JHWB wrote:
>
> Hm, hope I didn't make that subject to complex, resulting in zero replies.
> But hopefully you can answer this:
>
> I have a N(20,5) distribution and based on that I generated 25 values using
> Minitab and the Calc>Random data>Normal function. The result yielded a mean
> of 19,083 and a standard deviation of 6,0148.
>
> Now, how can I compare these results numerically and graphically?
>
> I mean, in the back of my head I have an image of a graph with a straight
> line (the basis for the values) and the plotted dots of the actual generated
> data following the line.
What you have in mind is a normal scores plot. This appears under Graph
> Probability Plot as the default option.
The hypothesis tests that come with this should be treated with great
caution (though testing the output of a RNG supposed to yield normally
distributed output *is* perhaps a valid use!) People have been known to
do one of these tests to see whether they must use a nonparametric
inference technique such as a sign or WMW test on a certain data set.
However, the hypothesis test answers the question "are these data
improbable under conditions of perfect normality?" and by extension "is
there evidence against perfect normality?". What you want to ask is
"are these data probably from a population that is normal enough for the
method to work?"
The gotcha is that while these may be roughly equivalent questions for
(say) N=20, for N small deviations from normality are important and the
test is poor at detecting them; for N large, deviations from normality
do not matter very much but the test is hypersensitive.
For instance: even when N=20, a uniform distribution can be treated as
normal for most purposes. However, it will generally fail the
Ryan-Joiner test at a 5% level!
-Robert Dawson
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