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

Mon Feb 16 19:51:41 CET 2009

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,

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Jason Rupert
> Sent: Saturday, February 14, 2009 4:48 PM
> To: David Winsemius
> Cc: R-help at r-project.org
> Subject: Re: [R] Website, book, paper, etc. that shows example plots of
> distributions?
> 
> Many thanks to Greg L. Snow and David Winsemius for their responses.
> 
> First off I can safely say I don't know enough statistics to be
> dangerous, but hopefully I will get to that point:)
> 
> Regarding the goal - ultimately I would like to use linear regression
> (constrained for using linear regression at this point) for my data.  I
> thought the requirements for using linear regression was the following
> (I pulled this list from
> www.utexas.edu/courses/schwab/sw318_spring_2004/SolvingProblems/Class27
> _RegressionNCorrHypoTest.ppt):
> 
> The assumptions required for utilizing a regression equation are the
> same as the assumptions for the test of significance of a correlation
> coefficient.
> Both variables are interval level.
> Both variables are normally distributed.
> The relationship between the two variables is linear.
> The variance of the values of the dependent variable is uniform for all
> values of the independent variable (equality of variance).
> 
> Thus, I was going to attempt to (1) identify which distribution my data
> most closely represents, (2) translate my data so that it is normal,
> and (3) then use linear regression on the data.
> 
> However, if
> "The assumptions of most regression methods is that the *errors* need
> to have the desired relationship between means and variance, and not
> that the dependent variable be "normal". Many times the apparent non-
> normality will be "explained" or "captured" by the regression model."
> 
> Does this mean I can just "do" linear regression without translating my
> data and it will be okay?
> 
> Note that I was using "lm" from R to access the errors, however, I had
> not an opportunity to do much analysis of those results to determine if
> they are Gaussian or not.
> 
> I guess I am going to try to track down the following documents:
> (1) Statistical Distributions (Paperback)
> by Merran Evans (Author), Nicholas Hastings (Author), Brian Peacock
> (Author)
> # ISBN-10: 0471371246
> # ISBN-13: 978-0471371243
> 
> (2) Regression Modeling Strategies (Hardcover)
> by Frank E. Jr. Harrell (Author)
> # ISBN-10: 0387952322
> # ISBN-13: 978-0387952321
> 
> Maybe electronic versions of those documents are available.  My wife is
> already giving me a hard time the volume of books around.
> 
> Thank you again for all your feedback and insights.
> 
> 
> --- On Fri, 2/13/09, David Winsemius <dwinsemius at comcast.net> wrote:
> From: David Winsemius <dwinsemius at comcast.net>
> Subject: Re: [R] Website, book, paper, etc. that shows example plots of
> distributions?
> To: jasonkrupert at yahoo.com
> Cc: "Gabor Grothendieck" <ggrothendieck at gmail.com>, R-help at r-
> project.org
> Date: Friday, February 13, 2009, 9:10 AM
> 
> This is probably the right time to issue a warning about the error of
> making
> transformations on the dependent variable before doing your analysis.
> The
> classic error that newcomers to statistics commit is to decide that
> they want to
> "make their data normal". The assumptions of most regression methods
> is that the *errors* need to have the desired relationship between
> means and
> variance, and not that the dependent variable be "normal". Many times
> the apparent non-normality will be "explained" or "captured"
> by the regression model. Other methods of modeling non-linear
> dependence are
> also available.
> 
> I found Harrell's book "Regression Modeling Strategies" to be an
> excellent source for alternatives. My copy of V&R's MASS is only the
> second edition but chapters 5 & 6 in that edition on linear models also
> had
> examples of using QQ plots on residuals. Checking that text's website I
> see
> that chapters 6 at least is probably similar. They include the scripts
> from
> their chapters along with the MASS package (installed as part of the VR
> bundle).
> My copy is entitled "ch06.r" and resides in the scripts subdirectory:
