Anderson-Darling Test in R, the Anderson-Darling Test is a statistical test used to determine whether a given dataset is drawn from a particular distribution, such as the normal distribution.
In this article, we will demonstrate how to conduct an Anderson-Darling Test in R using inbuilt datasets.
Formulation of the Hypothesis:
Before conducting the Anderson-Darling Test, it is necessary to formulate the null and alternative hypotheses.
The null hypothesis (H0) assumes that the dataset is drawn from a specific distribution. It is usually written as:
H0: The dataset is drawn from the specific distribution.
The alternative hypothesis (H1) assumes that the dataset is not drawn from the specific distribution. It is usually written as:
H1: The dataset is not drawn from the specific distribution.
In the following sections, we will provide examples of how to conduct an Anderson-Darling Test in R.
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Example 1: Testing the Normality of Inbuilt Dataset – ‘mtcars’
In this example, we will use the inbuilt mtcars dataset to test whether the dataset is normally distributed.
First, we will load the mtcars dataset:
data(mtcars)
Next, we can extract a specific variable from the dataset:
mpg <- mtcars$mpg library(nortest)
Then, we can conduct the Anderson-Darling Test using the ‘ad.test’ function:
ad_test <- ad.test(mpg) ad_test Anderson-Darling normality test data: mpg A = 0.57968, p-value = 0.1207
The output will display the test statistic, the p-value, and a conclusion based on the test results.
In this case, because the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the mpg variable of mtcars dataset is normally distributed.
Example 2: Testing the Exponentiality of Inbuilt Dataset – ‘trees’
In this example, we will use the inbuilt trees dataset to test whether the dataset is exponentially distributed.
First, we will load the trees dataset:
data(trees)
Then, we can extract a specific variable from the dataset:
height <- trees$Height
Next, we can conduct the Anderson-Darling Test using the ‘ad.test’ function:
ad_test <- ad.test(height)
Note that we have specified the distribution as “exp” to test if the height variable of the trees dataset is exponentially distributed.
ad_test Anderson-Darling normality test data: height A = 0.35926, p-value = 0.4282
The output will display the test statistic, the p-value, and a conclusion based on the test results.
In this case, because the p-value is less than 0.05, we reject the null hypothesis and conclude that the height variable of the trees dataset is not exponentially distributed.
Conclusion:
In this article, we have demonstrated how to conduct an Anderson-Darling Test in R using inbuilt datasets.
The Anderson-Darling Test is a statistical test used to determine whether a given dataset is drawn from a specific distribution.
By utilizing the examples provided in this article, researchers can use the Anderson-Darling Test to test hypotheses related to the distribution of their datasets.
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