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Parametric Sequential Sampling Based on Multistage Estimation of the Negative Binomial Parameter k

Published online by Cambridge University Press:  12 June 2017

Gregg A. Johnson ,
David A. Mortensen ,
Linda J. Young  and
Alex R. Martin
Gregg A. Johnson
Affiliation:
Dep. Agron., Univ. Nebraska, Lincoln, NE68583-0915
David A. Mortensen
Affiliation:
Dep. Agron., Univ. Nebraska, Lincoln, NE68583-0915
Linda J. Young
Affiliation:
Dep. Biom., Univ. Nebraska, Lincoln, NE68583-0915
Alex R. Martin
Affiliation:
Dep. Agron., Univ. Nebraska, Lincoln, NE68583-0915
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Abstract

An intensive survey of two farmer-managed corn and soybean fields in eastern Nebraska was conducted to investigate parametric sequential sampling of weed seedling populations using a multistage procedure to estimate k, of the negative binomial distribution. k is a nonspatial aggregation parameter related to the variance at a given mean value. Mean weed seedling density ranged from 0.18 to 3.11 plants 0.38 m−2 (linear meter of crop row) based on 806 sampling locations. The average value of k, derived from 200 multistage estimation procedures, ranged from 0.17 to 0.32. A sequential sampling plan was developed with the goal of estimating the mean with a coefficient of variation (CV) of 10, 20, 30, and 40% of the sample mean. A sampling plan was also constructed to estimate the mean within a specified distance H of the true mean (H(x̄)= 0.10, 0.50 and 1.0 plants 0.38 m−2) with 80, 85, and 90% confidence. Estimating mean weed seedling density within a specified CV of the true mean CV(x̄) using parametric sequential sampling techniques was superior to estimating the mean within a specified distance (H(x̄)) of the true mean when considering the frequency of sampling and probability of error, especially at intermediate k values. At a k: value of 0.32 and 0.25, the difference between the actual CV(x̄) obtained from sampling and the CV(x̄) specified by the sampler was minimal. However, the accuracy of weed seedling density estimates was reduced with decreasing k values below 0.25, especially as the specified CV(x̄) increased.

Keywords

Shattercane, Sorghum bicolor L. ♯ SORVUvelvetleaf, Abutilon theophrasti Medix.) ♯ ABUTHBioeconomic modelssequential estimation
Type
Weed Biology and Ecology
Information
Weed Science , Volume 44 , Issue 3 , September 1996 , pp. 555 - 559
Copyright
Copyright © 1996 by the Weed Science Society of America 

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References

Literature Cited

1. Audsley, E. 1993. Operational research analysis of patch spraying. Crop Prot. 12: 111–118.CrossRefGoogle Scholar
2. Berti, A., Zanin, G., Baldoni, G., Grignani, C., Mazzoncini, M., Montemurro, P., Tei, F., Vazzana, C., and Viggiani, P. 1992. Frequency distribution of weed counts and applicability of a sequential sampling method to integrated weed management. Weed Res. 32: 39–44.CrossRefGoogle Scholar
3. Brain, P. and Cousens, R. 1990. The effect of weed distribution on predictions of yield loss. J. Appl. Ecol. 27: 735–742.CrossRefGoogle Scholar
4. Ives, P. M. and Moon, R. D. 1987. Sampling theory and protocol for insects. Pages 49–74 in Teng, P. S., ed. Crop Loss Assessment and Pest Management, Am. Phytopath. Soc. Press, St. Paul.Google Scholar
5. Johnson, G. 1994. Model parameteritization, parametric sequential sampling, and geostatistical analysis of weed seedling population. , University of Nebraska, Lincoln, NE Google Scholar
6. Marshall, E.J.P. 1988. Field-scale estimates of grass weed populations in arable land. Weed Res. 28: 191–198.Google Scholar
7. Mortensen, D. A., Johnson, G. A., and Young, L. J. 1993. Weed distribution in agricultural fields. Pages 113–124 in Site Specific Crop Management, Robert, P. and Rust, R.H. (eds.). Am. Soc. Agron., Madison, WI.Google Scholar
8. Nyrop, J. P. and Simmons, G. A. 1984. Errors incurred when using Iwao's sequential decision rule in insect sampling. Environ. Ent. 13: 1459–1465.Google Scholar
9. Southwood, T.R.E. 1966. Ecological methods with particular reference to the study of insect populations. Methuen and Co. Ltd., London.Google Scholar
10. Wiles, L. J., Oliver, G. W., York, A. C., Gold, H. J., and Wilkerson, G. G. 1992. Spatial distribution of broadleaf weeds in North Carolina soybean (Glycine max) fields. Weed Sci. 40: 554–557.Google Scholar
11. Willson, L. J. 1981. Estimation and testing procedures for the parameters of the negative binomial distribution. . Oklahoma State Univ. Google Scholar
12. Willson, L. J. and Young, J. H. 1983. Sequential estimation of insect population densities with a fixed coefficient of variation. Environ. Entomol. 12: 669–672.CrossRefGoogle Scholar
13. Willson, L. J., Folks, J. L., and Young, J. H. 1984. Multistage estimation compared with fixed-sample-size estimation of the negative binomial parameter k . Biometrics 40: 109–117.CrossRefGoogle Scholar