Help for package NeutroBasicDesignsAnalysis

Type:

Package

Title:

Neutrosophic Analysis of Completely Randomized Designs and Randomized Complete Block Designs

Version:

0.0.1

Maintainer:

Vinaykumar L.N. <vinaymandya123@gmail.com>

Description:

Provides neutrosophic statistical methods for interval-valued data from completely randomized and randomized complete block designs. Methods include neutrosophic analysis of variance, analysis of covariance, multivariate analysis of variance, pooled analysis of variance, Levene's test, and Aitken transformation. When the lower and upper bounds are equal (crisp data), the methods reduce to their corresponding classical statistical analyses. The basic concept of neutrosophic statistics is based on Smarandache (2014) https://fs.unm.edu/NeutrosophicStatistics.pdf, while the statistical analysis procedures implemented in this package are newly developed.

License:

GPL (≥ 3)

Encoding:

UTF-8

Imports:

MASS, stats

RoxygenNote:

7.3.3

NeedsCompilation:

Packaged:

2026-08-05 04:16:59 UTC; admin

Author:

Neethu R.S. [aut, ctb], Boyina Devi Priyanka [aut, ctb], Cini Varghese [aut, ctb], Susheel Kumar Sarkar [aut, ctb], Mohd Harun [aut, ctb], Vinaykumar L.N. [aut, cre], Anindita Datta [aut, ctb]

Repository:

CRAN

Date/Publication:

2026-08-09 08:40:13 UTC

Neutrosophic Analysis of Covariance for Completely Randomized Design

Description

Performs Neutrosophic Analysis of Covariance (NANCOVA) for interval-valued response and covariate data from a Completely Randomized Design (CRD).

Usage

CRDnsANCOVA(
  Lower_y,
  Upper_y,
  Lower_z,
  Upper_z,
  design,
  alpha = 0.05,
  verbose = FALSE
)

Arguments

Lower_y

Numeric matrix of lower bounds of the response variable.

Upper_y

Numeric matrix of upper bounds of the response variable.

Lower_z

Numeric matrix of lower bounds of the covariate.

Upper_z

Numeric matrix of upper bounds of the covariate.

design

Numeric matrix representing the CRD treatment layout.

alpha

Significance level for interval-based LSD comparisons. Default is 0.05.

verbose

Logical. If TRUE, prints the NANCOVA table and LSD comparisons.

Value

A list containing the Neutrosophic ANCOVA table, interval LSD comparisons (if treatment effects are significant), and the interval LSD value.

Examples

Lower_y <- matrix(c(
  20,25,30,35,
  21,26,31,36,
  19,24,29,34,
  20,25,30,35,
  21,26,31,36
), nrow = 5, byrow = TRUE)

Upper_y <- matrix(c(
  22,27,32,37,
  23,28,33,38,
  21,26,31,36,
  22,27,32,37,
  23,28,33,38
), nrow = 5, byrow = TRUE)

Lower_z <- matrix(c(
  8,9,10,11,
  9,10,11,12,
  8,9,10,11,
  9,10,11,12,
  8,9,10,11
), nrow = 5, byrow = TRUE)

Upper_z <- matrix(c(
  9,10,11,12,
  10,11,12,13,
  9,10,11,12,
  10,11,12,13,
  9,10,11,12
), nrow = 5, byrow = TRUE)

design <- matrix(c(
  1,2,3,4,
  1,2,3,4,
  1,2,3,4,
  1,2,3,4,
  1,2,3,4
), nrow = 5, byrow = TRUE)

CRDnsANCOVA(Lower_y, Upper_y, Lower_z, Upper_z, design)

Neutrosophic Analysis of Variance for Completely Randomized Design

Description

Performs neutrosophic analysis of variance (NANOVA) for a completely randomized design using interval-valued observations.

Usage

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

Arguments

Lower_y

Matrix of lower bounds of the response variable.

Upper_y

Matrix of upper bounds of the response variable.

design

Matrix specifying treatment allocation.

alpha

Significance level for LSD test.

verbose

Logical. If TRUE, prints the analysis.

Value

A list containing the NANOVA table, treatment means, pairwise comparisons, and LSD interval.

Examples

Lower_y <- matrix(c(
  9.5, 19.5, 29.5, 39.5,
  10.0, 20.0, 30.0, 40.0,
  10.5, 20.5, 30.5, 40.5,
  9.8, 19.8, 29.8, 39.8,
  10.2, 20.2, 30.2, 40.2
), nrow = 5, byrow = TRUE)

Upper_y <- matrix(c(
  10.5, 20.5, 30.5, 40.5,
  11.0, 21.0, 31.0, 41.0,
  11.5, 21.5, 31.5, 41.5,
  10.8, 20.8, 30.8, 40.8,
  11.2, 21.2, 31.2, 41.2
), nrow = 5, byrow = TRUE)

design <- matrix(c(
  1, 2, 3, 4,
  1, 2, 3, 4,
  1, 2, 3, 4,
  1, 2, 3, 4,
  1, 2, 3, 4
), nrow = 5, byrow = TRUE)

CRDnsANOVA(
  Lower_y = Lower_y,
  Upper_y = Upper_y,
  design = design,
  alpha = 0.05,
  verbose = TRUE
)

Neutrosophic MANOVA for a Completely Randomized Design

Description

Performs neutrosophic multivariate analysis of variance (MANOVA) for interval-valued multivariate observations under a completely randomized design using Wilks' Lambda as the multivariate test criterion.

