Three-Factor Factorial ANOVA — anova_factorial

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

Usage

anova_factorial_3way(
  data,
  response,
  factor1,
  factor2,
  factor3,
  replication = NULL,
  alpha = 0.05,
  verbose = TRUE,
  posthoc = "lsd"
)

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).
factor3: Name of the third factor (C).
replication: Name of the replication (block) column, or NULL for a completely randomized layout.
alpha: Significance level for CD and letters. Default 0.05.
verbose: Logical. If TRUE (default), prints the report.
posthoc: Post-hoc method for the letters (see perform_posthoc). Default "lsd".

Value

An object of class aridagri_factorial3 with anova_table, model, grand_mean, cv, ms_error, df_error, comparisons (SEm, SEd and CD for all seven effects), means (a list of tables for A, B, C, A x B, A x C, B x C and A x B x C, with letters) and posthoc.

Author

Lalit Kumar Rolaniya, Ram Lal Jat, Monika Punia, Raja Ram Choudhary, Hemant Poonia

Examples

data <- expand.grid(rep = 1:3, A = c("A1", "A2"), B = c("B1", "B2"),
                    C = c("C1", "C2", "C3"))
set.seed(2)
data$yield <- rnorm(nrow(data), 1200, 60)
res <- anova_factorial_3way(data, "yield", "A", "B", "C", "rep")
#> 
#> ======================================================================
#>  THREE-FACTOR FACTORIAL (RCBD)
#> ======================================================================
#>  Response     : yield
#>  Factor A     : A
#>  Factor B     : B
#>  Factor C     : C
#>  Observations : 36
#> 
#>  Analysis of variance
#>  Source Df    Sum Sq  Mean Sq F value Pr(>F)   
#>   rep    2  42406.20 21203.10   6.852 0.0049 **
#>   A      1   5505.52  5505.52   1.779 0.1959 NS
#>   B      1  16395.94 16395.94   5.298 0.0312  *
#>   C      2   5626.54  2813.27   0.909 0.4175 NS
#>   A:B    1   2429.03  2429.03   0.785 0.3852 NS
#>   A:C    2    588.81   294.41   0.095 0.9096 NS
#>   B:C    2   3753.96  1876.98   0.607 0.5541 NS
#>   A:B:C  2   9538.89  4769.45   1.541 0.2364 NS
#>   Error 22  68081.18  3094.60                  
#>   Total 35 154326.07                           
#>  Signif. codes: *** p < 0.001, ** p < 0.01, * p < 0.05, NS not significant
#> 
#>  Grand mean = 1212.230   CV = 4.59%
#> 
#>  SE and CD (alpha = 0.05)
#>     Effect Obs_per_mean    SEm    SEd     CD
#>          A           18 13.112 18.543 38.456
#>          B           18 13.112 18.543 38.456
#>          C           12 16.059 22.710 47.099
#>      A x B            9 18.543 26.224 54.385
#>      A x C            6 22.710 32.117 66.608
#>      B x C            6 22.710 32.117 66.608
#>  A x B x C            3 32.117 45.421 94.197
#> 
#>  Means of A
#>   A    Mean     SE Obs Group
#>  A1 1224.60 13.112  18     a
#>  A2 1199.86 13.112  18     a
#> 
#>  Means of B
#>   B    Mean     SE Obs Group
#>  B1 1190.89 13.112  18     b
#>  B2 1233.57 13.112  18     a
#> 
#>  Means of C
#>   C    Mean     SE Obs Group
#>  C1 1217.55 16.059  12     a
#>  C2 1224.17 16.059  12     a
#>  C3 1194.97 16.059  12     a
#> 
#>  Two- and three-way tables are in $means.
res$comparisons
#>      Effect Obs_per_mean      SEm      SEd       CD
#> 1         A           18 13.11191 18.54304 38.45591
#> 2         B           18 13.11191 18.54304 38.45591
#> 3         C           12 16.05874 22.71049 47.09868
#> 4     A x B            9 18.54304 26.22382 54.38487
#> 5     A x C            6 22.71049 32.11749 66.60759
#> 6     B x C            6 22.71049 32.11749 66.60759
#> 7 A x B x C            3 32.11749 45.42099 94.19736