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Normality test

Source: R/check_normality.R
check_normality.Rd

A wrapper function for the normality tests available in this package.

Usage

check_normality(
  data,
  formula = NULL,
  alpha = 0.05,
  method = "SWR",
  summary = TRUE
)

Arguments

data

A data frame or a numeric vector.

formula

Formula (default: NULL). If data is a data frame, define the val ~ group.

alpha

Numeric (default: 0.05). Significance level used to determine whether the null hypothesis is rejected. Must be between 0 and 1.

method

Character. Abbreviation specifying the normality test to perform. Available options are c("AD", "CVM", "DAP", "JB", "LF", "SW", "SF", "SWR").

summary

Logical (default: TRUE). If TRUE, return a summary table of the test results.

Value

A list.

Details

The method argument specifies the statistical procedure used to assess whether a sample is consistent with a normal distribution. Different tests emphasize different characteristics of departures from normality, such as skewness, kurtosis, or discrepancies in the tails of the distribution. Because no single test performs optimally under all circumstances, the choice of method may depend on sample size and the expected type of non-normality.

Available methods are:

  • "AD": Anderson–Darling test. A modification of the empirical distribution function (EDF) approach that gives greater weight to observations in the tails of the distribution. Compared with several alternative normality tests, the Anderson–Darling procedure is often more sensitive to deviations occurring in extreme values and tail behavior. This test is applicable only for sample sizes n >= 8.

  • "CVM": Cramér–von Mises test. An empirical distribution function (EDF)-based goodness-of-fit test that measures the overall discrepancy between the empirical and theoretical cumulative distribution functions by assigning relatively uniform weight across the entire distribution. Compared with the Anderson–Darling test, the Cramér–von Mises test is generally less sensitive to deviations in the tails but performs well for detecting overall departures from normality. This test is applicable only for sample sizes n >= 8.

  • "DAP": D'Agostino–Pearson test. A combined omnibus moment test based on sample skewness and kurtosis. The procedure transforms the skewness and kurtosis statistics into approximately standard normal variables and combines them into a single test statistic. This method is designed to detect a broad range of departures from normality rather than emphasizing any particular feature. This test is applicable only for sample sizes n >= 20.

  • "JB": Jarque–Bera test. An omnibus moment test based on sample skewness and kurtosis. The test evaluates whether the observed skewness and kurtosis differ significantly from the values expected under a normal distribution. The method is commonly used in econometrics and is generally more appropriate for moderate to large sample sizes.

  • "LF": Lilliefors test. The Lilliefors test is an EDF omnibus test modified from Kolmogorov-Smirnov test for the composite hypothesis of normality. The test statistic is the maximal absolute difference between empirical and hypothetical cumulative distribution function.

  • "SW": Shapiro–Wilk test. The original normality test proposed by Shapiro and Wilk (1965), based on the correlation between ordered observations and their expected values under normality. It is widely regarded as one of the most powerful tests for detecting departures from normality in small samples. Applicable only for sample sizes 3 <= n <= 50.

  • "SF": Shapiro–Francia test. Proposed by Shapiro and Francia (1972) and subsequently simplified and extended by Royston (1993). This method is a computationally simpler modification of the Shapiro–Wilk procedure that performs particularly well for detecting departures associated with heavier-tailed distributions. Applicable only for sample sizes 5 <= n <= 5000.

  • "SWR": Shapiro–Wilk test with Royston's modifications. Uses Royston's (1992) approximations for the null distribution of the Shapiro–Wilk statistic and extends applicability to larger samples while maintaining behavior similar to the original test. Applicable only for sample sizes 3 <= n <= 5000.

In all methods, the null hypothesis is that the sample is drawn from a normal distribution. Small p-values indicate evidence against the assumption of normality.

Examples

out_AD <- check_normality(rnorm(20), method = "AD")
out_DAP <- check_normality(rnorm(20), method = "DAP")
out_SW <- check_normality(rnorm(20), method = "SW")