Analysis of variance for a randomized complete block design with standard errors, critical difference, CV, relative efficiency over a CRD, post-hoc letter groupings and assumption checks. Missing plots are handled by least squares: treatments are tested after blocks, means are least-squares (adjusted) means and every pair is compared with its own standard error.
Usage
anova_rbd(
data,
response,
treatment,
block,
posthoc = "lsd",
alpha = 0.05,
verbose = TRUE,
control = NULL
)Arguments
- data
Data frame containing the experimental data.
- response
Name of the response variable (character).
- treatment
Name of the treatment column.
- block
Name of the block (replication) column.
- 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.
- control
Control level for Dunnett's test (default: first level).
Value
An object of class aridagri_anova. In addition to the
components described in anova_crd it contains
relative_efficiency (percent, adjusted),
relative_efficiency_unadjusted and missing_plots.
Details
Relative efficiency of the RCBD over a CRD follows Gomez and Gomez (1984): $$RE = \frac{(r - 1) E_b + r (t - 1) E_e}{(r t - 1) E_e}$$ where \(E_b\) and \(E_e\) are the block and error mean squares, multiplied by the precision adjustment factor \(k = \frac{[(r-1)(t-1)+1][t(r-1)+3]}{[(r-1)(t-1)+3][t(r-1)+1]}\) when the error degrees of freedom are below 20. Values above 100% mean that blocking reduced the error.
References
Gomez, K.A. and Gomez, A.A. (1984). Statistical Procedures for Agricultural Research, 2nd ed. John Wiley and Sons, New York.
Examples
data(mothbean_rbd)
res <- anova_rbd(mothbean_rbd, response = "seed_yield",
treatment = "treatment", block = "block",
posthoc = "duncan")
#>
#> ======================================================================
#> RANDOMIZED COMPLETE BLOCK DESIGN (RCBD)
#> ======================================================================
#> Response : seed_yield
#> Treatment : treatment
#> Treatments : 8
#> Blocks : 4
#> Observations : 32
#>
#> Analysis of variance
#> Source Df Sum Sq Mean Sq F value Pr(>F)
#> Block 3 19781.59 6593.86 6.773 0.0023 **
#> Treatment 7 84544.22 12077.75 12.405 0.0000 ***
#> Error 21 20445.66 973.60
#> Total 31 124771.47
#> Signif. codes: *** p < 0.001, ** p < 0.01, * p < 0.05, NS not significant
#>
#> Grand mean = 627.781 CV (%) = 4.970 SEm = 15.601 SEd = 22.064 CD (5%) = 45.884
#> Relative efficiency of RCBD over CRD = 155.9%
#>
#> Treatment means (Duncan's MRT, alpha = 0.05)
#> Treatment Mean SD N SE Group
#> T5 RDF+Rhizobium+PSB 705.00 25.781 4 15.601 a
#> T6 75% RDF+FYM 662.75 67.609 4 15.601 ab
#> T3 RDF+Rhizobium 650.75 34.248 4 15.601 bc
#> T8 RDF+Zn5 639.75 53.238 4 15.601 bc
#> T4 RDF+PSB 632.25 26.887 4 15.601 bc
#> T7 RDF+S20 610.75 26.247 4 15.601 c
#> T2 RDF 604.75 49.815 4 15.601 c
#> T1 Control 516.25 16.520 4 15.601 d
#> Means sharing a letter do not differ significantly.
res$treatment_means
#> Treatment Mean SD N SE Group
#> 1 T5 RDF+Rhizobium+PSB 705.00 25.78113 4 15.6013 a
#> 2 T6 75% RDF+FYM 662.75 67.60855 4 15.6013 ab
#> 3 T3 RDF+Rhizobium 650.75 34.24787 4 15.6013 bc
#> 4 T8 RDF+Zn5 639.75 53.23767 4 15.6013 bc
#> 5 T4 RDF+PSB 632.25 26.88711 4 15.6013 bc
#> 6 T7 RDF+S20 610.75 26.24722 4 15.6013 c
#> 7 T2 RDF 604.75 49.81549 4 15.6013 c
#> 8 T1 Control 516.25 16.52019 4 15.6013 d
res$relative_efficiency
#> [1] 155.8643