most recent 30 from http://mathoverflow.net 2013-05-24T21:43:08Z http://mathoverflow.net/feeds/question/63972 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/63972/fit-to-a-normal-distribution unknown (google) 2011-05-05T03:34:22Z 2011-05-05T19:37:14Z

<p>I have some data points and, when I plot them on R, it looks like a normal distribution. I want to know how well my data fits the normal distribution. What kind of test should I do ?</p>

http://mathoverflow.net/questions/63972/fit-to-a-normal-distribution/63973#63973 Brian Borchers 2011-05-05T04:07:13Z 2011-05-05T04:07:13Z

<p>There's actually a much broader question that you should be asking yourself here- does it matter whether your data really is normally distributed, or will the procedures that you're going to perform on the data be reasonably robust in the presence of a distribution that is only approximately normal? </p> <p>There are various classical statistical tests for normality that you can use, such as the Anderon-Darling test. These tests return a p-value, which is the probability that a sample of your size would exhibit behavior as extreme or more extreme than the behavior of your sample. Small p-values (e.g. less than 0.05) tell you that it is unlikely that this data came from a normal distribution. High p-values (e.g. greater than 0.05) are consistent with normality but do not necessarily imply normality- these tests can be fooled by a small sample of data from a non-normal distribution. </p> <p>The Anderson-Darling test is extremely strict- in practice, virtually any real world data set that is sufficiently large (hundreds to thousands of data points) will fail the test. In many statistical applications a failure of this sort can safely be ignored, because the procedures used are not terribly sensitive to data distributions that are not quite normal. </p> <p>Graphical methods such as normal probability plots or Q-Q plots are another very good way to assess whether your data are normally distributed or close enough to normally distributed. </p>

http://mathoverflow.net/questions/63972/fit-to-a-normal-distribution/64040#64040 Michael Hardy 2011-05-05T19:37:14Z 2011-05-05T19:37:14Z

<p>The Wikipedia article titled <a href="http://en.wikipedia.org/wiki/Normality_test" rel="nofollow">Normality test</a> lists these frequentist tests: D'Agostino's K-squared test, the Jarque–Bera test, the Anderson–Darling test, the Cramér–von-Mises criterion, the Lilliefors test for normality (itself an adaptation of the Kolmogorov–Smirnov test), the Shapiro–Wilk test, the Pearson's chi-square test, and the Shapiro–Francia test.</p> <p>All but one of those link to Wikipedia articles.</p> <p>Some Bayesian tests are also mentioned.</p>