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D'Agostino–Pearson K2 Normality Test

Source: R/D.Agostino_Pearson_test.R
D.Agostino_Pearson_test.Rd

The D'Agostino–Pearson chi-squared (K2) test is a moment-based omnibus test for normality.

Usage

D.Agostino_Pearson_test(
  x,
  alpha = 0.05,
  alternative = c("two.sided", "less", "greater"),
  silent = FALSE,
  summary = TRUE,
  misc = FALSE
)

Arguments

x

Numeric vector. Must have length at least 20.

alpha

Numeric (default: 0.05). Significance level for hypothesis testing. Must be between 0 and 1.

alternative

Character (default: "two.sided"). Specifies the alternative hypothesis. Available options are c("two.sided", "less", "greater"). Note that this option is only applied to the skewness and kurtosis components of the test.

silent

Logical (default: FALSE). If FALSE, results are printed to the console.

summary

Logical (default: TRUE). Produce a summary table.

misc

Logical (default: FALSE). Output other unimportant parameters.

Value

A list

Details

It evaluates the null hypothesis that the data come from a normal distribution by combining standardized measures of skewness and kurtosis into a single chi-squared test statistic.

References

D’Agostino, R.B., Belanger, A., D’Agostino, R.B., 1990. A Suggestion for Using Powerful and Informative Tests of Normality. Am. Stat. 44, 316–321. https://doi.org/10.1080/00031305.1990.10475751

Examples

out <- D.Agostino_Pearson_test(rnorm(50))
#> 
#> --------------------------------------
#> D'Agostino-Pearson (K2) normality test 
#> 
#> Alternative: two.sided 
#> 
#> Skewness = 0.2137 ;  p-value = 0.4948 
#> Kurtosis = 3.5746 ;  p-value = 0.22623 
#> 
#> Statistic (K2) = 1.9305 
#> p-value = 0.3809
#> --------------------------------------
print(out$summary)
#>                         alpha statistic      pval signif standard_value
#> skewness (sqrt-b1)       0.05 0.2137053 0.4948003     ns      0.6826939
#> kurtosis (b2)            0.05 3.5745950 0.2262337     ns      1.2101177
#> D'Agostino-Pearson (K2)  0.05 1.9304559 0.3808964     ns      1.9304559
#>                         critical_value        SE  CI_lower  CI_upper  N
#> skewness (sqrt-b1)            1.959964 0.3366007 -0.446020 0.8734306 50
#> kurtosis (b2)                 1.959964 0.6619084  2.277278 4.8719116 50
#> D'Agostino-Pearson (K2)       5.991465        NA        NA        NA 50
#>                                AVG        MED       MIN      MAX       SD
#> skewness (sqrt-b1)      0.03656361 0.03804607 -2.274115 2.755418 1.050075
#> kurtosis (b2)           0.03656361 0.03804607 -2.274115 2.755418 1.050075
#> D'Agostino-Pearson (K2) 0.03656361 0.03804607 -2.274115 2.755418 1.050075