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I have three variables and I want to know which of them can be considered to have the normal distribution.

Variable A

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Variable B

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Variable C

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Ferdi
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shosho
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    It's not clear what you mean by "can be considered a normal distribution". None of the variables will actually be normally distributed; the question as to whether they might be close enough to normal for some purpose *depends on that purpose* -- and on a number of other things, none of which you have stated. Why would any of these variables need to have normal distributions? – Glen_b Dec 20 '17 at 03:14
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    The distributions of your variables deviate from a Normal only on the tails. Depending on what you want to do next, this might or might not be a serious problem actually. – wrong_path Dec 20 '17 at 08:14
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    One possible answer: https://stats.stackexchange.com/questions/82579/which-to-believe-kolmogorov-smirnov-test-or-q-q-plot/82584#82584 – Maarten Buis Dec 20 '17 at 09:04
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    You have asked at least two questions about identifying non-normality about QQplots here, and in neither of them have you made your goals clear. You are more likely to get useful feedback (and contribute questions of value) if you 1) combine questions that are essentially identical in their core, 2) make your goals clear, and 3) respond to the requests for clarification that you are getting. – mkt Dec 20 '17 at 10:50

2 Answers2

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The Q-Q plot (quantile-quantile plot) are used for checking normality visually not , obviously, for the quantitative analysis. To check the normality of your distribution (or also the residual distribution in case of test of the GLS or OLS regression) is in the line of teorical quantile distribution (the line). In the case the distribution diverge from the Theorical Quantile the distance reflect the difference from the normali distribution. The "banana" graph is the condition of the case of the estreme value is discoted from the normality. The normality of distribution can to be verified trough many test. The more used is the Shapiro Test but also the Kolmogorov-Smirnov test (K-S test - this test is already descipt in another comment), Jarque-Bera for the time series, ecc.

Luigi Biagini
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A good rule of thumb is for the points to align very closely over the diagonal at least for [-2,2] interval. I am afraid none of the distributions you have there are normal. If you want a more specific answer you can use the Kolmogorov-Smirnov test:

ks.test(varA, pnorm, mean(varA), sd(varA))

The null hypothesis of the test is that varA comes from the specified normal distribution.

oresthes
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