Difference between the two way of performing Kolmogorov-Smirnov normality test There are 2 ways to perform Kolmogorov-Smirnov test in SPSS:


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*Analyze; Nonparametric Tests; 1-Sample K-S

*Analyze; Descriptive Statistics; Explore; Plots; Normality plots with tests


What is the difference between these two tests?
Their results are different! When should we use each of them?
 A: Note that the Kolmogorov-Smirnov test is for a fully specified distribution; it would not be suitable for a general test of normality. 
Typically, for a general normal with unspecified mean and standard deviation the data will have been standardized by sample-based estimates of the mean and standard deviation.
My guess is that when used as a general normality test, they're actually performing a Lilliefors test - which is suitable when estimating the parameters from the sample (making the statistic no longer distributed like a Kolmogorov-Smirnov statistic).  The Lilliefors test will have smaller critical values for a given significance level.
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Looking at help on normality testing in SPSS, it looks like the "Analyze $\rightarrow$ Descriptive Statistics $\rightarrow$ Explore" route gets you a Lilliefors test. The other approach seems to be largely deprecated, and judging from comments in other fora was highly conservative. This suggests that what was done may have been using Kolmogorov-Smirnov tables to assess significance when dealing with the situation under Lilliefors (which would indeed be quite conservative).
