Analysis of variance in soil research: Examining the assumptions

A - Papers appearing in refereed journals

Webster, R. and Lark, R. M. 2019. Analysis of variance in soil research: Examining the assumptions. European Journal of Soil Science. 70 (5), pp. 990-1000.

AuthorsWebster, R. and Lark, R. M.

Three assumptions underly safe inference from an analysis of variance of soil data from designed experiments and surveys. They are (a) that the residuals are normally distributed, (b) that the within-groups variances are equal and (c) that effects of treatments and blocks are additive. Small departures from these assumptions are unlikely to affect conclusions because the analysis is robust. Large departures could have serious consequences, however. The most common departures in the real world of the soil are strongly positively skewed distributions of the observed values, many of which are approximately lognormal. In those situations, transformation of the data to logarithms should lead to analyses from which inferences are sound and to confidence limits on estimates. Mean values can be transformed back to the original scales to aid understanding. Measurements of nitrogen in the soil of the Broadbalk wheat experiment show how transformations of the strongly skewed data to logarithms are sufficient to satisfy the assumptions underlying the analysis. Those of nitrogen in the soil of Cashmore Field at Silsoe required the somewhat more complex Box–Cox transformation to satisfy the assumptions and lead to sensible conclusions. The statistical distributions in pH, already a logarithm, in the soil in sandy drift and chalky boulder clay at Broom's Barn Farm differed so strongly that no transformation would satisfy the assumptions. Non-parametric tests are available, but they should be used only if no suitable transformation can be found.

KeywordsAdditivity; Analysis of variance; Histograms; Homoscedacity; Normal distribution; Q-Q plots; Residuals
Year of Publication2019
JournalEuropean Journal of Soil Science
Journal citation70 (5), pp. 990-1000
Digital Object Identifier (DOI)
Open accessPublished as non-open access
FunderBiotechnology and Biological Sciences Research Council
Funder project or codeS2N - Soil to Nutrition [ISPG]
The Rothamsted Long Term Experiments [2017-2022]
Output statusPublished
Publication dates
Online04 Mar 2019
Publication process dates
Accepted04 Mar 2019

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