Normal distribution check within R can be done with functions available in nortest package. This package consists of several normality tests. In order to install package type install.packages('nortest'). Afterwards, you should consider running ks.test() only if mu and sigma parameters are known (these stand for population arithmetic mean and variance) - and that's only applicable if your data is gathered from the population. Therefor I recommend using lillie.test() function, which is Lilliefors' modification of Kolmogorov-Smirnov statistic. It's applicable both for data gathered from a sample, but can also be applied to population data. You can run ks.test(x, pnorm), but don't worry if you get several ties - these occur due to rounding of values, or if your data come from descrete probability function...
You can also try shapiro.test() function if your sample counts less then 50 responses (Shapiro-Wilks' test for small samples), or ad.test() for Anderson-Darling normality test. You should revise these statistical procedures in official literature, but there's also a lot of info on wikipedia about stated statistical techniques.
If absolute value of skewness is larger than 1.96 * standard error of skewness, your distribution significantly differs from normal. Also stands for kurtosis. Value 1.96 implies p-value lower than .05, and 2.58 lower than .01
Skewness function is called with skew(), and kurtosis with kurtosi() function.
Standard error of skewness is calculated from formula se.sk <- sqrt(6/length(x)) and standard error of kurtosis from formula se.ku <- sqrt(24/length(x))
If mean is not located in the middle of the range, this can also indicate a violation of normality.
I strongly recommend reading official help for nortest package, and consulting an official statistical literature!
P.S.
shapiro.test() is located in stats package, but running it on a large sample (N >> 50) is not quite applicable, hence use lillie.test() for those purposes, or ks.test(x, pnorm) - where x argument is variable which normality you're about to check, and pnorm stands for normal distribution function.
Noela Sánchez-2 wrote:
Hi,
I am dealing with how to check in R if some data that I have belongs to a
normal distribution or not. I am not interested in obtaining the
theoreticall frequencies. I am only interested in determing if (by means of
a test as Kolmogorov, or whatever), if my data are normal or not.
But I have tried with ks.test() and I have not got it.
--
Noela
Grupo de Recursos Marinos y Pesquerías
Universidad de A Coruña
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