Anderson-Darling Test in R (Quick Normality Check)

Anderson-Darling Test in R, The Anderson-Darling Test is a goodness-of-fit test that determines how well your data fits a given distribution.

This test is most typically used to see if your data follow a normal distribution or not.

This sort of test can be used to check for normality, which is a common assumption in many statistical tests such as regression, ANOVA, and t-tests.

Calculates the Anderson–Darling test statistic for a sample chosen from a specified distribution and determines whether to reject or accept the hypothesis that the sample was drawn from that distribution.

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Anderson-Darling Test in R

For the composite hypothesis of normality, the Anderson-Darling test is used.



x:- a numeric vector of data items with a length greater than seven. Values that are missing are acceptable.

The ad.test() function in the nortest package can be used to perform an Anderson-Darling Test in R.

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If you don’t already have yet installed it, run the command below to install the package and load the nortest library.


Example 1:- mtcars dataset

In R, we can also do an AD-test on a single column of a data frame. Take, for example, the built-in mtcars dataset.

view first six lines of mtcars dataset

                   mpg cyl disp  hp drat    wt  qsec vs am gear carb
Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1

Let’s say we want to see if the variable mpg is normally distributed or not. To visualize the distribution of values, we may first generate a histogram.

hist(mtcars$mpg, col = 'red', main = 'Distribution of mpg',xlab = 'MPG')

Distribution of mpg in mtcars dataset in R

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The data appears to be evenly dispersed. We may use an A-D test to formally check whether the data is normally distributed to confirm this.

conduct Anderson-Darling Test to test for normality

Anderson-Darling normality test
 data:  mtcars$mpg 
A = 0.57968, p-value = 0.1207

We don’t have enough evidence to reject the null hypothesis and infer that mpg follows a normal distribution because the test’s p-value is bigger than 0.05.

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