1sd of the mean has to contain 68% of data, 2sd's 95% and 3sd's 99.8%.
How close does your data have to be to these %'s in order to be normally distributed?
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- Thread Starter
Last edited by Snake_God; 23-02-2016 at 00:25.
- 19-02-2016 21:15
- 19-02-2016 21:16
- 19-02-2016 21:24
Necessary but not sufficient
- 19-02-2016 21:28
If there are doubts that the data is Normal then its usually better to just assume that it isnt, and use nonparametric procedures instead (eg Mann Whitney tests rather than T-tests, and so on).
If you want to check whether its Normal, then the usual procedure is to use a Goodness-of-Fit test like Shapiro-Wilk or Jacques-Bera.
Looking at how many observations fall within 1/2/3 standard deviations isnt a great procedure - the usual reason why data fails to be Normal is becuase it has non-zero kurtosis or skewness (3rd and fourth moments). The Jacques Bera test checks this directly, Shapiro-Wilk is more indirect (but is generally considered a more powerful test)