Performs the classical pooled analysis of variance for a strip plot (split block) design repeated over several environments, with three error strata handled explicitly.
PooledStPD(
data,
Response,
Location,
Replication,
RowFactor,
ColumnFactor,
alpha = 0.05,
Mult_Comp_Test = 1,
transform = c("auto", "always", "never"),
env_effect = c("fixed", "random")
)An object of class "cane". The structure is as described in
PooledCRD, except that Location_wise and
Treatments_Comparison are each a list with components
RowFactor, ColumnFactor and Interaction, computed
from the row strip, column strip and intersection error strata
respectively.
A data frame containing the experimental data. Rows with missing values in the variables used are dropped with a warning.
Character string naming the numeric response variable.
Character string naming the factor that identifies environments (locations, seasons or years).
Character string naming the replication factor.
Character string naming the factor applied in horizontal strips.
Character string naming the factor applied in vertical strips.
Significance level used for the variance-homogeneity test and
for the multiple comparison procedure. Default 0.05.
Integer selecting the multiple comparison procedure:
1 = Tukey's honestly significant difference (HSD) test,
2 = Duncan's multiple range test (DMRT),
3 = Fisher's least significant difference (LSD) test. Option
3 makes no adjustment for multiplicity and is intended for a small
number of pre-planned comparisons; a warning is issued if it is requested
for more than three treatments.
One of "auto" (default; transform only when the
variances are judged heterogeneous at level alpha),
"always" or "never".
One of "fixed" (default) or "random".
With "random" each treatment main effect is tested against its
interaction with environment, and in split plot and strip plot designs
the interaction of the two treatment factors is tested against the
three-way interaction with environment. The pooled comparison of means
then uses the same mean square and degrees of freedom as the F-test of
the factor compared. With few environments that interaction has few
degrees of freedom; if it has fewer than two, the Tukey and Duncan
comparisons for that factor are not computed and a warning is issued.
In a strip plot design the two factors are applied in perpendicular strips, which creates three error terms: a row strip error, a column strip error and an intersection error. The row factor must be tested against the row strip error \(Environment \times Replication \times Row\), the column factor against the column strip error \(Environment \times Replication \times Column\), and their interaction against the intersection (residual) error. The interaction is therefore estimated with the greatest precision, which is the characteristic merit of the design.
With \(l\) environments, \(r\) replications, \(a\) row levels and \(b\) column levels the three errors carry \(l(r-1)(a-1)\), \(l(r-1)(b-1)\) and \(l(r-1)(a-1)(b-1)\) degrees of freedom.
Homogeneity of error variances is assessed for all three strata: the main
Bartlett test uses the intersection error mean squares, and the row strip
and column strip error mean squares are tested separately and reported in
Bartlett_Test$other_strata.
Aitken's transformation, when applied, divides each observation by the
square root of the intersection error mean square of its own
environment, matching the definition used by the other functions in the
package. The lookup is by environment label, so it is unaffected by the row
order of data.
Aitken, A. C. (1935). On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42--48. tools:::Rd_expr_doi("10.1017/S0370164600014346")
Bartlett, M. S. (1937). Properties of sufficiency and statistical tests. Proceedings of the Royal Society of London A, 160, 268--282. tools:::Rd_expr_doi("10.1098/rspa.1937.0109")
Cochran, W. G. and Cox, G. M. (1957). Experimental Designs, 2nd ed. John Wiley and Sons, New York.
Dean, A., Voss, D. and Draguljic, D. (2017). Design and Analysis of Experiments, 2nd ed. Springer, Cham. tools:::Rd_expr_doi("10.1007/978-3-319-52250-0")
Gomez, K. A. and Gomez, A. A. (1984). Statistical Procedures for Agricultural Research, 2nd ed. John Wiley and Sons, New York.
PooledCRD, PooledRBD,
PooledLSD, PooledSPD
data(stpd_example)
out <- PooledStPD(stpd_example, Response = "Yield", Location = "Location",
Replication = "Replication", RowFactor = "RowFactor",
ColumnFactor = "ColumnFactor", alpha = 0.05,
Mult_Comp_Test = 1)
out
out$Pooled_ANOVA
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