Kolmogorov Smirnov test is based on the cumulative distribution function. It is used to test whether a distribution conforms to a certain theoretical distribution or compare whether there are significant differences between two empirical distributions. The original hypothesis is that the sample comes from a population subject to normal distribution
The full name of W test is Shapiro Wilk test, which is a correlation based algorithm. A correlation coefficient can be obtained by calculation. The closer it is to 1, the better it shows that the data fit the normal distribution. It is recommended by the national standard gb4882-85 to make the smallest type II error.
W test is a method to check whether the sample conforms to the normal distribution when the sample size is 8 ≤ n ≤ 50. (now the research has re