for article "Data Series Normalization Techniques" at Medium

stats-normal-distribution-checks.md

Test Name	Null Hypothesis	p-value Criteria	Limitations	Use Cases
Shapiro-Wilk Test	The data is normally distributed.	If p > 0.05, fail to reject H₀; the data is likely normal.	Sensitive to sample size; performance may degrade for large datasets (>5000 samples).	General-purpose normality test for small to medium datasets. A widely used test that checks how well the data aligns with a normal distribution.
Kolmogorov-Smirnov Test (K-S Test)	The data follows a specified distribution (e.g., normal).	If p > 0.05, fail to reject H₀; the data likely matches the specified distribution.	Sensitive to differences in the tails of distributions; less effective for small sample sizes.	Testing goodness-of-fit to any distribution, including normality. Compares the empirical distribution of data to a reference distribution.
Anderson-Darling Test	The data is normally distributed.	Critical values provided; if test statistic < critical value, fail to reject H₀.	Requires predefined significance levels; critical values are dataset-dependent.	Assessing normality in specific use cases requiring stricter tests. Enhances the K-S Test by giving more weight to tails of the distribution.
D’Agostino and Pearson's Test	The data is normally distributed.	If p > 0.05, fail to reject H₀; the data is likely normal.	Sensitive to skewness and kurtosis; less effective for small datasets (<20 samples).	Situations requiring an assessment of skewness and kurtosis for normality. Combines skewness and kurtosis to test for normality, focusing on distribution shape.