Choosing a Transformation in Analyses of Insect Counts from Contagious Distributions with Low Means

W.D. Pepper; S.J. Zarnoch; G.L. DeBarr; P. de Groot; C.D. Tangren

doi:10.2737/SRS-RP-5

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Choosing a Transformation in Analyses of Insect Counts from Contagious Distributions with Low Means

Informally Refereed

Authors:

W.D. Pepper, S.J. Zarnoch, G.L. DeBarr, P. de Groot, C.D. Tangren

Year:

1997

Type:

Research Paper

Station:

Southern Research Station

DOI:

https://doi.org/10.2737/SRS-RP-5

Source:

Res. Pap. SRS-5.Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station. 16 p.

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Abstract

Guidelines based on computer simulation are suggested for choosing a transformation of insect counts from negative binomial distributions with low mean counts and high levels of contagion. Typical values and ranges of negative binomial model parameters were determined by fitting the model to data from 19 entomological field studies. Random sampling of negative binomial distributions was simulated and ANOVA’s were performed on simulated data for randomized complete block designs with treatment means corresponding to means of negative binomial distributions. The influence of analysis variable, treatment-mean configuration, range in treatment means, significance level of statistical tests, level of contagion, number of blocks, and number of replications in time on observed power and Type I error of F-tests was studied. A computer program was developed to recompute observed power of F-tests for any combination of these factors. The program facilitates choosing a transformation and may also be used to evaluate tradeoffs and determine affordable experimental factors for a future design with a given set of statistical attributes.

Keywords

Contagious distribution, entomology, transformation, variance-mean relationship, variance stabilization

Citation

Pepper, W.D.; Zarnoch, S.J.; DeBarr, G.L.; de Groot, P.; Tangren, C.D. 1997. Choosing a Transformation in Analyses of Insect Counts from Contagious Distributions with Low Means. Res. Pap. SRS-5.Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station. 16 p.