Fisher's Least Significant Difference (LSD) Post-Hoc Mean Comparison Engine

The `compute_lsd` function executes a rigorous, high-precision pairwise post-hoc mean separation analysis using Fisher's Least Significant Difference protocol. It isolates critical differences, evaluates pairwise significance metrics, and outputs comprehensive ranking tables with group letters.

Usage

compute_lsd(
  data,
  trait,
  anova_results,
  total_replications,
  alpha = 0.05,
  reporting_level = 2
)

Arguments

data: A verified data.frame containing the columns Genotype and the phenotypic trait under investigation.
trait: A single character string specifying the column name of the target trait.
anova_results: A structured list derived from upstream ANOVA layouts containing an anova_table.
total_replications: An integer specifying the absolute number of replication blocks (\(r\)).
alpha: A numeric value defining the Type-I error rate probability threshold. Defaults to 0.05.
reporting_level: An integer vector flag defining console trace settings: 0 for silent execution, 1 for summary, and 2 for exhaustive tracking. Defaults to 2.

Value

A structured named list of class "list" containing 4 computational components:

lsd_value: A numeric scalar representing the absolute calculated value of Fisher's Least Significant Difference at the specified alpha level.
sed: A numeric scalar representing the isolated Standard Error of Difference (SED) between two treatment means.
comparison_matrix: A data.frame or NULL layout reserved for detailed pairwise lines differences.
ranked_means: A data.frame containing lines/cultivars sorted by mean performance alongside their assigned statistical significance group letters (LSD_Letters).

Examples

# Load integrated data matrices
data(gv_data, package = "AgriDataTools")

# Total replications matching the experimental design blocks
reps <- length(unique(gv_data$Replication))

# Generating upstream ANOVA structure from gv_data for the target trait (PH)
model_fit <- aov(PH ~ Genotype + Replication, data = gv_data)
anova_summary <- summary(model_fit)[[1]]

mock_anova <- list(
  anova_table = data.frame(
    Source = c("Genotype", "Replication", "Error"),
    Df = anova_summary$Df,
    MS = anova_summary$`Mean Sq`,
    stringsAsFactors = FALSE
  )
)

# Running post-hoc separation sweeps with clean letters group layout
lsd_output <- compute_lsd(
  data = gv_data, 
  trait = "PH", 
  anova_results = mock_anova, 
  total_replications = reps, 
  alpha = 0.05
)
print(lsd_output$ranked_means)
#>    Genotype      Mean LSD_Letters
#> 1       G16 103.66667           a
#> 2        G7 100.83333          ab
#> 3        G3 100.66667          ab
#> 4       G25  99.66667          bc
#> 5       G27  99.66667          bc
#> 6        G9  99.16667         bcd
#> 7        G2  97.50000        bcde
#> 8       G20  97.30000       bcdef
#> 9       G11  96.66667       cdefg
#> 10      G13  96.33333      cdefgh
#> 11      G18  95.33333      defghi
#> 12      G14  95.00000       efghi
#> 13      G23  95.00000       efghi
#> 14       G5  94.33333      efghij
#> 15      G29  93.66667     efghijk
#> 16      G31  93.66667     efghijk
#> 17      G33  93.50000     fghijkl
#> 18      G21  93.33333      ghijkl
#> 19       G1  92.66667      hijklm
#> 20      G22  92.66667      hijklm
#> 21      G38  92.66667      hijklm
#> 22      G26  92.33333       ijklm
#> 23       G8  92.00000       ijklm
#> 24      G15  91.83333       ijklm
#> 25      G17  91.66667       ijklm
#> 26      G30  91.66667       ijklm
#> 27      G40  91.66667       ijklm
#> 28      G37  91.00000       jklmn
#> 29      G24  90.50000      jklmno
#> 30       G4  90.50000      jklmno
#> 31       G6  89.83333       klmno
#> 32      G39  89.66667        lmno
#> 33      G32  89.00000         mno
#> 34      G36  89.00000         mno
#> 35      G19  87.66667         nop
#> 36      G12  87.33333         nop
#> 37      G34  87.33333         nop
#> 38      G10  87.00000          op
#> 39      G28  84.83333           p
#> 40      G35  84.33333           p