8) 545.1 (33.7)
Rhode Island 4.6 (3.1) -2.6 (2.4) 200.6 (16.3) 6.6 (2.0)
South Carolina 2,319.3 (122.5) -436.2 (56.4) 2,097.3 (104.3) 362.0 (38.6)
South Dakota 14,340.0 (345.4) -64.6 (149.7) 959.7 (89.2) 57.8 (20.8)
Tennessee 3,261.7 (132.5) -380.6 (86.4) 2,370.6 (108.2) 401.9 (37.0)
Texas 26,330.0 (591.1) -1,225.3 (250.1) 8,567.0 (287.3) 893.5 (78.2)
Utah 705.3 (147.0) -195.4 (159.9) 661.6 (74.7) 81.3 (24.3)
Vermont 138.7 (25.3) -6.7 (20.6) 317.5 (29.2) 11.5 (3.9)
Virginia 1,636.6 (112.3) -169.9 (54.7) 2,625.8 (102.3) 343.5 (29.8)
Washington 5,577.1 (363.0) -182.8 (119.6) 2,065.0 (174.4) 240.8 (46.6)
West Virginia 166.1 (37.0) -48.3 (19.2) 873.6 (65.9) 176.8 (21.6)
Wisconsin 8,752.0 (241.3) -57.7 (153.9) 2,417.9 (127.4) 188.2 (26.7)
Wyoming 978.0 (181.3) 3.0 (82.3) 643.7 (98.0) 34.4 (15.1)
Caribbean 174.2 (22.7) -108.5 (21.2) 506.8 (29.6) 112.4 (10.2)
Total 326,783.7 (1,838.3) -8,456.5 (741.1) 98,251.7 (884.4) 11,217.0 (247.9)


Appendix Table 2. Estimated average annual sheet and rill erosion for 1997 cultivated cropland, with estimated margins of error in parentheses (in tons/acre/year)
State Erosion rate Margin of error
Alabama 6.7 (0.32)
Arizona 0.7 (0.07)
Arkansas 3.5 (0.09)
California 0.7 (0.17)
Colorado 1.7 (0.12)
Connecticut 5.6 (1.53)
Delaware 2.0 (0.19)
Florida 1.8 (0.28)
Georgia 5.9 (0.30)
Hawaii 2.5 (0.47)
Idaho 3.3 (0.31)
Illinois 4.1 (0.10)
Indiana 3.0 (0.10)
Iowa 4.9 (0.13)
Kansas 2.2 (0.04)
Kentucky 4.4 (0.23)
Louisiana 3.3 (0.09)
Maine 3.9 (0.93)
Maryland 4.4 (0.41)
Massachusetts 4.5 (1.61)
Michigan 2.0 (0.09)
Minnesota 2.1 (0.07)
Mississippi 5.3 (0.23)
Missouri 5.6 (0.23)
Montana 1.9 (0.13)
Nebraska 2.9 (0.10)
Nevada 0.2 (0.05)
New Hampshire 3.5 (2.07)
New Jersey 5.6 (0.63)
New Mexico 0.9 (0.08)
New York 3.8 (0.26)
North Carolina 5.0 (0.37)
North Dakota 1.4 (0.04)
Ohio 2.6 (0.10)
Oklahoma 2.8 (0.10)
Oregon 3.0 (0.33)
Pennsylvania 5.1 (0.26)
Rhode Island 3.5 (0.99)
South Carolina 3.2 (0.19)
South Dakota 2.0 (0.07)
Tennessee 7.7 (0.41)
Texas 2.6 (0.05)
Utah 1.6 (0.75)
Vermont 3.1 (0.67)
Virginia 5.9 (0.42)
Washington 4.7 (0.27)
West Virginia 4.3 (1.19)
Wisconsin 3.7 (0.19)
Wyoming 1.1 (0.17)
Caribbean 12.2 (2.71)
National average 3.1 (0.03)



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