[R] Normal distribution test

[Duncan Murdoch]

On 11/17/2009 10:07 AM, rkevinburton at charter.net wrote:
> This is probably an even more basic question but shapiro.test return both the statistic (w) and the significance (pw) of the statistic. For this test the null-hypothesis is that the distirbution is not normal so very small values of pw would mean that there is very little chance that the distiribution is not normal. Correct?

I think you have an extra "not" in your description of the null.  But 
more importantly, a small p-value just means that you had a value of the 
test statistic that would be unusually extreme if the null was true.

Whether that means there is a small probability of the null being true 
depends on information outside the test.  It's essentially a Bayesian 
question, and Bayesians wouldn't base their decision on just the p-value.

For example, if I flip a fair coin 100 times and see 30 heads, 
binom.test() tells me that the p value would be 7.85e-05.  That doesn't 
mean the probability that the coin is fair is low:  it just means I saw 
an unusually small number of heads.

Now if I wasn't sure whether the coin was fair or not, I'd take the low 
p-value as evidence that it was not.  But the p-value alone isn't 
sufficient to let me calculate a probability of the null being true.

Duncan Murdoch

> Thank you.
> 
> Kevin
> 
> ---- Johannes Graumann <johannes_graumann at web.de> wrote: 
>> Markus Mehrwald wrote:
>> 
>> > Hi all,
>> > 
>> > I am completely new to R and my knowledge of statistics is quite small
>> > so I hope you can help my.
>> > I have three dimensional point data which represents (and this is what I
>> > do not know for sure) a normal distribution. Now I want to test if this
>> > is true or not and as I can remember from statistics lessons I can use
>> > Chi-Square test for distribution test. BUT: I have realy no idea how to
>> > do this with R and additionally if my assumptions are correct and if
>> > this is possible with R at all.
>> > 
>> > Thank you very much in advance for any answer.
>> > Markus
>> 
>> See
>> ?shapiro.test
>> or
>> ?ks.test
>> 
>> HTH, Joh
>> 
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.