Re: Interpreting Q-Q plot

On May 24, 10:39 am, shi...@xxxxxxxxx wrote:
On May 23, 5:58 pm, "David Jones" <dajx...@xxxxxxxxx> wrote:



shi...@xxxxxxxxx wrote:
Hi,

I would use Q-Q plot as a GoF (Goodness of Fit) test (not for
normality test!), but instead of evaluating the goodness of fit
graphically I'd like to use some analytic formula

Actually I've drawn two a line:
1. one passing for the 25th and 75th quantile
2. one obtained through a simple linear regression between the X and Y
quantiles.
With line #1 the only information I have is slope and intercept (these
isn't very useful since there might be a goodness of fit even if the
line is y=ax+b, with a <> 1 and b <> 0 beacause of location or scale
deviations)
With line #2 I have a lot of additional information (such as
residuals, R^2, ...)

What kind of line is better (eventually tell me an even better kind of
line) for a GoF?
... and what kind of statistically analysis can I do with that?
(e.g. with line #2 I thought to use the R^2 statistic to assess the
goodness of fit if R^2 ~ 1 or the lack of fit if R^2 ~ 0)

Any help is very appreciated!

Thank you very much!

Best regards,

-- Marco

You could try a PP or SP plot instead: see Michael (1983) The stabilized probability plot. Biometrika 70,11-17

Thank you for the reference!

I've just read this article. I'll try to apply the suggested method,
even if I have to calculate ad-hoc p-values for my probability
distributions (phase type, extreme value, alpha-stable,...) ... at the
moment I've no time.
By the way this article adds a new kind of test one can do on a QQ
plot (yes I have to use QQ plot).
So since many literatures talk about the 25th - 75th quantile line and
others suggests the linear regression, and now there is the "Michael's
way" ... well what is "better"?

Sincerely,

-- Marco


The best GOF test for the kind of data you seem to have must surely be
the Kolmogorov-Smirnov.

.

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