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# Help! How close to the figures does your data have be to fit the normal distribution? watch

1. 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?
2. Context?
3. Necessary but not sufficient
4. 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)

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Updated: February 19, 2016
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