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

FAT2DBC(
f1,
f2,
block,
response,
norm = "sw",
homog = "bt",
alpha.f = 0.05,
alpha.t = 0.05,
quali = c(TRUE, TRUE),
mcomp = "tukey",
grau = c(NA, NA),
grau12 = NA,
grau21 = NA,
transf = 1,
constant = 0,
geom = "bar",
theme = theme_classic(),
ylab = "Response",
xlab = "",
xlab.factor = c("F1", "F2"),
legend = "Legend",
fill = "lightblue",
angle = 0,
textsize = 12,
labelsize = 4,
dec = 3,
width.column = 0.9,
width.bar = 0.3,
family = "sans",
point = "mean_sd",
addmean = TRUE,
errorbar = TRUE,
CV = TRUE,
sup = NA,
color = "rainbow",
posi = "right",
ylim = NA,
angle.label = 0
)

## Arguments

f1

Numeric or complex vector with factor 1 levels

f2

Numeric or complex vector with factor 2 levels

block

Numerical or complex vector with blocks

response

Numerical vector containing the response of the experiment.

norm

Error normality test (default is Shapiro-Wilk)

homog

Homogeneity test of variances (default is Bartlett)

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)

mcomp

Multiple comparison test (Tukey (default), LSD, Scott-Knott and Duncan)

grau

Polynomial degree in case of quantitative factor (default is 1). Provide a vector with two elements.

grau12

Polynomial degree in case of quantitative factor (default is 1). Provide a vector with n levels of factor 2, in the case of interaction f1 x f2 and qualitative factor 2 and quantitative factor 1.

grau21

Polynomial degree in case of quantitative factor (default is 1). Provide a vector with n levels of factor 1, in the case of interaction f1 x f2 and qualitative factor 1 and quantitative factor 2.

transf

Applies data transformation (default is 1; for log consider 0; angular for angular transformation)

constant

Add a constant for transformation (enter value)

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)

xlab.factor

Provide a vector with two observations referring to the x-axis name of factors 1 and 2, respectively, when there is an isolated effect of the factors. This argument uses parse.

legend

Legend title name

fill

Defines chart color (to generate different colors for different treatments, define fill = "trat")

angle

x-axis scale text rotation

textsize

font size

labelsize

label size

dec

number of cells

width.column

Width column if geom="bar"

width.bar

Width errorbar

family

font family

point

This function defines whether the point must have all points ("all"), mean ("mean"), standard deviation (default - "mean_sd") or mean with standard error ("mean_se") if quali= FALSE. For quali=TRUE, mean_sd and mean_se change which information will be displayed in the error bar.

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)

sup

Number of units above the standard deviation or average bar on the graph

color

Column chart color (default is "rainbow")

posi

Legend position

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 order of the chart follows the alphabetical pattern. Please use scale_x_discrete from package ggplot2, limits argument to reorder x-axis. 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.

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.

## References

Principles and procedures of statistics a biometrical approach Steel, Torry and 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., and de Mendiburu, M. F. (2019). Package ‘agricolae’. R Package, Version, 1-2.

