Combined (Pooled) Analysis of RCBD Experiments over Environments

Combined analysis of variance for the same set of treatments tested in a randomized complete block design in several environments (years, seasons or locations). Gives the analysis of each environment, Bartlett's test of homogeneity of error variances, the combined ANOVA with the correct error term for every source, SE and CD for treatment, environment and interaction means, and letter groupings for the treatment means.

Usage

anova_rbd_pooled(
  data,
  response,
  treatment,
  environment,
  block,
  posthoc = "lsd",
  alpha = 0.05,
  verbose = TRUE,
  env_effect = c("fixed", "random"),
  control = NULL
)

Arguments

data: Data frame containing the experimental data.
response: Name of the response variable (character).
treatment: Name of the treatment column.
environment: Name of the environment (year, season or location) column.
block: Name of the block column (blocks are nested within environments; labels may repeat across environments).
posthoc: Post-hoc test(s): "lsd", "duncan", "tukey", "snk", "scheffe", "bonferroni", "dunnett", a vector of these, "all" or "none". The first method supplies the letters in the means table.
alpha: Significance level for the CD and the post-hoc tests (default 0.05).
verbose: Logical. If TRUE (default), prints the report.
env_effect: Either "fixed" (default; years or seasons of interest) or "random" (locations or years treated as a sample).
control: Control level for Dunnett's test (default: first level).

Value

An object of class aridagri_pooled with pooled_anova (combined ANOVA with correct F-tests), individual_anovas, environment_summary (mean, MSE, CV, F, p and CD of each environment), bartlett_test, treatment_means (with letters), interaction_means, se_treatment, cd_treatment, se_environment, cd_environment, se_interaction, cd_interaction, posthoc, cv, grand_mean, mse_values and model.

Details

Sources and their F-tests (McIntosh, 1983; Gomez and Gomez, 1984): environment is tested against blocks within environments; the treatment x environment interaction against the pooled error; the treatment effect against the pooled error when environments are fixed and against the treatment x environment mean square when they are random. With random environments the usual restricted mixed model is assumed, so environment is still tested against blocks within environments. The SE and CD of treatment means use the same denominator as the treatment F-test. Bartlett's chi-square tests whether the error variances of the environments can be pooled; when it is significant, interpret the combined analysis with care.

References

McIntosh, M.S. (1983). Analysis of combined experiments. Agronomy Journal, 75(1), 153-155. doi:10.2134/agronj1983.00021962007500010041x

Gomez, K.A. and Gomez, A.A. (1984). Statistical Procedures for Agricultural Research, 2nd ed. John Wiley and Sons, New York.

Author

Lalit Kumar Rolaniya, ICAR-IIPR, Bikaner

Examples

data(pearlmillet_met)
res <- anova_rbd_pooled(pearlmillet_met, response = "grain_yield",
                        treatment = "genotype", environment = "environment",
                        block = "rep", verbose = FALSE)
res$pooled_anova
#>                       Df     Sum Sq    Mean Sq    F value       Pr(>F)
#> environment            5 21126520.4 4225304.08 198.051226 4.253250e-11
#> rep(environment)      12   256012.8   21334.40   2.042170 2.705284e-02
#> genotype               9  1529257.1  169917.46  16.264830 1.408097e-16
#> environment:genotype  45  1479461.6   32876.92   3.147043 6.349451e-07
#> Residuals            108  1128267.9   10446.92         NA           NA
res$bartlett_test
#> $chi_sq
#> [1] 5.375261
#> 
#> $df
#> [1] 5
#> 
#> $p_value
#> [1] 0.3718179
#> 
#> $variance_ratio
#> [1] 2.779661
#> 
#> $homogeneous
#> [1] TRUE
#>