The Anderson-Darling test is a statistical test used to determine if a sample comes from a population with a specific distribution. It is particularly useful for assessing whether a dataset follows a normal distribution.
Key Points
- The Anderson-Darling test calculates a statistic that measures how well the data fits the specified distribution.
- The smaller the statistic, the better the data fits the distribution.
- The test provides a p-value that can be used to determine if the null hypothesis (that the data follows the specified distribution) should be rejected.
- If the p-value is less than a chosen significance level (usually 0.05 or 0.10), the null hypothesis is rejected.
Advantages of the Anderson-Darling Test
- It is more sensitive to deviations from normality, especially in the tails of the distribution, compared to other normality tests like the Kolmogorov-Smirnov test.
- It can be applied to complete samples or truncated data, allowing for greater flexibility in data analysis.
- It is efficient for detecting various types of non-normal distributions, including skewed, heavy-tailed, and bimodal distributions.
- The test provides a clear decision criterion based on the calculated test statistic and the corresponding critical values or p-value, facilitating a straightforward interpretation of the results.
Performing the Anderson-Darling Test in Python
You can perform the Anderson-Darling test in Python using the anderson() function from the scipy.stats module. Here’s an example:
import numpy as np
from scipy.stats import anderson
# Generate sample data
data = np.random.normal(loc=0, scale=1, size=100)
# Perform the Anderson-Darling test
result = anderson(data)
# Print the test statistic and critical values
print(f'Statistic: {result.statistic:.3f}')
print('Critical values:')
for i, cv in enumerate(result.critical_values):
print(f'Significance level: {result.significance_levels[i]}%, Critical value: {cv:.3f}')The output will display the test statistic and the critical values for various significance levels. If the test statistic is greater than or equal to a critical value, the null hypothesis (that the data follows the specified distribution) can be rejected at that significance level.
Interpreting the Results
- If the p-value is less than the chosen significance level (e.g., 0.05), the null hypothesis is rejected, indicating that the data does not follow the specified distribution.
- If the p-value is greater than the chosen significance level, there is not enough evidence to reject the null hypothesis, suggesting that the data could follow the specified distribution.
- When comparing the fit of several distributions, the distribution with the lowest Anderson-Darling statistic is considered the best fit, provided the difference is substantial. If the statistics are close, additional criteria, such as probability plots, should be used to choose between them.
By using the Anderson-Darling test, researchers and practitioners can make informed decisions about the appropriateness of parametric tests and ensure the validity of their statistical analyses.
Citations:
[1] https://www.spcforexcel.com/knowledge/basic-statistics/anderson-darling-test-for-normality/
[2] https://leanscape.io/an-introduction-to-the-anderson-darling-normality-test/
[3] https://www.geeksforgeeks.org/how-to-perform-an-anderson-darling-test-in-python/
[4] https://support.minitab.com/en-us/minitab/help-and-how-to/statistics/basic-statistics/supporting-topics/normality/the-anderson-darling-statistic/
[5] https://www.6sigma.us/six-sigma-in-focus/anderson-darling-normality-test/
[6] https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.anderson.html
[7] https://www.itl.nist.gov/div898/handbook/eda/section3/eda35e.htm