分步说明
Sort Your Data
First, sort your data in ascending order. This is necessary because the Anderson-Darling formula requires the data to be in order.
Calculate the Standardized Data Points
Next, calculate the standardized data points by subtracting the mean and dividing by the standard deviation for each data point. This will give you a set of z-scores.
Calculate the Cumulative Distribution Function (CDF)
Calculate the CDF of the standard normal distribution for each standardized data point. This can be done using a standard normal distribution table or a calculator.
Apply the Anderson-Darling Formula
Now, plug the values into the Anderson-Darling formula. Calculate the sum of the logarithms of the CDF and the sum of the logarithms of 1 minus the CDF. Then, calculate the final A² statistic.
Compare to Critical Values
Finally, compare the calculated A² statistic to the critical values for the Anderson-Darling test. If the A² statistic is less than the critical value, you fail to reject the null hypothesis that the data comes from a normal distribution.
Use the Calculator for Convenience
While it is possible to calculate the Anderson-Darling statistic by hand, it is often more convenient to use a calculator or software package. This can save time and reduce the chance of errors.
The Anderson-Darling test is a statistical test used to determine if a dataset comes from a normal distribution. It is often used to check the assumptions of many statistical tests. In this guide, we will walk through the steps to calculate the Anderson-Darling statistic by hand. ## Introduction to the Anderson-Darling Test The Anderson-Darling test is a powerful tool for determining normality. It is based on the idea that if the data comes from a normal distribution, then the cumulative distribution function (CDF) of the data should be close to the CDF of the standard normal distribution. ## The Anderson-Darling Formula The Anderson-Darling statistic is calculated using the following formula: A² = -n - ∑[2i-1]/n * ln(F(x_i)) - ∑[2(n-i)+1]/n * ln(1-F(x_i)) where n is the sample size, x_i is the i-th data point, and F(x_i) is the cumulative distribution function of the standard normal distribution evaluated at x_i.
Step-by-Step Calculation
The steps to calculate the Anderson-Darling statistic by hand are as follows: