Data Normality Calculator

Anderson-Darling Test:

\[ A^2 = -n - \frac{1}{n} \sum_{i=1}^{n} (2i - 1) \left[ \ln(\Phi(Y_i)) + \ln(1 - \Phi(Y_{n+1-i})) \right] \]

Anderson-Darling Statistic (A²):

p-value:

Normality Conclusion (α=0.05):

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1. What is the Anderson-Darling Test?

The Anderson-Darling test is a statistical test used to determine whether a given sample of data comes from a specific probability distribution (in this case, the normal distribution). It's more sensitive to deviations in the tails of the distribution than similar tests like the Kolmogorov-Smirnov test.

2. How Does the Calculator Work?

The calculator uses the Anderson-Darling formula:

\[ A^2 = -n - \frac{1}{n} \sum_{i=1}^{n} (2i - 1) \left[ \ln(\Phi(Y_i)) + \ln(1 - \Phi(Y_{n+1-i})) \right] \]

Where:

\( n \) — Sample size
\( Y_i \) — Ordered standardized data
\( \Phi \) — Standard normal CDF

Explanation: The test compares the empirical distribution function of your data with the expected normal distribution. A larger A² value indicates greater deviation from normality.

3. Interpreting the Results

Key values:

A² statistic: Measures how far your data deviates from normality. Higher values indicate greater deviation.
p-value: The probability of obtaining results at least as extreme as observed if the data is normal. p > 0.05 suggests normality.
Conclusion: Based on comparing p-value to significance level (α=0.05).

4. Using the Calculator

Tips: Enter your numerical data points separated by commas. At least 5 data points are recommended for reliable results. The test works best with sample sizes between 5 and 2000.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Anderson-Darling and Shapiro-Wilk?
A: Both test for normality. Shapiro-Wilk is more powerful for small samples (<50), while Anderson-Darling is better at detecting non-normality in the tails.

Q2: What sample size is needed?
A: Minimum 5 points, but at least 20-30 is recommended for reliable results. Very large samples may show significant deviations even for trivial departures from normality.

Q3: What if my data isn't normal?
A: Consider data transformations (log, square root) or non-parametric statistical methods.

Q4: Can I use this for non-normal distributions?
A: The test specifically checks for normality. Other goodness-of-fit tests exist for different distributions.

Q5: Why does the p-value sometimes show 0.0000?
A: This indicates extremely strong evidence against normality (p < 0.0001).