On Tue, Jun 19, 2012 at 12:42 PM, Özgür Asar <[hidden email]> wrote:
> Following a straight line indicates less evidence towards non-normality. But
> QQ-Plot is an exploratory tool.
> You can confirm your ideas obtained from the QQ-Plot via noramlity tests
> such as Shapiro-Wilk test.
Hmm, some gurus on this list would likely disagree.
Usually (but not always) doing tests of normality reflect a lack of
understanding of the power of rank tests, and an assumption of high power for
the tests (qq plots don't always help with that because of their subjectivity).
When possible it's good to choose a robust method. Also, doing pre-testing for
normality can affect the type I error of the overall analysis.
-- Frank Harrell
R-help (April 2005)
The issue really comes down to the fact that the questions: "exactly normal?",
and "normal enough?" are 2 very different questions (with the difference
becoming greater with increased sample size) and while the first is the easier
to answer, the second is generally the more useful one.
-- Greg Snow (answering a question about a "normality test" suitable for
R-help (April 2009)
For more on this, see ?SnowsPenultimateNormalityTest in TeachingDemos
and the references within. Also search the archives as this topic pops
Simulated point-wise confidence envelopes are available from qqPlot() only for studentized residuals from linear and generalized linear models. For an independent sample of observations, the confidence envelopes produced by qqPlot() are based on the standard errors of the order statistics for the reference distribution.
Sen. William McMaster Prof. of Social Statistics
Department of Sociology
Hamilton, Ontario, Canada
On Tue, 19 Jun 2012 15:21:07 -0400
Kjetil Halvorsen <[hidden email]> wrote:
>So in my example, I can say that the data comes from a moderate normal distribution because the points more at the >right lay straight to a straight line, then the points at the left. Please a confirmation here.
>But what is the information above (that the data is from a normal distribution) say about the relationship between two >variables?
On Wed, Jun 20, 2012 at 7:37 AM, Özgür Asar <[hidden email]> wrote:
> Why do you prefer robust methods in the example of Noor and why you need
> exact normality here?
The idea is that when you do hypothesis testing to check whether a
given distribution is normal, the results are rarely informative:
- if you do not reject the null: you couldn't find sufficient
evidence to reject normality, but you don't know what distribution
your data follows. You cannot conclude from this result that your data
- if you reject the null: according to the assumptions of the specific
test chosen, you find that your distribution doesn't follow normality.
But you still don't know what distribution it follows.
And at this point you should decide whether you want to check for
"exact" normality, which no distribution conforms to, or "approximate"
normality. Again, see ?SnowsPenultimateNormalityTest and the numerous
comments of Greg Snow on this subject on r-help. For example . I
also like Uwe Liggs take here  (which largely inspired my comments