## Author

Gabriel Danilo Shimizu, shimizu@uel.br

Leandro Simoes Azeredo Goncalves

Rodrigo Yudi Palhaci Marubayashi

## Examples


#================================================
# Example cloro
#================================================
library(AgroR)
data(cloro)
attach(cloro)
#> The following objects are masked from cloro (pos = 3):
#>
#>     bloco, f1, f2, resp
#> The following object is masked from simulate3:
#>
#>     resp
#> The following object is masked from simulate1:
#>
#>     resp
#> The following object is masked from aristolochia (pos = 6):
#>
#>     resp
#> The following objects are masked from simulate2:
#>
#>     bloco, resp
#> The following objects are masked from laranja:
#>
#>     bloco, resp
#> The following object is masked from aristolochia (pos = 9):
#>
#>     resp
#> The following objects are masked from cloro (pos = 10):
#>
#>     bloco, f1, f2, resp
#> The following object is masked from passiflora:
#>
#>     bloco
FAT2DBC(f1, f2, bloco, resp, ylab="Number of nodules", legend = "Stages")
#>
#> -----------------------------------------------------------------
#> Normality of errors
#> -----------------------------------------------------------------
#>                          Method Statistic   p.value
#>  Shapiro-Wilk normality test(W) 0.9548911 0.1117923
#>
#> As the calculated p-value is greater than the 5% significance level, hypothesis H0 is not rejected. Therefore, errors can be considered normal
#>
#> -----------------------------------------------------------------
#> Homogeneity of Variances
#> -----------------------------------------------------------------
#>                               Method Statistic    p.value
#>  Bartlett test(Bartlett's K-squared)  16.11086 0.02412261
#>
#> As the calculated p-value is less than the 5% significance level, H0 is rejected. Therefore, the variances are not homogeneous
#>
#> -----------------------------------------------------------------
#> Independence from errors
#> -----------------------------------------------------------------
#>                  Method Statistic  p.value
#>  Durbin-Watson test(DW)  2.050729 0.179264
#>
#> As the calculated p-value is greater than the 5% significance level, hypothesis H0 is not rejected. Therefore, errors can be considered independent
#>
#> -----------------------------------------------------------------
#> Additional Information
#> -----------------------------------------------------------------
#>
#> CV (%) =  30.49
#> Mean =  218.35
#> Median =  185
#> Possible outliers =  No discrepant point
#>
#> -----------------------------------------------------------------
#> Analysis of Variance
#> -----------------------------------------------------------------
#>               Df   Sum Sq    Mean.Sq    F value        Pr(F)
#> Fator1         1  16160.4  16160.400  3.6462291 6.649143e-02
#> Fator2         3 116554.5  38851.500  8.7659631 2.933552e-04
#> bloco          4  11613.6   2903.400  0.6550866 6.282168e-01
#> Fator1:Fator2  3 452096.2 150698.733 34.0017642 1.790168e-09
#> Residuals     28 124098.4   4432.086
#>
#>
#>  Your analysis is not valid, suggests using a non-parametric test and try to transform the data
#> -----------------------------------------------------------------
#>
#> Significant interaction: analyzing the interaction
#>
#> -----------------------------------------------------------------
#>
#> -----------------------------------------------------------------
#> Analyzing  F1  inside of each level of  F2
#> -----------------------------------------------------------------
#>                          Df Sum Sq Mean Sq F value    Pr(>F)
#> bloco                     4  11614    2903  0.6551 0.6282168
#> Fator2                    3 116554   38851  8.7660 0.0002934 ***
#> Fator2:Fator1             4 468257  117064 26.4129 3.786e-09 ***
#>   Fator2:Fator1: Plantio  1  26112   26112  5.8916 0.0218981 *
#>   Fator2:Fator1: R1+15    1  70896   70896 15.9962 0.0004207 ***
#>   Fator2:Fator1: V1+15    1 258888  258888 58.4123 2.518e-08 ***
#>   Fator2:Fator1: V3+15    1 112360  112360 25.3515 2.520e-05 ***
#> Residuals                28 124098    4432
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> -----------------------------------------------------------------
#> Analyzing  F2  inside of the level of  F1
#> -----------------------------------------------------------------
#>
#>                     Df Sum Sq Mean Sq F value    Pr(>F)
#> bloco                4  11614    2903  0.6551  0.628217
#> Fator1               1  16160   16160  3.6462  0.066491 .
#> Fator1:Fator2        6 568651   94775 21.3839 2.917e-09 ***
#>   Fator1:Fator2: IN  3  75470   25157  5.6760  0.003625 **
#>   Fator1:Fator2: NI  3 493181  164394 37.0917 6.882e-10 ***
#> Residuals           28 124098    4432
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> -----------------------------------------------------------------
#> Final table
#> -----------------------------------------------------------------
#>     Plantio     R1+15    V1+15    V3+15
#> IN 272.8 aA 236.6 aAB 140.4 bB 304.0 aA
#> NI 170.6 bB   68.2 bB 462.2 aA  92.0 bB
#>
#>
#> Averages followed by the same lowercase letter in the column
#> and uppercase in the row do not differ by the tukey (p< 0.05 )