> /Library/Frameworks/R.framework/Versions/2.8/Resources/library/MASS/scr
> ipts/ch06.R
> 
> --David Winsemius
> 
> 
> On Feb 13, 2009, at 8:11 AM, Jason Rupert wrote:
> 
> > Thank you very much.  Thank you again regarding the suggestion below.
> I
> will give that a shot and I guess I've got my work counted out for me.
> I
> counted 45 different distributions.
> >
> > Is the best way to get a QQPlot of each, to run through producing a
> data
> set for each distribution and then using the qqplot function to get a
> QQplot of
> the distribution and then compare it with my data distribution?
> >
> > As you can tell I am not a trained statistician, so any guidance or
> suggested further reading is greatly appreciated.
> >
> > I guess I am pretty sure my data is not a normal distribution due to
> doing
> some of the empirical "Goodness of Fit" tests and comparing the QQplot
> of my data against the QQPlot of a normal distribution with the same
> number of
> points.  I guess the next step is to figure out which distribution my
> data most
> closely matches.
> >
> > Also, I guess I could also fool around and take the log, sqrt, etc.
> of my
> data and see if it will then more closely resemble a normal
> distribution.
> >
> > Thank you again for assisting this novice data analyst who is trying
> to
> gain a better understanding of the techniques using this powerful
> software
> package.
> >
> >
> >
> >
> > --- On Fri, 2/13/09, Gabor Grothendieck <ggrothendieck at gmail.com>
> wrote:
> > From: Gabor Grothendieck <ggrothendieck at gmail.com>
> > Subject: Re: [R] Website, book, paper, etc. that shows example plots
> of
> distributions?
> > To: jasonkrupert at yahoo.com
> > Cc: R-help at r-project.org
> > Date: Friday, February 13, 2009, 5:43 AM
> >
> > You can readily create a dynamic display for using qqplot and similar
> functions
> > in conjunction with either the playwith or TeachingDemos packages.
> >
> > For example, to investigate the effect of the shape parameter in the
> skew
> > normal distribution on its qqplot relative to the normal
> distribution:
> >
> >   library(playwith)
> >   library(sn)
> >   playwith(qqnorm(rsn(100, shape = shape)),
> >       parameters = list(shape = seq(-3, 3, .1)))
> >
> > Now move the slider located at the bottom of the window that
> > appears and watch the plot change in response to changing
> > the shape value.
> >
> > You can find more distributions here:
> > http://cran.r-project.org/web/views/Distributions.html
> >
> > On Thu, Feb 12, 2009 at 1:04 PM, Jason Rupert
> <jasonkrupert at yahoo.com>
> > wrote:
> >> By any chance is any one aware of a website, book, paper, etc. or
> > combinations of those sources that show plots of different
> distributions?
> >>
> >> After reading a pretty good whitepaper I became aware of the benefit
> of I
> > the benefit of doing Q-Q plots and histograms to help assess a
> distribution.
> > The whitepaper is called:
> >> "Univariate Analysis and Normality Test Using SAS, Stata, and
> > SPSS*" , (c) 2002-2008 The Trustees of Indiana University Univariate
> > Analysis and Normality Test: 1, Hun Myoung Park
> >>
> >> Unfortunately the white paper does not provide an extensive amount
> of
> > example distributions plotted using Q-Q plots and histograms, so I am
> curious if
> > there is a "portfolio"-type  website or other whitepaper shows
> > examples of various types of distributions.
> >>
> >> It would be helpful to see a bunch of Q-Q plots and their associated
> > histograms to get an idea of how the distribution looks in comparison
> against
> > the Gaussian.
> >>
> >> I think seeing the plot really helps.
> >>
> >> Thank you for any insights.
> >>
> >>
> >>
> >>       [[alternative HTML version deleted]]
> >>
> >>
> >> ______________________________________________
> >> R-help at r-project.org mailing list
> >> https://stat.ethz.ch/mailman/listinfo/r-help
> >> PLEASE do read the posting guide
> > http://www.R-project.org/posting-guide.html
> >> and provide commented, minimal, self-contained, reproducible code.
> >>
> >>
> >
> >
> >
> >
> > 	[[alternative HTML version deleted]]
> >
> > ______________________________________________
> > R-help at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> 
> 
> 
> 
> 
> 	[[alternative HTML version deleted]]