Is data comes from a normal distribution? i am new in statistics but what i learn i can say because points between third and first quantile lie on the qqline. But one thing that confuses me is that boxplot of the (quantile plot data where an outliers is also) has larger whisker to the down side then upside but median lies in center. can someone tell me if data comes from normal distribution?
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$\begingroup$ Why do you need these variables to be normal? $\endgroup$– Glen_bCommented Dec 5, 2016 at 1:35
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$\begingroup$ @Glen_b i want to use test-statistics to compare the means of both variables. Whether mean of X is less than mean of y. $\endgroup$– Khan SaabCommented Dec 5, 2016 at 16:14
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$\begingroup$ 1. There are ways to test for a difference in means without having to assume normality. (for example, via a permutation test) ... 2. However, the t-test is not badly affected by mild deviations from normality; one pretty mild outlier.should present no great problem. There would be little issue with simply performing a t-test $\endgroup$– Glen_bCommented Dec 5, 2016 at 16:59
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$\begingroup$ thanks :-) and i am new in statistics so i know limited methods only :( $\endgroup$– Khan SaabCommented Dec 5, 2016 at 21:49
1 Answer
Your data are probably not exactly normally distributed because few real-world datasets are. However, your question might be better understood as "Are my data normal enough?" The answer depends on the purposes for which you wish to assume a normal distribution, but even without knowing your purpose (you get better answers if you give more detail) I can say from the Q-Q plots that your data are probably normal enough. For many purposes the central limit theorem will negate the influence of minor departures from normality when you are focussed on the mean and when you have lots of data.
This question has an answer that may also be of interest to you: Normality test before testing the difference between two groups. Is it necessary?
(Your confusion seems to relate to the whiskers of the boxplot. That is understandable given that Tukey presented about half a dozen variants of boxplots in the germinal paper and given that there seems to be little consistency in the variants used. However, searching for box and whisker plots on this site will probably help you.)