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There are 2 ways to perform Kolmogorov-Smirnov test in SPSS:

  1. Analyze; Nonparametric Tests; 1-Sample K-S
  2. 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?

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  • $\begingroup$ Just saying "results are different" doesn't tell us (especially people not using SPSS, almost all people here) exactly what you did. There is, I guess, a statistical confusion at the heart of your question, despite its focus on SPSS, but you need to show precise results (ideally, your data too) for us to explain why there is a difference. So, show us the data, the exact command syntax used, and the SPSS results. (At a guess, what you label 1 is not, and does not purport to be, a normality test at all, as Kolmogorov-Smirnov is only a normality test in one application of it.) $\endgroup$ – Nick Cox Jun 14 '15 at 9:12
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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).

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