Analysis of variance for a split-split-plot design with main-plot sources tested against Error(a), sub-plot sources against Error(b) and sub-sub-plot sources against Error(c). Gives CVs for the three strata, SEm, SEd and CD for every type of comparison (including those that mix error terms) and letter groupings.
Usage
anova_sspd(
data,
response,
main_plot,
sub_plot,
sub_sub_plot,
replication,
verbose = TRUE,
posthoc = "lsd",
alpha = 0.05
)Arguments
- data
Data frame containing the experimental data.
- response
Name of the response variable.
- main_plot
Name of the main-plot factor (A).
- sub_plot
Name of the sub-plot factor (B).
- sub_sub_plot
Name of the sub-sub-plot factor (C).
- replication
Name of the replication column.
- verbose
Logical. If TRUE (default), prints the report.
- posthoc
Method for the letters (default
"lsd").- alpha
Significance level. Default 0.05.
Value
An object of class aridagri_sspd with the corrected
anova_table, cv, ms_error_a/b/c,
df_error_a/b/c, se_cd, factor_means,
letters, interaction_means and model.
References
Gomez, K.A. and Gomez, A.A. (1984). Statistical Procedures for Agricultural Research, 2nd ed. John Wiley and Sons, New York.
Examples
data <- expand.grid(rep = 1:3, A = c("A1", "A2"), B = c("B1", "B2"),
C = c("C1", "C2", "C3"))
set.seed(6)
data$yield <- rnorm(nrow(data), 1200, 80)
res <- anova_sspd(data, response = "yield", main_plot = "A",
sub_plot = "B", sub_sub_plot = "C", replication = "rep")
#>
#> ======================================================================
#> SPLIT-PLOT TYPE DESIGN
#> ======================================================================
#> Response : yield
#> Design : Split-Split-Plot Design
#> Replications : 3
#> Factors : A (2), B (2), C (3)
#>
#> Analysis of variance
#> Source Df Sum Sq Mean Sq F value Pr(>F)
#> rep 2 51771.46 25885.73 1.879 0.3474 NS
#> A 1 4601.34 4601.34 0.334 0.6217 NS
#> Error(a) 2 27557.97 13778.99
#> B 1 5890.51 5890.51 0.248 0.6447 NS
#> A:B 1 12874.33 12874.33 0.542 0.5025 NS
#> Error(b) 4 95059.76 23764.94
#> C 2 591.31 295.65 0.094 0.9111 NS
#> A:C 2 15060.09 7530.05 2.386 0.1239 NS
#> B:C 2 9381.79 4690.89 1.486 0.2558 NS
#> A:B:C 2 1559.73 779.86 0.247 0.7840 NS
#> Error(c) 16 50492.63 3155.79
#> Total 35 274840.93
#> Signif. codes: *** p < 0.001, ** p < 0.01, * p < 0.05, NS not significant
#>
#> Grand mean = 1210.100
#> Error(a) [main]: df = 2, MS = 13778.9855, CV = 9.70%
#> Error(b) [sub]: df = 4, MS = 23764.9388, CV = 12.74%
#> Error(c) [subsub]: df = 16, MS = 3155.7897, CV = 4.64%
#>
#> SEm, SEd and CD (alpha = 0.05)
#> Comparison SEm SEd CD
#> A means 27.668 39.128 168.354
#> B means 36.336 51.386 142.671
#> C means 16.217 22.934 48.618
#> A levels at the same or different B 45.670 64.588 215.501
#> B levels at the same A 51.386 72.671 201.767
#> A levels at the same or different C 33.409 47.247 170.889
#> C levels at the same A 22.934 32.433 68.756
#> B levels at the same or different C 40.877 57.809 152.538
#> C levels at the same B 22.934 32.433 68.756
#> A levels at the same or different B x C 52.793 74.660 226.252
#> B levels at the same A, at the same or different C 57.809 81.754 215.721
#> C levels at the same A x B 32.433 45.868 97.236
#> Error
#> Ea
#> Eb
#> Ec
#> Ea+Eb
#> Eb
#> Ea+Ec
#> Ec
#> Eb+Ec
#> Ec
#> Ea+Eb+Ec
#> Eb+Ec
#> Ec
#> CD for comparisons mixing error terms uses the weighted t of Cochran and Cox.
#>
#> Means of A (Fisher's LSD)
#> Level Mean Group
#> A1 1198.79 a
#> A2 1221.41 a
#>
#> Means of B (Fisher's LSD)
#> Level Mean Group
#> B1 1222.89 a
#> B2 1197.31 a
#>
#> Means of C (Fisher's LSD)
#> Level Mean Group
#> C1 1210.69 a
#> C2 1214.74 a
#> C3 1204.87 a
#>
#> Interaction means: A x B
#> B1 B2
#> A1 1192.67 1204.91
#> A2 1253.11 1189.70
#>
#> Interaction means: A x C
#> C1 C2 C3
#> A1 1199.77 1228.29 1168.32
#> A2 1221.60 1201.20 1241.42
#>
#> Interaction means: B x C
#> C1 C2 C3
#> B1 1235.04 1204.71 1228.93
#> B2 1186.34 1224.78 1180.81