Visualisation of the normality distribution of the standardised residuals of the ANOVA

vis_anova_assumptions checks for normality of the standardised residuals of the ANOVA. Both the Shapiro-Wilk test shapiro.test() and the Anderson-Darling test ad.test() check the null that the standardised residuals are normally distributed. It generates a scatter plot of the standardised residuals versus the fitted mean values of the linear models for each level of fact. Furthermore a normal QQ plot of the standardised residuals is generated. The null of homogeneity of variances of each factor level is tested with the bartlett.test().

Usage

vis_anova_assumptions(
  samples,
  fact,
  conf.level = 0.95,
  samplename = "",
  factorname = "",
  cex = 1
)

Arguments

samples

vector containing dependent variable, datatype numeric

fact

vector containing independent variable, datatype factor

conf.level

confidence level, 0.95=default

samplename

name of sample used in graphical output, dataype character , ""=default

factorname

name of sample used in graphical output, dataype character, ""=default

cex

number indicating the amount by which plotting text and symbols should be scaled relative to the default. 1=default, 1.5 is 50% larger, 0.5 is 50% smaller, etc.

Value

list containing the test statistics of the anova, the p values generated by the Shapiro-Wilk test shapiro.test(), the Anderson-Darling test ad.test() and the bartlett.test().

Examples

ToothGrowth$dose <- as.factor(ToothGrowth$dose)
vis_anova_assumptions(ToothGrowth$len, ToothGrowth$dose)

#> $summary_anova
#>             Df Sum Sq Mean Sq F value   Pr(>F)    
#> fact         2   2426    1213   67.42 9.53e-16 ***
#> Residuals   57   1026      18                     
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> $shapiro_test
#> 
#> 	Shapiro-Wilk normality test
#> 
#> data:  rstandard(anova)
#> W = 0.96731, p-value = 0.1076
#> 
#> 
#> $ad_test
#> 
#> 	Anderson-Darling normality test
#> 
#> data:  rstandard(anova)
#> A = 0.68679, p-value = 0.06928
#> 
#> 
#> $bartlett_test
#> 
#> 	Bartlett test of homogeneity of variances
#> 
#> data:  samples by fact
#> Bartlett's K-squared = 0.66547, df = 2, p-value = 0.717
#> 
#> 

vis_anova_assumptions(ToothGrowth$len, ToothGrowth$supp)

#> $summary_anova
#>             Df Sum Sq Mean Sq F value Pr(>F)  
#> fact         1    205  205.35   3.668 0.0604 .
#> Residuals   58   3247   55.98                 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> $shapiro_test
#> 
#> 	Shapiro-Wilk normality test
#> 
#> data:  rstandard(anova)
#> W = 0.96949, p-value = 0.1378
#> 
#> 
#> $ad_test
#> 
#> 	Anderson-Darling normality test
#> 
#> data:  rstandard(anova)
#> A = 0.51449, p-value = 0.185
#> 
#> 
#> $bartlett_test
#> 
#> 	Bartlett test of homogeneity of variances
#> 
#> data:  samples by fact
#> Bartlett's K-squared = 1.4217, df = 1, p-value = 0.2331
#> 
#> 
vis_anova_assumptions(iris$Petal.Width, iris$Species)

#> $summary_anova
#>              Df Sum Sq Mean Sq F value Pr(>F)    
#> fact          2  80.41   40.21     960 <2e-16 ***
#> Residuals   147   6.16    0.04                   
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> $shapiro_test
#> 
#> 	Shapiro-Wilk normality test
#> 
#> data:  rstandard(anova)
#> W = 0.97217, p-value = 0.003866
#> 
#> 
#> $ad_test
#> 
#> 	Anderson-Darling normality test
#> 
#> data:  rstandard(anova)
#> A = 1.8447, p-value = 9.831e-05
#> 
#> 
#> $bartlett_test
#> 
#> 	Bartlett test of homogeneity of variances
#> 
#> data:  samples by fact
#> Bartlett's K-squared = 39.213, df = 2, p-value = 3.055e-09
#> 
#>