# FANOVA: Computes a FANOVA model by a convenient metric, an exact... In FuzzySTs: Fuzzy Statistical Tools

## Description

Computes a FANOVA model by a convenient metric, an exact calculation or an approximation

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```FANOVA( formula, dataset, data.fuzzified, sig, method, distance.type = "DSGD", i = 1, j = 1, theta = 1/3, thetas = 1, p = 2, q = 0.5, breakpoints = 100, int.method = "int.simpson", plot = TRUE ) ```

## Arguments

 `formula` a description of the model to be fitted. `dataset` the data frame containing all the variables of the model. `data.fuzzified` the fuzzified data set constructed by a call to the function FUZZ or the function GFUZZ, or a similar matrix. `sig` a numerical value representing the significance level of the test. `method` the choices are the following: "distance", "exact", "approximation". `distance.type` type of distance chosen from the family of distances. The different choices are given by: "Rho1", "Rho2", "Bertoluzza", "Rhop", "Delta.pq", "Mid/Spr", "wabl", "DSGD", "DSGD.G", "GSGD". `i` parameter of the density function of the Beta distribution, fixed by default to i = 1. `j` parameter of the density function of the Beta distribution, fixed by default to j = 1. `theta` a numerical value between 0 and 1, representing a weighting parameter. By default, theta is fixed to 1/3 referring to the Lebesgue space. This measure is used in the calculations of the following distances: d_Bertoluzza, d_mid/spr and d_phi-wabl/ldev/rdev. `thetas` a decimal value between 0 and 1, representing the weight given to the shape of the fuzzy number. By default, thetas is fixed to 1. This parameter is used in the calculations of the d_theta star and the d_GSGD distances. `p` a positive integer such that 1 ≤ p < infinity, referring to the parameter of the Rho_p and Delta_pq. By default, p is fixed to 2. `q` a decimal value between 0 and 1, referring to the parameter of the metric Delta_pq. By default, p is fixed to 0.5. `breakpoints` a positive arbitrary integer representing the number of breaks chosen to build the numerical alpha-cuts. It is fixed to 100 by default. `int.method` the method of numerical integration. It is set by default to the Simpson method, i.e. int.method="int.simpson". `plot` fixed by default to "TRUE". plot="FALSE" if a plot of the fuzzy number is not required.

## Value

Returns a list of all the arguments of the function, the total, treatment and residuals sums of squares, the coefficients of the model, the test statistics with the corresponding p-values, and the decision made.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```mat <- matrix(c(1,1,1,1,1,1,1,2,2,2,2,3,2,3,4,2,3,3,2,4), ncol = 2) data <- data.frame(mat) data\$X1 <- factor(data\$X1) MF121 <- TrapezoidalFuzzyNumber(0,1,1,2.2) MF122 <- TrapezoidalFuzzyNumber(1.8,1.9,2.2,2.8) MF123 <- TrapezoidalFuzzyNumber(1.9,2.3,3.1,3.3) MF124 <- TrapezoidalFuzzyNumber(3.1,3.4,4.1,4.2) PA12 <- c(1,2,3,4) data.fuzzified <- GFUZZ(data, 1, 2, PA12, "Identical") formula = X2 ~ X1 res <- FANOVA(formula, dataset = data, method ="distance", data.fuzzified = data.fuzzified, sig = 0.05, distance.type = "wabl") ```

FuzzySTs documentation built on Nov. 23, 2020, 5:11 p.m.