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

FAT2DBC.ad(
  f1,
  f2,
  block,
  response,
  responseAd,
  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",
  ad.label = "Additional",
  color = "rainbow",
  fill = "lightblue",
  textsize = 12,
  labelsize = 4,
  addmean = TRUE,
  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

block

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)

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 and Duncan)

grau

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

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

labelsize

Label 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 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.

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.

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.

See also

Author

Gabriel Danilo Shimizu, shimizu@uel.br

Leandro Simoes Azeredo Goncalves

Rodrigo Yudi Palhaci Marubayashi

Examples

library(AgroR)
data(cloro)
respAd=c(268, 322, 275, 350, 320)
with(cloro, FAT2DBC.ad(f1, f2, bloco, resp, respAd, 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)  2.047899 0.1769663
#> 
#> 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 (%) =  27.38
#> Mean Factorial =  218.35
#> Median Factorial =  185
#> Mean Aditional =  307
#> Median Aditional =  320
#> Possible outliers =  No discrepant point
#> 
#> -----------------------------------------------------------------
#> Analysis of Variance
#> -----------------------------------------------------------------
#>                Df   Sum Sq    Mean.Sq     F value        Pr(F)
#> Fator1          1  16160.4  16160.400   4.1407431 4.927778e-02
#> Fator2          3 116554.5  38851.500   9.9548327 6.428916e-05
#> block           4  11613.6   2903.400   0.7439317 5.684322e-01
#> Fator1:Fator2   3 452096.2 150698.733  38.6131986 2.411216e-11
#> Ad x Factorial  1 475410.7 475410.700 121.8134178 4.174439e-13
#> Residuals      36 140500.0   3902.778                         
#> 
#> 
#> Your analysis is not valid, suggests using a non-parametric test and try to transform the data
#> 
#> -----------------------------------------------------------------
#> Significant interaction: analyzing the interaction
#> -----------------------------------------------------------------
#>                          Df Sum Sq Mean Sq F value    Pr(>F)    
#> Fator2                    3 116554   38851  9.9548 6.429e-05 ***
#> block                     4  11614    2903  0.7439 0.5684322    
#> Fator2:Fator1             4 468257  117064 29.9951 5.126e-11 ***
#>   Fator2:Fator1: Plantio  1  26112   26112  6.6906 0.0138814 *  
#>   Fator2:Fator1: R1+15    1  70896   70896 18.1656 0.0001393 ***
#>   Fator2:Fator1: V1+15    1 258888  258888 66.3343 1.101e-09 ***
#>   Fator2:Fator1: V3+15    1 112360  112360 28.7898 4.897e-06 ***
#> ---
#> 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)    
#> Fator1               1  16160   16160  4.1407  0.049278 *  
#> block                4  11614    2903  0.7439  0.568432    
#> Fator1:Fator2        6 568651   94775 24.2840 2.774e-11 ***
#>   Fator1:Fator2: IN  3  75470   25157  6.4458  0.001317 ** 
#>   Fator1:Fator2: NI  3 493181  164394 42.1222 7.282e-12 ***
#> ---
#> 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 )