FAT2DBC(f1, f2, bloco, resp, mcomp="sk", ylab="Number of nodules", legend = "Stages")
#>
#> -----------------------------------------------------------------
#> Normality of errors
#> -----------------------------------------------------------------
#>                          Method Statistic   p.value
#>  Shapiro-Wilk normality test(W) 0.9548911 0.1117923
#>
#> As the calculated p-value is greater than the 5% significance level, hypothesis H0 is not rejected. Therefore, errors can be considered normal
#>
#> -----------------------------------------------------------------
#> Homogeneity of Variances
#> -----------------------------------------------------------------
#>                               Method Statistic    p.value
#>  Bartlett test(Bartlett's K-squared)  16.11086 0.02412261
#>
#> As the calculated p-value is less than the 5% significance level, H0 is rejected. Therefore, the variances are not homogeneous
#>
#> -----------------------------------------------------------------
#> Independence from errors
#> -----------------------------------------------------------------
#>                  Method Statistic  p.value
#>  Durbin-Watson test(DW)  2.050729 0.179264
#>
#> As the calculated p-value is greater than the 5% significance level, hypothesis H0 is not rejected. Therefore, errors can be considered independent
#>
#> -----------------------------------------------------------------
#> Additional Information
#> -----------------------------------------------------------------
#>
#> CV (%) =  30.49
#> Mean =  218.35
#> Median =  185
#> Possible outliers =  No discrepant point
#>
#> -----------------------------------------------------------------
#> Analysis of Variance
#> -----------------------------------------------------------------
#>               Df   Sum Sq    Mean.Sq    F value        Pr(F)
#> Fator1         1  16160.4  16160.400  3.6462291 6.649143e-02
#> Fator2         3 116554.5  38851.500  8.7659631 2.933552e-04
#> bloco          4  11613.6   2903.400  0.6550866 6.282168e-01
#> Fator1:Fator2  3 452096.2 150698.733 34.0017642 1.790168e-09
#> Residuals     28 124098.4   4432.086
#>
#>
#>  Your analysis is not valid, suggests using a non-parametric test and try to transform the data
#> -----------------------------------------------------------------
#>
#> Significant interaction: analyzing the interaction
#>
#> -----------------------------------------------------------------
#>
#> -----------------------------------------------------------------
#> Analyzing  F1  inside of each level of  F2
#> -----------------------------------------------------------------
#>                          Df Sum Sq Mean Sq F value    Pr(>F)
#> bloco                     4  11614    2903  0.6551 0.6282168
#> Fator2                    3 116554   38851  8.7660 0.0002934 ***
#> Fator2:Fator1             4 468257  117064 26.4129 3.786e-09 ***
#>   Fator2:Fator1: Plantio  1  26112   26112  5.8916 0.0218981 *
#>   Fator2:Fator1: R1+15    1  70896   70896 15.9962 0.0004207 ***
#>   Fator2:Fator1: V1+15    1 258888  258888 58.4123 2.518e-08 ***
#>   Fator2:Fator1: V3+15    1 112360  112360 25.3515 2.520e-05 ***
#> Residuals                28 124098    4432
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> -----------------------------------------------------------------
#> Analyzing  F2  inside of the level of  F1
#> -----------------------------------------------------------------
#>
#>                     Df Sum Sq Mean Sq F value    Pr(>F)
#> bloco                4  11614    2903  0.6551  0.628217
#> Fator1               1  16160   16160  3.6462  0.066491 .
#> Fator1:Fator2        6 568651   94775 21.3839 2.917e-09 ***
#>   Fator1:Fator2: IN  3  75470   25157  5.6760  0.003625 **
#>   Fator1:Fator2: NI  3 493181  164394 37.0917 6.882e-10 ***
#> Residuals           28 124098    4432
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> -----------------------------------------------------------------
#> Final table
#> -----------------------------------------------------------------
#>     Plantio    R1+15    V1+15    V3+15
#> IN 272.8 aA 236.6 aA 140.4 bB 304.0 aA
#> NI 170.6 bB  68.2 bC 462.2 aA  92.0 bC
#>
#>
#> Averages followed by the same lowercase letter in the column
#> and uppercase in the row do not differ by the sk (p< 0.05 )

