The Transformation of Data From Entomological Field Experiments So That the Analysis of Variance Becomes Applicable

Beall, Geoffrey

doi:10.1093/biomet/32.3-4.243

Cited by 75 publications

(21 citation statements)

References 10 publications

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“…An attempt was made to reduce this correlation b y application of four commonlj-used transformations. Logarithmic transformation of the form log (x+ 1) is commonly used t o adjust data with a negative binomial distribution although Beall (1942) and Bliss (1958) suggest log (x +k/2). Logarithmic transformation of the form log (x+ 1) is commonly used t o adjust data with a negative binomial distribution although Beall (1942) and Bliss (1958) suggest log (x +k/2).…”

Section: Transformations Of Datamentioning

confidence: 99%

DISTRIBUTIONS OF SCOLYTUS VENTRALIS ATTACKS, EMERGENCE, AND PARASITES IN GRAND FIR

Berryman

1968

Can Entomol

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The distributions of Scolytus ventralis LeConte attacks, emergence, and parasites were studied by stratified sampling of 20 grand fir. Of the theoretical distributions tested the negative binomial gave the best fit to all three sets of data. Three sample unit sizes were analyzed (1/4, 1/2, and 1 sq. ft) and all gave similar estimates of the mean, although the smallest sample unit influenced the distribution by increasing the frequency of the zero class. Approximate normality was achieved by applying logarithmic transformation to the attack data and the Taylor power transformation to the emergence and parasite data. Analysis of variance showed that the vertical position of the sample in the tree was die most consistent factor influencing the distribution of attacks, emergence, and parasitism, while cardinal aspect had little effect. Considerable variation also occurred among trees within a group. The density of attacks was extremely variable both within and between trees, although it was slightly higher on rough bark. Emergence was generally greater in the basal half of the tree, being reduced in the upper levels by competition with other insects. Emergence increased with attack density up to about 13 attacks per square foot. Thereafter survival was probably limited by intraspecific competition. Parasitism appeared to be reduced near the base of the tree by thick bark and at the top by lack of host larvae.Sampling designs for the fir engraver will have to consider variations between trees and vertical strata within the tree.

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Section: Transformations Of Datamentioning

confidence: 99%

DISTRIBUTIONS OF SCOLYTUS VENTRALIS ATTACKS, EMERGENCE, AND PARASITES IN GRAND FIR

Berryman

1968

Can Entomol

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“…From the linear relationship, a new variate, y = f(x), was derived where the variance of y is constant. Beall (1942) extended this relationship to the nonlinear case, which is required to describe some Pgrpes of field data. This relationship is characteristic of the NB distribution where llb = k, the contagion parameter in the NB model.…”

Section: Statistical Distributions and Transformationsmentioning

confidence: 99%

“…This relationship is characteristic of the NB distribution where llb = k, the contagion parameter in the NB model. From this nonlinear relationship, Beall (1942) derived the variate, where the vasiance of y is consmt.…”

Section: Statistical Distributions and Transformationsmentioning

confidence: 99%

“…Thus, by estimting b in terms of the sample m a n and frequency of zero counts and applying the transformation, one obtains the variate y that is theoretically appropriate for use in parmtric statistical analyses. It can be shown that the square root and logarithmic trans cases of Beall's (1942) transformation. This equation includes Beall's (1942) formula as a special case.…”

Section: Statistical Distributions and Transformationsmentioning

confidence: 99%

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

Pepper¹,

Zarnoch²,

DeBarr³

et al. 1997

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guidelines are available on how to choose a transfomtion in parametric analyses of data where insect counts are low or Guidelines based on computer simulation are suggested for choosing a ttansformation of insect counts from negative binomial distributions with how to determine the influence of various controllable low mean counts and high levels of contagion. Typical values and ranges factors on the method of analyses. Thus, our objective was of negative binomial model parameters were determined by fitting the to develop guidelines to help researchers choose a model to data from 19 entomological field studies. Random sampling of transformation and to develop a simple program1 that negative binomial distributions was simulated and ANOVA's were performed on simulated data for randomized complete block designs with evaluates various tradeoffs and identifies an affordable treatment means corresponding to means of negative binomial experimental design with acceptable statistical test attributes. 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 Methods computer program was developed to recompute observed power of F-tests for any combination of these factors. The program facilitates choosing a Field Data 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. Preliminary observations on frequency distributions of insect counts were obtained from data sets collected in 19 field

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“…An approximate normalizing and variance equalizing transformation, suggested by Beall (1942), is Y = go(U) = sinh -lUO, where sinh-(*) is the inverse hyperbolic sine function. Our goal is to find a 0 that will linearize the model (of Y vs.…”

Section: A More General Casementioning

confidence: 99%

An Empirical Nonlinear Data-Fitting Approach for Transforming Data to Normality

Li¹,

Vonesh²

1989

The American Statistician

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The Transformation of Data From Entomological Field Experiments So That the Analysis of Variance Becomes Applicable

Cited by 75 publications

References 10 publications

DISTRIBUTIONS OF SCOLYTUS VENTRALIS ATTACKS, EMERGENCE, AND PARASITES IN GRAND FIR

DISTRIBUTIONS OF SCOLYTUS VENTRALIS ATTACKS, EMERGENCE, AND PARASITES IN GRAND FIR

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

An Empirical Nonlinear Data-Fitting Approach for Transforming Data to Normality

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