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Use of the Arcsine and Square Root Transformations for Subjectively Determined Percentage Data

Published online by Cambridge University Press:  12 June 2017

William H. Ahrens ,
Darrell J. Cox  and
Girish Budhwar
William H. Ahrens
Affiliation:
Crop and Weed Sci. Dep., North Dakota State Univ., Fargo, ND 58105
Darrell J. Cox
Affiliation:
Crop and Weed Sci. Dep., North Dakota State Univ., Fargo, ND 58105
Girish Budhwar
Affiliation:
Statistics Dep., North Dakota State Univ.
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Abstract

The arcsine and square root transformations were tested on 82 weed control data sets and 62 winter wheat winter survival data sets to determine effects on normality of the error terms, homogeneity of variance, and additivity of the model. Transformations appeared to correct deficiencies in these three parameters in the majority of data sets, but had adverse effects in certain other data sets. Performing the recommended transformation in conjunction with omitting treatments having identical replicate observations provided a high percentage of correction of non-normality, heterogeneity of variance, and nonadditivity. The arcsine transformation, not generally recommended for data sets having values from 0 to 20% or 80 to 100%, was as effective in correcting non-normality, heterogeneity of variance, and nonadditivity in these data sets as was the recommended square root transformation. A majority of data sets showed differences between transformed and nontransformed data in mean separations determined using LSD (0.05), although most of these differences were minor and had little effect on interpretation of results.

Keywords

Normalityhomogeneity of variancehomoscedasticityadditivity
Type
Special Topics
Information
Weed Science , Volume 38 , Issue 4-5 , September 1990 , pp. 452 - 458
Copyright
Copyright © 1990 by the Weed Science Society of America 

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References

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