#================================================
# Example covercrops
#================================================
library(AgroR)
data(covercrops)
attach(covercrops)
FAT2DBC(A, B, Bloco, Resp, ylab=expression("Yield"~(Kg~"100 m"^2)),
legend = "Cover crops")
#>
#> -----------------------------------------------------------------
#> Normality of errors
#> -----------------------------------------------------------------
#>                          Method Statistic   p.value
#>  Shapiro-Wilk normality test(W) 0.9758908 0.6061712
#>
#> As the calculated p-value is greater than the 5% significance level, hypothesis H0 is not rejected. Therefore, errors can be considered normal
#>
#> -----------------------------------------------------------------
#> Homogeneity of Variances
#> -----------------------------------------------------------------
#>                               Method Statistic   p.value
#>  Bartlett test(Bartlett's K-squared)  10.19232 0.2517862
#>
#> As the calculated p-value is greater than the 5% significance level, hypothesis H0 is not rejected. Therefore, the variances can be considered homogeneous
#>
#> -----------------------------------------------------------------
#> Independence from errors
#> -----------------------------------------------------------------
#>                  Method Statistic   p.value
#>  Durbin-Watson test(DW)  2.335214 0.3781148
#>
#> As the calculated p-value is greater than the 5% significance level, hypothesis H0 is not rejected. Therefore, errors can be considered independent
#>
#> -----------------------------------------------------------------
#> Additional Information
#> -----------------------------------------------------------------
#>
#> CV (%) =  2.65
#> Mean =  37.4583
#> Median =  37.45
#> Possible outliers =  No discrepant point
#>
#> -----------------------------------------------------------------
#> Analysis of Variance
#> -----------------------------------------------------------------
#>               Df     Sum Sq   Mean.Sq   F value        Pr(F)
#> Fator1         2 146.585000 73.292500 74.645449 4.979960e-11
#> Fator2         2  23.021667 11.510833 11.723318 2.805884e-04
#> bloco          3   2.167500  0.722500  0.735837 5.409183e-01
#> Fator1:Fator2  4   6.008333  1.502083  1.529811 2.252749e-01
#> Residuals     24  23.565000  0.981875
#>
#> -----------------------------------------------------------------
#> No significant interaction
#> -----------------------------------------------------------------
#>
#> -----------------------------------------------------------------
#> F1
#> -----------------------------------------------------------------
#> Multiple Comparison Test: Tukey HSD
#>      resp groups
#> A3 39.800      a
#> A2 37.700      b
#> A1 34.875      c
#>
#>
#>
#> -----------------------------------------------------------------
#> F2
#> -----------------------------------------------------------------
#> Multiple Comparison Test: Tukey HSD
#>        resp groups
#> B3 38.53333      a
#> B1 37.22500      b
#> B2 36.61667      b
#>
#>
#> $residplot #> #>$graph1

#>
#> $graph2 #> FAT2DBC(A, B, Bloco, Resp, mcomp="sk", ylab=expression("Yield"~(Kg~"100 m"^2)), legend = "Cover crops") #> #> ----------------------------------------------------------------- #> Normality of errors #> ----------------------------------------------------------------- #> Method Statistic p.value #> Shapiro-Wilk normality test(W) 0.9758908 0.6061712 #> #> As the calculated p-value is greater than the 5% significance level, hypothesis H0 is not rejected. Therefore, errors can be considered normal #> #> ----------------------------------------------------------------- #> Homogeneity of Variances #> ----------------------------------------------------------------- #> Method Statistic p.value #> Bartlett test(Bartlett's K-squared) 10.19232 0.2517862 #> #> As the calculated p-value is greater than the 5% significance level, hypothesis H0 is not rejected. Therefore, the variances can be considered homogeneous #> #> ----------------------------------------------------------------- #> Independence from errors #> ----------------------------------------------------------------- #> Method Statistic p.value #> Durbin-Watson test(DW) 2.335214 0.3781148 #> #> As the calculated p-value is greater than the 5% significance level, hypothesis H0 is not rejected. Therefore, errors can be considered independent #> #> ----------------------------------------------------------------- #> Additional Information #> ----------------------------------------------------------------- #> #> CV (%) = 2.65 #> Mean = 37.4583 #> Median = 37.45 #> Possible outliers = No discrepant point #> #> ----------------------------------------------------------------- #> Analysis of Variance #> ----------------------------------------------------------------- #> Df Sum Sq Mean.Sq F value Pr(F) #> Fator1 2 146.585000 73.292500 74.645449 4.979960e-11 #> Fator2 2 23.021667 11.510833 11.723318 2.805884e-04 #> bloco 3 2.167500 0.722500 0.735837 5.409183e-01 #> Fator1:Fator2 4 6.008333 1.502083 1.529811 2.252749e-01 #> Residuals 24 23.565000 0.981875 #> #> ----------------------------------------------------------------- #> No significant interaction #> ----------------------------------------------------------------- #> #> ----------------------------------------------------------------- #> F1 #> ----------------------------------------------------------------- #> Multiple Comparison Test: Scott-Knott #> resp groups #> A3 39.800 a #> A2 37.700 b #> A1 34.875 c #> #> #> #> ----------------------------------------------------------------- #> F2 #> ----------------------------------------------------------------- #> Multiple Comparison Test: Scott-Knott #> resp groups #> B3 38.53333 a #> B1 37.22500 b #> B2 36.61667 b #> #> #>$residplot

#>
#> $graph1 #> #>$graph2

#>