% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/CRDnsMANOVA.R
\name{CRDnsMANOVA}
\alias{CRDnsMANOVA}
\title{Neutrosophic MANOVA for a Completely Randomized Design}
\usage{
CRDnsMANOVA(Lower_y, Upper_y, group, alpha = 0.05, verbose = TRUE)
}
\arguments{
\item{Lower_y}{A numeric matrix containing the lower bounds of the response
variables. Rows represent observations and columns represent response
variables.}

\item{Upper_y}{A numeric matrix containing the upper bounds of the response
variables. Must have the same dimensions as \code{Lower_y}.}

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

\item{alpha}{Significance level used to obtain the critical F value.
Defaults to \code{0.05}.}

\item{verbose}{Logical; if \code{TRUE}, prints the neutrosophic MANOVA table.
Defaults to \code{TRUE}.}
}
\value{
A list containing the results of the neutrosophic MANOVA with the following
components:
\describe{
\item{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.}
\item{Wilks.Lambda}{A named numeric vector containing the lower and upper
bounds of Wilks' Lambda.}
\item{Approx.F}{A named numeric vector containing the lower and upper
bounds of the approximate F-statistic.}
\item{F.critical}{The critical F value at the specified significance
level.}
\item{Decision}{The hypothesis testing decision ("Significant",
"Not Significant", or "Indeterminate").}
\item{treatment_ss}{A list containing the lower, upper, determinate, and
indeterminate treatment sum of squares matrices.}
\item{total_ss}{A list containing the lower, upper, determinate, and
indeterminate total sum of squares matrices.}
\item{residual_ss}{A list containing the lower, upper, determinate, and
indeterminate residual sum of squares matrices.}
}
}
\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.
}
\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
}
