## Analysis: DIC experiment in double factorial design with an additional treatment

### Description

Analysis of an experiment conducted in a completely randomized design in a double factorial scheme using analysis of variance of fixed effects.

### Usage

```FAT2DIC.ad(
f1,
f2,
repe,
response,
norm = "sw",
homog = "bt",
mcomp = "tukey",
alpha.f = 0.05,
alpha.t = 0.05,
quali = c(TRUE, TRUE),
grau = NA,
transf = 1,
geom = "bar",
theme = theme_classic(),
ylab = "Response",
xlab = "",
legend = "Legend",
color = "rainbow",
fill = "lightblue",
textsize = 12,
errorbar = TRUE,
CV = TRUE,
dec = 3,
angle = 0,
posi = "right",
family = "sans",
point = "mean_sd",
sup = NA,
ylim = NA,
angle.label = 0
)
```

### Arguments

 `f1` Numeric or complex vector with factor 1 levels `f2` Numeric or complex vector with factor 2 levels `repe` Numeric or complex vector with repetitions `response` Numerical vector containing the response of the experiment. `responseAd` Numerical vector with additional treatment responses `norm` Error normality test (default is Shapiro-Wilk) `homog` Homogeneity test of variances (default is Bartlett) `mcomp` Multiple comparison test (Tukey (default), LSD and Duncan) `alpha.f` Level of significance of the F test (default is 0.05) `alpha.t` Significance level of the multiple comparison test (default is 0.05) `quali` Defines whether the factor is quantitative or qualitative (qualitative) `grau` Degree of polynomial in case of quantitative factor (default is 1) `transf` Applies data transformation (default is 1; for log consider 0) `geom` Graph type (columns or segments (For simple effect only)) `theme` ggplot2 theme (default is theme_classic()) `ylab` Variable response name (Accepts the expression() function) `xlab` Treatments name (Accepts the expression() function) `legend` Legend title name `ad.label` Aditional label `color` Column chart color (default is "rainbow") `fill` Defines chart color (to generate different colors for different treatments, define fill = "trat") `textsize` Font size `addmean` Plot the average value on the graph (default is TRUE) `errorbar` Plot the standard deviation bar on the graph (In the case of a segment and column graph) - default is TRUE `CV` Plotting the coefficient of variation and p-value of Anova (default is TRUE) `dec` Number of cells `angle` x-axis scale text rotation `posi` legend position `family` Font family `point` if quali=F, defines whether to plot all points ("all"), mean ("mean"), standard deviation ("mean_sd") or mean with standard error (default - "mean_se"). `sup` Number of units above the standard deviation or average bar on the graph `ylim` y-axis scale `angle.label` label angle

### Value

The table of analysis of variance, the test of normality of errors (Shapiro-Wilk, Lilliefors, Anderson-Darling, Cramer-von Mises, Pearson and Shapiro-Francia), the test of homogeneity of variances (Bartlett or Levene), the test of independence of Durbin-Watson errors, the test of multiple comparisons (Tukey, LSD, Scott-Knott or Duncan) or adjustment of regression models up to grade 3 polynomial, in the case of quantitative treatments. The column chart for qualitative treatments is also returned.

### Note

The ordering of the graph is according to the sequence in which the factor levels are arranged in the data sheet. The bars of the column and segment graphs are standard deviation.

The function does not perform multiple regression in the case of two quantitative factors.

The assumptions of variance analysis disregard additional treatment

In the final output when transformation (transf argument) is different from 1, the columns resp and respo in the mean test are returned, indicating transformed and non-transformed mean, respectively.

### Author(s)

Gabriel Danilo Shimizu, shimizu@uel.br

Leandro Simoes Azeredo Goncalves

Rodrigo Yudi Palhaci Marubayashi

### References

Principles and procedures of statistics a biometrical approach Steel & Torry & Dickey. Third Edition 1997

Multiple comparisons theory and methods. Departament of statistics the Ohio State University. USA, 1996. Jason C. Hsu. Chapman Hall/CRC.

Practical Nonparametrics Statistics. W.J. Conover, 1999

Ramalho M.A.P., Ferreira D.F., Oliveira A.C. 2000. Experimentacao em Genetica e Melhoramento de Plantas. Editora UFLA.

Scott R.J., Knott M. 1974. A cluster analysis method for grouping mans in the analysis of variance. Biometrics, 30, 507-512.

Mendiburu, F., & de Mendiburu, M. F. (2019). Package ‘agricolae’. R Package, Version, 1-2.

```library(AgroR)