Usage

CRDnsMANOVA(Lower_y, Upper_y, group, alpha = 0.05, verbose = TRUE)

Arguments

Lower_y

A numeric matrix containing the lower bounds of the response variables. Rows represent observations and columns represent response variables.

Upper_y

A numeric matrix containing the upper bounds of the response variables. Must have the same dimensions as Lower_y.

group

A vector or factor identifying the treatment group for each observation. Its length must equal nrow(Lower_y).

alpha

Significance level used to obtain the critical F value. Defaults to 0.05.

verbose

Logical; if TRUE, prints the neutrosophic MANOVA table. Defaults to TRUE.

Value

A list containing the results of the neutrosophic MANOVA with the following components:

MANOVA.table: A data frame containing the neutrosophic MANOVA table, including the source of variation, degrees of freedom, Wilks' Lambda interval, approximate F-statistic interval, and decision.
Wilks.Lambda: A named numeric vector containing the lower and upper bounds of Wilks' Lambda.
Approx.F: A named numeric vector containing the lower and upper bounds of the approximate F-statistic.
F.critical: The critical F value at the specified significance level.
Decision: The hypothesis testing decision ("Significant", "Not Significant", or "Indeterminate").
treatment_ss: A list containing the lower, upper, determinate, and indeterminate treatment sum of squares matrices.
total_ss: A list containing the lower, upper, determinate, and indeterminate total sum of squares matrices.
residual_ss: A list containing the lower, upper, determinate, and indeterminate residual sum of squares matrices.

Examples

YL <- matrix(c(8.27, 2.50, 5.30, 1.41,
               8.40, 6.27, 0.00, 3.42),
             ncol = 2, byrow = TRUE)

YU <- matrix(c(9.73, 3.50, 6.70, 2.59,
               9.60, 7.73, 0.00, 4.58),
             ncol = 2, byrow = TRUE)

g <- c(1, 1, 2, 2)

fit <- CRDnsMANOVA(
  Lower_y = YL,
  Upper_y = YU,
  group = g
)

fit$MANOVA.table
fit$Decision

Pooled Neutrosophic ANOVA for a Completely Randomized Design

Description

Performs pooled neutrosophic analysis of variance for a completely randomized design.

Usage

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

Arguments

Lower_y

Numeric matrix of lower response bounds. Columns must be arranged in consecutive year or location blocks, each containing all treatments.

Upper_y

Numeric matrix of upper response bounds.

design

Numeric treatment-layout matrix with the same dimensions as Lower_y.

alpha

Significance level. Default is 0.05.

verbose

Logical; print results when TRUE.

Value

A list containing the initial and final NANOVA tables, interaction test, decision, and pooled MSE when applicable.

Examples

# Three replications, three treatments, and two years.
# Columns 1-3 are Year 1; columns 4-6 are Year 2.

Lower_y <- matrix(c(
  20, 25, 30, 21, 26, 31,
  22, 27, 32, 23, 28, 33,
  21, 26, 31, 22, 27, 32
), nrow = 3, byrow = TRUE)

Upper_y <- matrix(c(
  22, 27, 32, 23, 28, 33,
  24, 29, 34, 25, 30, 35,
  23, 28, 33, 24, 29, 34
), nrow = 3, byrow = TRUE)

# Treatment layout:
# Year 1 = Treatments 1, 2, 3
# Year 2 = Treatments 1, 2, 3
design <- matrix(c(
  1, 2, 3, 1, 2, 3,
  1, 2, 3, 1, 2, 3,
  1, 2, 3, 1, 2, 3
), nrow = 3, byrow = TRUE)

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

result$NANOVA.table

Pooled Neutrosophic Analysis of Variance for a Randomized Block Design

Description

Performs the pooled neutrosophic ANOVA calculation for interval-valued observations measured in a Randomized Block Design over multiple years or locations or seasons.

Usage

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

Arguments

Lower_y

Numeric matrix of lower response bounds. Columns must be ordered in consecutive year blocks, each containing all treatments.

Upper_y

Numeric matrix of upper response bounds, with the same dimensions as Lower_y.

design

Numeric matrix giving the treatment labels for Lower_y.

alpha

Significance level for the treatment-by-year interaction test.

verbose

Logical; print the neutrosophic ANOVA table when TRUE.

