Sounds right to me. From the wiki page, https://en.wikipedia.org/wiki/Shapiro–Wilk_test:Mayhem said:
Thanks. I just wanted to be sure, as I was implementing the formula in Python.Mark44 said:
The Wiki page seems to be saying explicitly that in general ##x_{(i)} \neq x_i##.Mark44 said:
But if the elements of the sequence are already ordered from smallest to largest, then ##x_{(i)} = x_i##.Orodruin said:
Yes, but for computation, finding the special case where ##x_{(i)} = x_i## makes life easier, which I did, and I got the right results when debugging random samples against known calculators.Orodruin said:
The Shapiro-Wilks test is a statistical test used to determine if a given data set follows a normal distribution. It is based on the comparison of the observed data with the expected values from a normal distribution. This test is commonly used in data analysis to check the assumption of normality before performing other statistical tests.
The Shapiro-Wilks test works by calculating a test statistic, W, which measures the discrepancy between the observed data and the expected values from a normal distribution. This test statistic is then compared to a critical value from a table or calculated using statistical software. If the test statistic is less than the critical value, the data is considered to be normally distributed.
The Shapiro-Wilks test is used to determine if a data set follows a normal distribution. This is important because many statistical tests, such as t-tests and ANOVA, assume that the data is normally distributed. If the data is not normally distributed, these tests may produce inaccurate results. Therefore, the Shapiro-Wilks test is used to ensure the validity of these statistical tests.
The Shapiro-Wilks test assumes that the data is independent, continuous, and comes from a normally distributed population. Additionally, the test is most accurate when used with a sample size of at least 3 but less than 5000. If these assumptions are not met, the results of the Shapiro-Wilks test may not be reliable.
The Shapiro-Wilks test uses the order statistic, which is the rank of each data point when the data is sorted in ascending order, to calculate the test statistic, W. The order statistic is used to determine the expected values from a normal distribution, which are then compared to the observed data to determine if the data is normally distributed. Therefore, the Shapiro-Wilks test and the order statistic are closely related in their calculation and interpretation.