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Website, book, paper, etc. that shows example plots of distributions?

Greg Snow 
I had a Murphy's law calendar a while back with many different laws in it.  One of those laws was along the lines of:

An easily understood, simple falsehood is often more useful than a complicated, often misunderstood truth

(though the original was probably much better phrased than my memory).

Many rules in textbooks and classes follow this principle, especially when outside pressures force teachers to cover 4-6 hours of material in a 3 hour course.  The set of assumptions you list below are of this type.  They are a good simple place to start, and good enough for an introductory class, but a full discussion of the truth would take more time than is reasonable for an intro class.

Yes, the theory on which linear models is based was originally derived using the assumptions of normality, but linear models are amazingly robust, meaning that if the normality assumptions don't hold, the results (p-values, confidence intervals) will still usually be "close enough".  How "close" and if it is "enough" depends on sample size, how nonnormal the residuals are, and the specific question(s).

For regression, start by "doing" the regression, but then look at the diagnostic plots of the residuals (see ?plot.lm).  If you sample size is large and the residuals do not show strong skewness/outliers, then you are probably safe using the output of lm as is (Central Limit Thoerem, but still check other assumptions and make sure that what you are seeing/saying makes sense).  If there is more skewness/outliers than you are comfortable with, then there are robust methods that will be more helpful here.


Also note that if you know enough to find and use the lm function in R, then you know enough statistics to be dangerous (unless you are not allowed to make any decisions or communicate with anyone else (comma patients maybe)).  The goal now is to learn to use that power to do good, posting/reading here and Frank's book are a good start in that direction.

Hope this helps,

Thread (13 messages)

Jason Rupert Website, book, paper, etc. that shows example plots of distributions? Feb 12 Juliet Hannah Website, book, paper, etc. that shows example plots of distributions? Feb 12 Jason Rupert Website, book, paper, etc. that shows example plots of distributions? Feb 12 Gabor Grothendieck Website, book, paper, etc. that shows example plots of distributions? Feb 13 Jason Rupert Website, book, paper, etc. that shows example plots of distributions? Feb 13 Gabor Grothendieck Website, book, paper, etc. that shows example plots of distributions? Feb 13 David Winsemius Website, book, paper, etc. that shows example plots of distributions? Feb 13 Greg Snow Website, book, paper, etc. that shows example plots of distributions? Feb 13 davidr at rhotrading.com Website, book, paper, etc. that shows example plots of distributions? Feb 13 Jason Rupert Website, book, paper, etc. that shows example plots of distributions? Feb 14 Gabor Grothendieck Website, book, paper, etc. that shows example plots of distributions? Feb 14 David Winsemius Website, book, paper, etc. that shows example plots of distributions? Feb 15 Greg Snow Website, book, paper, etc. that shows example plots of distributions? Feb 16