Package {NeutroSplitStripAnalysis}

Neutrosophic Analysis of Variance for Split-Plot Designs

Description

Performs Neutrosophic Analysis of Variance (NANOVA) for split-plot designs using interval-valued observations. The function provides neutrosophic ANOVA tables, interval-valued F-tests, significance tests, and Least Significant Difference (LSD) based multiple comparisons. For crisp data, users may provide identical lower and upper response values to obtain results equivalent to classical split-plot ANOVA.

Usage

SplitPlotDnsANOVA(Lower_y, Upper_y, design, alpha = 0.05, verbose = FALSE)

Arguments

Value

A list containing:

Split_Plot_NANOVA

Neutrosophic ANOVA table containing sources of variation, degrees of freedom, neutrosophic sums of squares, mean squares, F-statistics, and significance levels.

LSD_MainPlot

Neutrosophic LSD interval for main plot effects, returned only when the main plot effect is significant.

LSD_SubPlot

Neutrosophic LSD interval for sub plot effects, returned only when the sub plot effect is significant.

LSD_Interaction

Neutrosophic LSD interval for interaction effects, returned only when the interaction effect is significant.

Comparison_MainPlot

Pairwise neutrosophic comparisons among main plot treatment means.

Comparison_SubPlot

Pairwise neutrosophic comparisons among sub plot treatment means.

Comparison_Interaction

Pairwise neutrosophic comparisons among interaction treatment means.

Examples

Lower_y <- matrix(c(
  13.81,13.11,18.16,
  18.54,19.84,28.43,
  11.48,14.33,14.29,
  14.50,15.99,21.19,
  11.65,18.08,17.37,
  11.78,12.46,17.21,
  11.67,11.28,8.65,
  18.81,16.27,21.46,
  11.96,16.15,18.19,
  10.34,11.28,16.91,
  9.08,14.91,11.95,
  11.04,10.80,6.48
), ncol = 3, byrow = TRUE)

Upper_y <- matrix(c(
  17.19,21.89,23.44,
  22.46,29.16,31.97,
  19.72,22.07,22.71,
  23.30,24.41,27.81,
  18.35,22.92,20.43,
  20.22,19.14,19.39,
  14.13,17.72,18.35,
  21.59,20.73,29.34,
  19.84,24.85,26.81,
  15.46,15.72,20.09,
  17.92,20.09,17.85,
  13.96,13.00,14.52
), ncol = 3, byrow = TRUE)

Rep <- factor(rep(paste0("R",1:4), each = 9))
MainPlot <- factor(rep(rep(paste0("M",1:3), each = 3), 4))
SubPlot <- factor(rep(paste0("S",1:3), 12))
design <- data.frame(Rep, MainPlot, SubPlot)

result <- SplitPlotDnsANOVA(Lower_y = Lower_y, Upper_y = Upper_y, design = design,
 alpha = 0.05, verbose = TRUE)

Neutrosophic Analysis of Variance for Strip-Plot Designs

Description

Performs Neutrosophic Analysis of Variance (NANOVA) for strip-plot designs using interval-valued observations. The function provides neutrosophic ANOVA tables, interval-valued F-tests, significance tests, and Least Significant Difference (LSD) based multiple comparisons for horizontal factors, vertical factors, and their interaction effects. For crisp data, users may provide identical lower and upper response values to obtain results equivalent to classical strip-plot ANOVA.

Usage

StripPlotDnsANOVA(Lower_y, Upper_y, design, alpha = 0.05, verbose = FALSE)

Arguments

Value

A list containing:

Strip_Plot_NANOVA

Neutrosophic ANOVA table containing sources of variation, degrees of freedom, neutrosophic sums of squares, mean squares, F-statistics, and significance levels.

LSD_Horizontal

Neutrosophic LSD interval for horizontal factor effects, returned only when the horizontal factor effect is significant.

LSD_Vertical

Neutrosophic LSD interval for vertical factor effects, returned only when the vertical factor effect is significant.

LSD_Interaction

Neutrosophic LSD interval for horizontal x vertical interaction effects, returned only when the interaction effect is significant.

Comparison_Horizontal

Pairwise neutrosophic comparisons among horizontal factor treatment means.

Comparison_Vertical

Pairwise neutrosophic comparisons among vertical factor treatment means.

Comparison_Interaction

Pairwise neutrosophic comparisons among horizontal x vertical treatment combinations.

Examples

Lower_y <- matrix(c(
  10,12,
  11,13,
  12,14,
  13,15,
  11,12,
  12,13
), nrow = 6, byrow = TRUE)

Upper_y <- matrix(c(
  12,14,
  13,15,
  14,16,
  15,17,
  13,14,
  14,15
), nrow = 6, byrow = TRUE)

# Strip-plot design
# 2 Replications x 3 Horizontal Factors x 2 Vertical Factors
Rep <- factor(rep(c("R1","R2"), each = 6))
Horizontal <- factor(rep(c("H1","H2","H3"), each = 2, times = 2))
Vertical <- factor(rep(c("S1","S2"), times = 6))
design <- data.frame(Rep, Horizontal, Vertical)

result <- StripPlotDnsANOVA(
  Lower_y = Lower_y,
  Upper_y = Upper_y,
  design = design,
  alpha = 0.05,
  verbose = TRUE
)