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At what point does does a departure from the normal constitute inflation (QQ plot)

I'm trying to interpret a QQ plot I have from Matrix eQTL, to see if there is a factor I haven't accounted for. I know a departure from the x=y at low values can indicate a confounding factor, but at what point is a digression from the normal inflation, and when is it acceptable? Is there a "rule of thumb"?

Edit: uploaded the wrong QQ-plot:

qq-plot eqtl
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updated by Ram Ram • written by Alexander Skates Alexander Skates

I refer to R-fortunes:

library(fortunes) 
fortune('chicken') 

A sufficiently trained statistician can read the vagaries of a Q-Q plot like a shaman can read a chicken's entrails, with a similar recourse to scientific principles. Interpreting Q-Q plots is more a visceral than an intellectual exercise. The uninitiated are often mystified by the process. Experience is the key here.
   -- Department of Mathematics and Statistics, Murdoch University
      StatsNotes

But because I don't want my comment to be completely useless, this thread might help you, in particular the latest 3 replies. Failing that, I am inclined to agree with Jean-Karim in that visually your plot suggests non-normality and normal distribution can be tested with the mentioned tests (though I have only used the Shapiro-Wilk test).

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updated by Ram Ram • written by A. Domingues A. Domingues

1 answer

I don't know of any rule of thumb for deciding when a distribution is normal or not based on a QQ plot. Any visually strong departure from the diagonal line like in your plot is definitely a sign of non-normality. However, even small deviations from the line can indicate non-normality but in these cases normality can be a good approximation. If you need statistical motivation for deciding whether your data is normally distributed, there are a number of tests you could use, the most sensitive being Shapiro-Wilk and Anderson-Darling tests.

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updated by Ram Ram • written by Jean-Karim Heriche Jean-Karim Heriche

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