Assess univariate and multivariate normality

Install required packages

DescTools, MVN, mvtnorm

Univariate normality

Histogram and density estimate

plot of chunk rerNormality01a
plot of chunk rerNormality01a

QQ-plot

plot of chunk rerNormality01b
plot of chunk rerNormality01b

Skewness and kurtosis

[1] 0.1503207
[1] -0.5277173

Shapiro-Wilk-test

Composite null hypothesis: any normal distribution


    Shapiro-Wilk normality test

data:  DV
W = 0.97894, p-value = 0.7966

Anderson-Darling-test

Composite null hypothesis: any normal distribution


    Anderson-Darling test of goodness-of-fit
    Null hypothesis: uniform distribution

data:  DV
An = Inf, p-value = 2e-05

Cramer-von-Mises-test

Composite null hypothesis: any normal distribution


    Cramer-von Mises normality test

data:  DV
W = 0.028604, p-value = 0.8596

Shapiro-Francia-test

Composite null hypothesis: any normal distribution


    Shapiro-Francia normality test

data:  DV
W = 0.98598, p-value = 0.9015

Jarque-Bera-test

Composite null hypothesis: any normal distribution


    Robust Jarque Bera Test

data:  DV
X-squared = 0.50907, df = 2, p-value = 0.7753

Kolmogorov-Smirnov-test

Exact null hypothesis: fully specified normal distribution


    One-sample Kolmogorov-Smirnov test

data:  DV
D = 0.15182, p-value = 0.4498
alternative hypothesis: two-sided

Lilliefors-test

Composite null hypothesis: any normal distribution


    Lilliefors (Kolmogorov-Smirnov) normality test

data:  DV
D = 0.091059, p-value = 0.7587

Pearson \(\chi^{2}\)-test

Tests weaker null hypothesis (any distribution with the same probabilities for the given class intervals).

Cave: Strictly speaking, result is incorrect: PearsonTest() does not use grouped ML-estimate or maximum \(\chi^{2}\)-estimate of the mean and standard deviation.


    Pearson chi-square normality test

data:  DV
P = 1.2, p-value = 0.753

Multivariate normality

Energy-test

         Test Statistic p value MVN
1 E-statistic  1.026584    0.08 YES

Mardia skewness and kurtosis test

             Test         Statistic           p value Result
1 Mardia Skewness  14.0883039547516 0.169001764623724    YES
2 Mardia Kurtosis 0.110806002772418 0.911770185144381    YES
3             MVN              <NA>              <NA>    YES

Detach (automatically) loaded packages (if possible)

Get the article source from GitHub

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