I'm pretty new to statistics and I need your help.
I have a small sample, as follows:
H4U
0.269
0.357
0.2
0.221
0.275
0.277
0.253
0.127
0.246
I ran the Shapiro-Wilk test using R:
shapiro.test(precisionH4U$H4U)
and I got the following result:
W = 0.9502, p-value = 0.6921
Now, if I assume the significance level at 0.05 than the p-value is larger then alpha (0.6921 > 0.05) and I cannot reject the null hypothesis about the normal distribution, but does it allow me to say that the sample has a normal distribution?
Best Answer
No - you cannot say "the sample has a normal distribution" or "the sample comes from a population which has a normal distribution", but only "you cannot reject the hypothesis that the sample comes from a population which has a normal distribution".
In fact the sample does not have a normal distribution (see the qqplot below), but you would not expect it to as it is only a sample. The question as to the distribution of the underlying population remains open.