Should I conduct a normality test (e.g. Shapiro-Wilk test) before conducting every parametric test (e.g. independent T-test, ANOVA or Pearson correlation) despite I have a large sample size (more than 300 N)?
i.e. Can I use parametric tests when I have N more than 30 assuming Central Limit Theorem?
I find Shapiro-Wilk test always significant although I have a large convenience sample size and histogram looks normally distributed (bell shape) which forces me to use non-parametric tests. Should I change my approach and assume normality when I have large sample size in order to use parametric tests?
Thank you
Ali
I suspect you mean the Shapiro-Wilk test of normality, not linearity.
- https://en.wikipedia.org/wiki/Shapiro%E2%80%93Wilk_test
Assuming you do, my thoughts on testing for normality prior to using parametric methods are summarized in this short conference presentation.
Presentation Silly or Pointless Things People Do When Analyzing Data: 1. ...
HTH.
I suspect you mean the Shapiro-Wilk test of normality, not linearity.
- https://en.wikipedia.org/wiki/Shapiro%E2%80%93Wilk_test
Assuming you do, my thoughts on testing for normality prior to using parametric methods are summarized in this short conference presentation.
Presentation Silly or Pointless Things People Do When Analyzing Data: 1. ...
HTH.
The large sample size doesn't mean normality. The distribution can be skewed. The Shapiro-Wilk normality test is a good way to check whether the samples come from a population that has a normal distribution.
The size of the sample can not be used to indicate the normality of the data.
@Ali Azeez Al-Jumaili
Shapiro-wilk test for normality test of the distribution not linearity..when you want to do parametric test of distribution you should go through the normality test of the distribution if normal data is basic assumption of the test...if the the data fails a normality test...you may try data transformation such as log, square root etc...if a transformation is not viable you have to go through the non parametric test...for non parametric test do not requires normality test....
Always Large sample size reduces the probability of non-normality of data.extreme type of non normality always detected with less samples size.but you have large sample size it does not mean data is normally distributed.so you have to go through the normality test.
Sorry for the typo, Yes I meant normality test Dipankar Bera Bruce Weaver
Thank you all for your feedback.
I appreciate your feedback Bruce Weaver and sharing your informative and nice slides
I am puzzled by the answers here. Bruce Weaver provided a useful link, why it is not reasonable to solely rely on statistical tests to check for normality (and it is not about the normality of the data, but the errors (for the test: residuals)!).
Large sample sizes also increase the power of "tests for normality" and hence will be significant, although the deviation may be small. I would neither rely on a single number/test to rule out normality, nor would I rely on rules of thumb that large samples will "fix" deviations from normality. Simulations have shown that this is not necessarily the case (or at least you need larger samples than typically provided by rules of thumb).
Ali Azeez Al-Jumaili already mentioned that his "data" (I assume you checked it correctly) look pretty normal, therefore (without seeing the data) it is plausible the assume normality (please Bruce, provide the Box quote ;-) ) and use according tests. But you should check for extreme outliers (heavy tails), which may cause power problems, if existing, and may be not directly visible in the histograms.
Hi Rainer Duesing. Are you remembering what Box said about normal distributions not existing in nature? See the 2nd paragraph of Section 2.3 here:
http://mkweb.bcgsc.ca/pointsofsignificance/img/Boxonmaths.pdf
Of course I know that there was never a normal distribution or a straight line in nature and that all models are wrong. Maybe I was not clear, I just wanted to defer to you to quote Box, because you did it several times in the past ;-)
And with my statement "...pretty normal, therefore (without seeing the data) it is plausible the assume normality..." I wanted to refer to what is probably "importantly wrong". If it looks normal "enough", I would not ponder all too much.
Sorry Rainer Duesing, I did not mean to suggest that you had forgotten it. I should have asked if that was the quote you were thinking of. ;-)
I always thought that what needs to be normally distributed are the parameters in the sampling distribution. Am I wrong here?
On a funny side note, the claim of the paper in the link (tests for normality don't make sense) is the same claim Hussy and Jain already made in their book in 2002, and I would believe that they got it from Bortz who got it from someone else. Why don't they update the textbooks after two decades?
Dear Ali Azeez Al-Jumaili
If you want to assess if your data normally distributed, I suggest using the Kolmogorov-Smirnov test.
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