Value

An invisible list containing the neutrosophic ANOVA table, interaction F interval and critical value, interaction decision, and the mean-square interval used for subsequent F intervals.

Examples

# Three blocks, three treatments, and two years.
# Columns 1-3 are Year 1; columns 4-6 are Year 2.
# Each block contains every treatment once in each year.

Lower_y <- matrix(c(
  20, 25, 30, 22, 28, 23,
  27, 32, 21, 33, 24, 29,
  31, 22, 26, 25, 30, 34
), nrow = 3, byrow = TRUE)

Upper_y <- matrix(c(
  22, 27, 32, 24, 30, 25,
  29, 34, 23, 35, 26, 31,
  33, 24, 28, 27, 32, 36
), nrow = 3, byrow = TRUE)

# Treatment layout for each block:
# Year 1 occupies columns 1-3.
# Year 2 occupies columns 4-6.
design <- matrix(c(
  1, 2, 3, 2, 3, 1,
  2, 3, 1, 3, 1, 2,
  3, 1, 2, 1, 2, 3
), nrow = 3, byrow = TRUE)

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

result$NANOVA.table

Neutrosophic Analysis of Covariance for RCBD

Description

Performs neutrosophic analysis of covariance for a Randomized Complete Block Design using interval-valued response and covariate data.

Usage

RCBDnsANCOVA(
  Lower_y,
  Upper_y,
  Lower_z,
  Upper_z,
  design,
  alpha = 0.05,
  verbose = FALSE
)

Arguments

Lower_y

Numeric matrix of lower response values.

Upper_y

Numeric matrix of upper response values.

Lower_z

Numeric matrix of lower covariate values.

Upper_z

Numeric matrix of upper covariate values.

design

Numeric matrix representing the RCBD layout.

alpha

Significance level for LSD test. Default is 0.05.

verbose

Logical; if TRUE, prints the analysis. Default is FALSE.

Value

A list containing the NANCOVA table, LSD interval, and treatment comparisons (if treatment effect is significant).

Examples

Lower_y <- matrix(c(
  46.84, 97.69, 39.30, 49.20,
  51.52, 83.38, 56.48, 42.15,
  44.42, 49.64, 44.21, 35.79,
  32.77, 74.30, 55.72, 70.55
), nrow = 4, byrow = TRUE)

Upper_y <- matrix(c(
  49.66,101.31,47.70,55.80,
  60.98,87.62,60.52,44.85,
  52.26,59.36,52.79,44.61,
  42.23,82.70,59.28,75.45
), nrow = 4, byrow = TRUE)

Lower_z <- matrix(c(
  224.95,245.87,245.19,259.41,
  222.06,213.83,253.10,247.51,
  255.67,230.55,265.05,246.67,
  137.98,214.68,251.49,257.70
), nrow = 4, byrow = TRUE)

Upper_z <- matrix(c(
  229.05,250.13,252.81,268.59,
  229.94,222.17,258.90,256.49,
  262.33,237.45,274.95,249.33,
  142.02,219.32,260.51,264.30
), nrow = 4, byrow = TRUE)

design <- matrix(c(
  1,2,3,4,
  1,2,3,4,
  1,2,3,4,
  1,2,3,4
), nrow = 4, byrow = TRUE)

result <- RCBDnsANCOVA(
  Lower_y,
  Upper_y,
  Lower_z,
  Upper_z,
  design,
  alpha = 0.05,
  verbose = TRUE
)

Neutrosophic Analysis of Variance for Randomized Complete Block Design

Description

Performs Neutrosophic Analysis of Variance (NANOVA) for interval-valued response data from a Randomized Complete Block Design (RCBD).

Usage

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

Arguments

Lower_y

Numeric matrix of lower bounds of the response variable.

Upper_y

Numeric matrix of upper bounds of the response variable.

design

Numeric matrix representing the RCBD layout.

alpha

Significance level for interval-based LSD test. Default is 0.05.

verbose

Logical. If TRUE, prints the NANOVA table and LSD comparisons.

Value

A list containing the Neutrosophic ANOVA table, interval-based LSD comparisons (if applicable), and the interval LSD.

