Omar Baqueiro wrote: > Hello, > > I have tested a distribution for normality using the Shapiro-Welch > statistic. The result of this is the following: > > > Shapiro-Wilk normality test > > data: mydata > W = 0.9989, p-value = 0.8791 > > > I know that the p-value > 0.05 (for my purposes) means that the data > IS normally distributed but what I am not sure is with the W value, > what values tell me that the data is normally distributed. I know > that my data is normally distributed, but what I want to know if how > to interpret the W value, I have read that "if W is very small then > the distribution is probably not normally distributed", but how > "small" is "very small", and also, what happens is, say W = 0.000001 > but the p-value is > my significance level (0.05)? is the hypothesis > rejected? >
There is some confusion in your query. First, how do you know that your data are indeed normally distributed? That's *not* what the p-value of the test says. Consider the following result of the Shapiro-Wilk test applied to a vector x: data: x W = 0.9856, p-value = 0.988 Here x was not sampled from a normal distribution (code at end). Second, the point of a p-value is to formalize decision-making so that critical regions of tests are converted to p-value intervals. Thus, your emphasis on the value of W is misplaced. It's not how small W is but how small it is for the given sample size, and the p-value takes care of the significance. (This is not to say, of course, that the distribution of W is not of interest.) Finally, what exactly, in your view, is "the hypothesis"? I hope this doesn't sound too critical. I'm trying to be helpful. Peter Ehlers > thank you! > > Omar > > ______________________________________________ > R-help@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. > > set.seed(34); shapiro.test(rexp(10)) ______________________________________________ R-help@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.
