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Kurtosis test

Source: R/kurtosis.R
kurtosis.Rd

Performs a kurtosis test to assess whether a distribution deviates from normality in terms of tail heaviness.

Usage

kurtosis(
  x,
  alpha = 0.05,
  alternative = c("two.sided", "less", "greater"),
  method = c("G2", "b2", "g2"),
  silent = FALSE,
  summary = TRUE
)

Arguments

x

Numeric vector containing the input data.

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").

method

Character (default: "G2"). Formula used to estimate kurtosis. Available options are c("G2", "b2", "g2"). The "g2" statistic is the classical sample kurtosis estimator, while "G2" and "b2" are bias-corrected versions of "g2".

silent

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

summary

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

Value

A list

Details

The test evaluates the null hypothesis that the population kurtosis is equal to 3, which is the kurtosis of a normal distribution. Values significantly different from 3 indicate deviations from normality, such as heavy-tailed or light-tailed behavior.

References

Joanes, D.N., Gill, C.A., 1998. Comparing measures of sample skewness and kurtosis. J. R. Stat. Soc. D (The Statistician) 47, 183–189. https://doi.org/10.1111/1467-9884.00122

Wright, D.B., Herrington, J.A., 2011. Problematic standard errors and confidence intervals for skewness and kurtosis. Behav. Res. Methods 43, 8–17. https://doi.org/10.3758/s13428-010-0044-x

Examples

x <- c(10:17, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 15, 15)
kurtosis(x)
#> 
#> --------------------------------------
#> Kurtosis test 
#> 
#> Alternative: two.sided 
#> 
#> Kurtosis (G2) = 3.2743
#> p-value = 0.78222
#> --------------------------------------