Examples

Lower_y <- matrix(c(
  120.230,125.488,132.987,127.086,127.672,128.013,
  122.594,121.009,123.969,120.358,120.424,122.197,
  121.183,130.671,128.794,114.863,122.595,122.073,
  127.620,124.532,132.893,125.528,125.850,127.550
), nrow = 4, byrow = TRUE)

Upper_y <- matrix(c(
  127.6967536,131.2116955,141.2127373,136.1540904,130.6884772,136.8474149,
  129.8264289,130.3314544,133.3113414,126.5063118,128.4362999,130.2714433,
  124.5068016,139.3287297,134.1060197,124.2774447,127.2248520,130.3948469,
  131.0638721,129.8884785,135.5666716,127.7580663,132.0178679,133.3903886
), nrow = 4, byrow = TRUE)

design <- matrix(c(
  1,2,3,4,5,6,
  1,2,3,4,5,6,
  1,2,3,4,5,6,
  1,2,3,4,5,6
), nrow = 4, byrow = TRUE)

RCBDnsANOVA(Lower_y, Upper_y, design)

Aitken Transformation for Neutrosophic Interval Data

Description

Applies an Aitken variance-stabilizing transformation to interval-valued observations using group-specific interval MSE values.

Usage

nsAitkenTransform(Lower_y, Upper_y, group, MSE_lower, MSE_upper)

Arguments

Lower_y

Numeric matrix of lower interval bounds.

Upper_y

Numeric matrix of upper interval bounds.

group

Vector identifying the group/year for every row of the input.

MSE_lower

Numeric vector of lower MSE bounds, one per group.

MSE_upper

Numeric vector of upper MSE bounds, one per group.

Value

A list containing transformed lower/upper matrices and their determinate and indeterminate components.

Examples

Lower_y <- matrix(
  c(8.2, 5.1,
    7.9, 5.4,
    9.0, 6.2,
    8.8, 6.0,
    7.5, 4.8,
    7.8, 5.0,
    8.6, 5.8,
    8.4, 5.6),
  ncol = 2,
  byrow = TRUE
)

Upper_y <- matrix(
  c(8.8, 5.7,
    8.5, 6.0,
    9.6, 6.8,
    9.4, 6.6,
    8.1, 5.4,
    8.4, 5.6,
    9.2, 6.4,
    9.0, 6.2),
  ncol = 2,
  byrow = TRUE
)

group <- rep(1:4, each = 2)

transformed <- nsAitkenTransform(
  Lower_y = Lower_y,
  Upper_y = Upper_y,
  group = group,
  MSE_lower = c(29.83, 16.30, 21.21, 3.62),
  MSE_upper = c(30.02, 16.43, 21.24, 3.89)
)

transformed$weights

Neutrosophic Levene's Test for Interval-Valued Data

Description

Tests homogeneity of variances for interval-valued observations using neutrosophic lower and upper test-statistic bounds.

Usage

nsLeveneTest(Lower_y, Upper_y, design, alpha = 0.05, verbose = TRUE)

Arguments

Lower_y

Numeric matrix of lower interval bounds.

Upper_y

Numeric matrix of upper interval bounds; same dimensions as Lower_y.

design

Treatment-design matrix. Treatment labels in each row must be arranged in consecutive year blocks.

alpha

Significance level. Default is 0.05.

verbose

Logical; print the test table when TRUE.

Value

An invisible list containing the Levene statistic interval, critical F value, homogeneity decision, and ANOVA table.

Examples

# Two replications, three treatments, and two years.
# Columns are ordered as:
# Year 1 (T1, T2, T3), Year 2 (T1, T2, T3).

Lower_y <- matrix(c(
  10, 12, 11, 13, 14, 12,
   9, 11, 10, 12, 13, 11
), nrow = 2, byrow = TRUE)

Upper_y <- matrix(c(
  12, 14, 13, 15, 16, 14,
  11, 13, 12, 14, 15, 13
), nrow = 2, byrow = TRUE)

design <- matrix(c(
  1, 2, 3, 1, 2, 3,
  1, 2, 3, 1, 2, 3
), nrow = 2, byrow = TRUE)

levene_result <- nsLeveneTest(
  Lower_y = Lower_y,
  Upper_y = Upper_y,
  design = design,
  alpha = 0.05,
  verbose = TRUE
)

levene_result$Homogeneity

Package {NeutroBasicDesignsAnalysis}

Neutrosophic Analysis of Covariance for Completely Randomized Design

Description

Usage

Arguments

Value

Examples

Neutrosophic Analysis of Variance for Completely Randomized Design

Description

Usage

Arguments

Value

Examples

Neutrosophic MANOVA for a Completely Randomized Design

Description

Usage

Arguments

Value

Examples

Pooled Neutrosophic ANOVA for a Completely Randomized Design

Description

Usage

Arguments

Value

Examples

Pooled Neutrosophic Analysis of Variance for a Randomized Block Design

Description

Usage

Arguments

Value

Examples

Neutrosophic Analysis of Covariance for RCBD

Description

Usage

Arguments

Value

Examples

Neutrosophic Analysis of Variance for Randomized Complete Block Design

Description

Usage

Arguments

Value

Examples

Aitken Transformation for Neutrosophic Interval Data

Description

Usage

Arguments

Value

Examples

Neutrosophic Levene's Test for Interval-Valued Data

Description

Usage

Arguments

Value

Examples