Analysis of variance for a strip-plot design, where factor A is applied to horizontal strips and factor B to vertical strips in each replication. A is tested against Error(a) = Rep x A, B against Error(b) = Rep x B, and A x B against Error(c). Gives CV(a), CV(b), CV(c), SEm, SEd and CD for the four standard comparisons, and letter groupings.
Usage
anova_strip(
data,
response,
horizontal_factor,
vertical_factor,
replication,
alpha = 0.05,
verbose = TRUE,
posthoc = "lsd"
)Arguments
- data
Data frame containing the experimental data.
- response
Name of the response variable.
- horizontal_factor
Factor applied in horizontal strips (A).
- vertical_factor
Factor applied in vertical strips (B).
- replication
Name of the replication column.
- alpha
Significance level. Default 0.05.
- verbose
Logical. If TRUE (default), prints the report.
- posthoc
Method for the letters (default
"lsd").
Value
An object of class aridagri_strip with the corrected
anova_table, cv (a, b, c), error mean squares and df,
se_cd, horizontal_means and vertical_means (with
letters), interaction_means, letters and model.
Details
Standard errors of difference (Gomez and Gomez, 1984, table 3.15), with \(a\) and \(b\) levels of A and B and \(r\) replications: A means \(\sqrt{2E_a/(rb)}\); B means \(\sqrt{2E_b/(ra)}\); A means at the same level of B \(\sqrt{2[(b-1)E_c + E_a]/(rb)}\); B means at the same level of A \(\sqrt{2[(a-1)E_c + E_b]/(ra)}\). The last two use the weighted t of Cochran and Cox.
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 = 1:4, irrigation = c("I1", "I2", "I3"),
tillage = c("CT", "MT", "ZT"))
set.seed(9)
data$yield <- rnorm(nrow(data), 1200, 70)
anova_strip(data, response = "yield", horizontal_factor = "irrigation",
vertical_factor = "tillage", replication = "rep")
#>
#> ======================================================================
#> STRIP-PLOT DESIGN
#> ======================================================================
#> Response : yield
#> Horizontal factor (A) : irrigation
#> Vertical factor (B) : tillage
#> Replications : 4
#>
#> Analysis of variance
#> Source Df Sum Sq Mean Sq F value Pr(>F)
#> rep 3 19500.79 6500.26
#> irrigation 2 6335.68 3167.84 0.631 0.5639 NS
#> Error(a) 6 30109.73 5018.29
#> tillage 2 1705.41 852.70 0.100 0.9062 NS
#> Error(b) 6 51067.71 8511.29
#> irrigation:tillage 4 16957.44 4239.36 1.186 0.3658 NS
#> Error(c) 12 42886.15 3573.85
#> Total 35 168562.92
#> Signif. codes: *** p < 0.001, ** p < 0.01, * p < 0.05, NS not significant
#>
#> Grand mean = 1201.579 CV(a) = 5.90% CV(b) = 7.68% CV(c) = 4.98%
#>
#> SEm, SEd and CD (alpha = 0.05)
#> Comparison SEm SEd CD Error
#> irrigation means 20.450 28.920 70.765 Ea
#> tillage means 26.632 37.664 92.160 Eb
#> irrigation levels at the same tillage 31.841 45.030 103.091 Ea+Ec
#> tillage levels at the same irrigation 36.124 51.086 118.752 Eb+Ec
#>
#> Means of irrigation (Fisher's LSD)
#> Level Mean Group
#> I1 1201.83 a
#> I2 1185.21 a
#> I3 1217.70 a
#>
#> Means of tillage (Fisher's LSD)
#> Level Mean Group
#> CT 1191.94 a
#> MT 1205.22 a
#> ZT 1207.58 a
#>
#> Interaction means
#> CT MT ZT
#> I1 1164.96 1214.19 1226.33
#> I2 1207.41 1155.99 1192.23
#> I3 1203.46 1245.48 1204.17