[R] shapiro.test

[Richard A. Bilonick]

Ernesto Jardim wrote:

>Hi
>
>It's a bootstrap empirical distribution and has 1000 replicates.
>
>EJ
>
>On Mon, 2003-02-10 at 15:33, Richard A. Bilonick wrote:
>  
>
>>It depends on how non-Normal the distribution and the size of the 
>>sample. A t-distribution with df = 30 isn't Normal but it is close to 
>>being Normal. A small sample size probably won't detect it:
>>
>> > shapiro.test(rt(100,30))
>>
>>        Shapiro-Wilk normality test
>>
>>data:  rt(100, 30)
>>W = 0.9927, p-value = 0.8708
>>
>>But a large enough sample size will:
>>
>> > shapiro.test(rt(2000,30))
>>
>>        Shapiro-Wilk normality test
>>
>>data:  rt(2000, 30)
>>W = 0.9968, p-value = 0.0003097
>>
>>You haven't told us your sample size.
>>
>>Rick B.
>>
>>______________________________________________
>>R-help at stat.math.ethz.ch mailing list
>>http://www.stat.math.ethz.ch/mailman/listinfo/r-help
>>    
>>
First, the convention is to place replies at the bottom of the last 
message. (I would prefer it otherwise, but that is the convention.)

Apparently even with your "large" sample size, it is not large enough to 
differentiate a difference between your distribution and the Normal. The 
difference can't be distinguished from a chance departure from the 
Normal for the given sample size. There is nothing unusual in this that 
I can see. It just tends to take huge sample sizes to pick up small 
differences (assuming your distribution actually differs from the Normal!).

Rick B.