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What is the best method for testing for normality? I have a smaller data set today (30 in each group) and on the histograms none of them look normally distributed at all, whereas with the skewness test skewness<2X standard error of skewness, they all appear to be normal. I also did the shapiro wilk test, which told me that 8 out of my nine variables were normally distributed?

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    $\begingroup$ Shapiro-Wilk told you that one of your variables is not normally distributed. It can't tell you if the variables are normally distributed. The opposite of "significant" is "I don't know". $\endgroup$ – Horst Grünbusch Nov 25 '14 at 12:22
  • $\begingroup$ what?im asking which test is the most accurate... $\endgroup$ – Zoe Campbell Nov 25 '14 at 12:29
  • $\begingroup$ im getting the mean of transformational shifts for 9 images for thirty patients, if i use the 270 figures i get very good normal distribution on histograms and pp plot, however I am finding the average per patient and getting the average of that and testing for significance between different image matching technqiues. This means I am getting the mean of 30 mean figures, and the distribution is no longer normal! $\endgroup$ – Zoe Campbell Nov 25 '14 at 12:32
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    $\begingroup$ It depends: there are many ways in which a variable can be non-normal and some test are more sensitive to one type of deviation and others more sensitive to other types of deviations. Why do you want to test for normality? The reason I ask is that it is a very common error to test for normality when you should not do so. If that is also the case for you (very likely), then we have a very simple solution... $\endgroup$ – Maarten Buis Nov 25 '14 at 14:21
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    $\begingroup$ The answer to your previous question validly points out that this issue is irrelevant. $\endgroup$ – whuber Nov 25 '14 at 15:00
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Short answer: there is no BEST method for testing for normality. Different methods are superior than others in (1) detecting different types of departure from normality (2) simplicity and easy to use.

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