Pooled analysis of a series of designed experiments repeated over locations, seasons or years, where the treatment-by-environment interaction is of primary interest.
When Aitken's transformation is applied, the pooled analysis of variance and the multiple comparison tests are performed on the transformed scale, and the returned objects say so. The environment main effect on that scale is not interpretable in the units of the original response, because each environment has been rescaled by its own error standard deviation. Treatment means are reported on the transformed scale, which is the scale on which the test was conducted and to which the grouping letters refer, alongside the arithmetic means on the original scale for interpretation.
Maintainer: Vinayaka [email protected] (ORCID)
Authors:
One design-specific function call performs the whole classical workflow:
analysis of variance within each environment, with every effect tested against its proper error stratum;
formal assessment of homogeneity of the error variances, by Bartlett's test computed on the environment-wise error mean squares and by the median-centred Brown-Forsythe form of Levene's test, which is robust to non-normality, together with environment-wise Shapiro-Wilk tests of the normality that Bartlett's test assumes;
an optional Aitken transformation, dividing each observation by the square root of the error mean square of its own environment, applied automatically, always, or never at the user's choice;
pooled analysis of variance partitioning the treatment-by-environment interaction, with each effect tested against the mean square appropriate to its stratum, which is reported in the table; and
multiple comparison of means by Tukey's HSD, Duncan's multiple range test or Fisher's LSD, using the error mean square and degrees of freedom of the stratum in which the factor being compared belongs.
Five designs are supported, one function each:
PooledCRDcompletely randomised design
PooledRBDrandomised block design
PooledLSDLatin square design
PooledSPDsplit plot design
PooledStPDstrip plot design
The package implements the fixed-effects pooled analysis of a balanced series of experiments. It is not a substitute for a mixed-model analysis: for unbalanced or partially overlapping treatment sets, for explicit modelling of variance heterogeneity, or for best linear unbiased prediction, use a mixed-model package such as nlme or lme4; for augmented designs see augmentedRCBD; for multiplicative models and stability analysis see metan.
Useful links: