README.md

In chrsshn/checknormality: Check the Normality of Data Using Statistical Tests

checknormality: because you should always check your assumptions

Overview

The goal of checknormality is to provide implementations of popular normality tests that return the test statistics and p-values. As of 2020/11/30, the package contains an implementation of the Shapiro-Wilk Test of Normality.

A Note on the Algorithms

Shapiro-Wilk Test

• For n > 50, the J. P. Royston approach for the Shapiro-Wilk test as described here must be used.

• For 3 \<= n \<= 50, there are three “approaches”: the original approach for the Shapiro-Wilk test as described here, a modified approach that is compatible with the Royston approach as described in the last paragraph here, and the Royston approach for n > 20.

Inverse of Normal CDF (Phi inverse)

• The Royston approach requires the inverse of the normal CDF, which is calculated in R using

stats::qnorm(p)

• In the Rcpp implementation of the Royston approach, a freely-available stand-alone C++ implementation was used.

Installation

You can install the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("chrsshn/checknormality")

Usage

Example 1: Testing a small sample from an exponential distribution using the original, modified, and Royston approaches

set1 <- rexp (30, .8)
checknormality::sw_test (set1, "original")
#> 
#>  Shapiro-Wilk Test of Normality
#> 
#> data:  set1
#> W = 0.83101, p-value = 0.001
checknormality::sw_test (set1, "modified")
#> 
#>  Shapiro-Wilk Test of Normality
#> 
#> data:  set1
#> W = 0.83101, p-value = 0.001
checknormality::sw_test (set1, "royston")
#> 
#>  Shapiro-Wilk Test of Normality
#> 
#> data:  set1
#> W = 0.82613, p-value = 2e-04
stats::shapiro.test (set1) 
#> 
#>  Shapiro-Wilk normality test
#> 
#> data:  set1
#> W = 0.82643, p-value = 0.0002067
plot(density (set1))

Note: you can also get the W test statistic using the functions checknormality::R_get_W () and checknormality::C_get_W()

Example 2: Testing a small sample from a normal distribution using the original, modified, and Royston approaches

set2 <- rnorm (40, 20, 5)
checknormality::sw_test (set2, "original")
#> 
#>  Shapiro-Wilk Test of Normality
#> 
#> data:  set2
#> W = 0.96354, p-value = 0.355
checknormality::sw_test (set2, "modified")
#> 
#>  Shapiro-Wilk Test of Normality
#> 
#> data:  set2
#> W = 0.96354, p-value = 0.355
checknormality::sw_test (set2, "royston")
#> 
#>  Shapiro-Wilk Test of Normality
#> 
#> data:  set2
#> W = 0.9722, p-value = 0.4215
stats::shapiro.test (set2)
#> 
#>  Shapiro-Wilk normality test
#> 
#> data:  set2
#> W = 0.96989, p-value = 0.3569
plot(density (set2))   

Example 3: Testing a large sample from a Poisson distribution using the Royston approach

note: the original and modified approaches are only valid for n \< 50 points

set3 <- rpois(4000, .787)
checknormality::sw_test (set3, "royston")
#> 
#>  Shapiro-Wilk Test of Normality
#> 
#> data:  set3
#> W = 0.78822, p-value < 2.2e-16
stats::shapiro.test (set3)
#> 
#>  Shapiro-Wilk normality test
#> 
#> data:  set3
#> W = 0.78829, p-value < 2.2e-16
plot(density (set3))   

Example 4: Testing a large sample from a normal distribution using the Royston approach

note: the original and modified approaches are only valid for n \< 50 points

set4 <- rnorm(4000)
checknormality::sw_test (set4, "royston")
#> 
#>  Shapiro-Wilk Test of Normality
#> 
#> data:  set4
#> W = 0.99926, p-value = 0.1011
stats::shapiro.test (set4)
#> 
#>  Shapiro-Wilk normality test
#> 
#> data:  set4
#> W = 0.99934, p-value = 0.1608
plot(density (set4))   

chrsshn/checknormality documentation built on Dec. 31, 2020, 10:01 p.m.