Two-Factor Factorial ANOVA — anova

Analysis of variance for a two-factor factorial experiment in a randomized complete block design (when replication is given) or a completely randomized design, with SEm, SEd and CD for both main effects and the interaction, and letter groupings for factor means and treatment combinations.

Usage

anova_factorial(
  data,
  response,
  factor1,
  factor2,
  replication = NULL,
  posthoc = "lsd",
  alpha = 0.05,
  verbose = TRUE
)

Arguments

data: Data frame containing the data.
response: Name of the response variable.
factor1: Name of the first factor (A).
factor2: Name of the second factor (B).
replication: Name of the replication (block) column, or NULL for a completely randomized layout.
posthoc: Post-hoc method for the letters (see perform_posthoc). Default "lsd".
alpha: Significance level for CD and letters. Default 0.05.
verbose: Logical. If TRUE (default), prints the report.

Value

An object of class aridagri_factorial with anova_table, model, grand_mean, cv, ms_error, df_error, comparisons (SEm, SEd and CD for A, B and A x B), se_a, cd_a, se_b, cd_b, se_ab, cd_ab, mean_a, mean_b (with letters), interaction_means (all combinations with letters), mean_ab (two-way table) and posthoc.

Author

Lalit Kumar Rolaniya, ICAR-IIPR, Bikaner

Examples

data <- expand.grid(rep = 1:4, nitrogen = c("N0", "N40", "N80"),
                    phosphorus = c("P0", "P30"))
set.seed(1)
data$yield <- 900 + 3 * as.numeric(sub("N", "", data$nitrogen)) +
  2 * as.numeric(sub("P", "", data$phosphorus)) + rnorm(nrow(data), 0, 40)
res <- anova_factorial(data, response = "yield", factor1 = "nitrogen",
                       factor2 = "phosphorus", replication = "rep")
#> 
#> ======================================================================
#>  TWO-FACTOR FACTORIAL (RCBD)
#> ======================================================================
#>  Response     : yield
#>  Factor A     : nitrogen
#>  Factor B     : phosphorus
#>  Observations : 24
#> 
#>  Analysis of variance
#>               Source Df    Sum Sq   Mean Sq F value Pr(>F)    
#>  rep                  3   2910.24    970.08   0.545 0.6588  NS
#>  nitrogen             2 265228.51 132614.26  74.540 0.0000 ***
#>  phosphorus           1  15300.49  15300.49   8.600 0.0103   *
#>  nitrogen:phosphorus  2   1973.02    986.51   0.554 0.5857  NS
#>  Error               15  26686.66   1779.11                   
#>  Total               23 312098.91                             
#>  Signif. codes: *** p < 0.001, ** p < 0.01, * p < 0.05, NS not significant
#> 
#>  Grand mean = 1055.995   CV = 3.99%
#> 
#>  SE and CD (alpha = 0.05)
#>                 Effect Obs_per_mean    SEm    SEd     CD
#>               nitrogen            8 14.913 21.090 44.952
#>             phosphorus           12 12.176 17.220 36.703
#>  nitrogen x phosphorus            4 21.090 29.825 63.571
#> 
#>  Means of nitrogen (Fisher's LSD)
#>  Level    Mean     SE Obs Group
#>     N0  922.80 14.913   8     c
#>    N40 1065.39 14.913   8     b
#>    N80 1179.79 14.913   8     a
#> 
#>  Means of phosphorus (Fisher's LSD)
#>  Level    Mean     SE Obs Group
#>     P0 1030.75 12.176  12     b
#>    P30 1081.24 12.176  12     a
#> 
#>  Treatment combinations (Fisher's LSD)
#>  nitrogen phosphorus    Mean     SE Obs Group
#>        N0         P0  903.17 21.090   4     d
#>       N40         P0 1027.35 21.090   4     c
#>       N80         P0 1161.72 21.090   4    ab
#>        N0        P30  942.44 21.090   4     d
#>       N40        P30 1103.43 21.090   4     b
#>       N80        P30 1197.86 21.090   4     a
res$interaction_means
#>   nitrogen phosphorus      Mean       SE Obs Group
#> 1       N0         P0  903.1684 21.08975   4     d
#> 2      N40         P0 1027.3479 21.08975   4     c
#> 3      N80         P0 1161.7202 21.08975   4    ab
#> 4       N0        P30  942.4406 21.08975   4     d
#> 5      N40        P30 1103.4277 21.08975   4     b
#> 6      N80        P30 1197.8633 21.08975   4     a