[R] Normal tests disagree?

Wed Dec 2 10:15:19 CET 2009

rkevinburton at charter.net wrote:
> If I have data that I feed into shapio.test and jarque.bera.test yet they seem to disagree. What do I use for a decision?

I feel those testing for normality in real applied work always have some 
masochistic attitude. This attitude is squared if they/you even try out 
a second test. There are three possible results:

1. Both tests do not reject: You still do not know if the underlying 
distribution is normal. Hence a useless result.

2. Both tests do reject: You know with some probability 1-\alpha that 
your data are not normal but you do not know what to do next now - 
except for things that are obvious when looking at you data - and you 
should have done that before the analysis anyway. If nothing was obvious 
before, you will hide your finding about the non-normality now - or use 
another method that might be less powerful given the difference from 
normality is not really big.

3. Your case, one test rejects, the other one not: Welcome, you finally 
arrived in hell.

Best wishes,
Uwe Ligges

> For my data set I have p.value of 0.05496421 returned from the shapiro.test and 0.882027 returned from the jarque.bera.test. I have included the data set below.
> 
> Thank you.
> 
> Kevin
> 
> 
> "Category","Period","Residual"
> "CHILD HATS, WIGS & MASKS",1/1/2005,-0.449735723758323
> "CHILD HATS, WIGS & MASKS",2/1/2005,0.281461045050074
> "CHILD HATS, WIGS & MASKS",3/1/2005,0.591383050911335
> "CHILD HATS, WIGS & MASKS",4/1/2005,0.239998659520616
> "CHILD HATS, WIGS & MASKS",5/1/2005,0.00343879474063987
> "CHILD HATS, WIGS & MASKS",6/1/2005,-2.64372061292663
> "CHILD HATS, WIGS & MASKS",7/1/2005,0.381630655290173
> "CHILD HATS, WIGS & MASKS",8/1/2005,-1.79543281552347
> "CHILD HATS, WIGS & MASKS",9/1/2005,1.90631012440313
> "CHILD HATS, WIGS & MASKS",10/1/2005,-0.256232543929779
> "CHILD HATS, WIGS & MASKS",11/1/2005,1.83452602676812
> "CHILD HATS, WIGS & MASKS",12/1/2005,-1.06869719416837
> "CHILD HATS, WIGS & MASKS",1/1/2006,1.04378655286183
> "CHILD HATS, WIGS & MASKS",2/1/2006,0.232655831328322
> "CHILD HATS, WIGS & MASKS",3/1/2006,-0.939084802643773
> "CHILD HATS, WIGS & MASKS",4/1/2006,0.854132879285335
> "CHILD HATS, WIGS & MASKS",5/1/2006,-1.71217066877156
> "CHILD HATS, WIGS & MASKS",6/1/2006,1.28040273099582
> "CHILD HATS, WIGS & MASKS",7/1/2006,-0.386415431325857
> "CHILD HATS, WIGS & MASKS",8/1/2006,-0.769127669783483
> "CHILD HATS, WIGS & MASKS",9/1/2006,-0.810996835089867
> "CHILD HATS, WIGS & MASKS",10/1/2006,0.0477292147635991
> "CHILD HATS, WIGS & MASKS",11/1/2006,0.294672848750557
> "CHILD HATS, WIGS & MASKS",12/1/2006,-0.0841330473924862
> "CHILD HATS, WIGS & MASKS",1/1/2007,0.231663729192233
> "CHILD HATS, WIGS & MASKS",2/1/2007,-0.601790650547443
> "CHILD HATS, WIGS & MASKS",3/1/2007,0.285635768516625
> "CHILD HATS, WIGS & MASKS",4/1/2007,-0.963154959558619
> "CHILD HATS, WIGS & MASKS",5/1/2007,1.52188112949994
> "CHILD HATS, WIGS & MASKS",6/1/2007,-0.826092842933196
> "CHILD HATS, WIGS & MASKS",7/1/2007,1.91937201229077
> "CHILD HATS, WIGS & MASKS",8/1/2007,-0.317789483136924
> "CHILD HATS, WIGS & MASKS",9/1/2007,-0.865011007394312
> "CHILD HATS, WIGS & MASKS",10/1/2007,-0.0281604973711276
> "CHILD HATS, WIGS & MASKS",11/1/2007,-0.123887049811822
> "CHILD HATS, WIGS & MASKS",12/1/2007,-0.0327727730592468
> "CHILD HATS, WIGS & MASKS",1/1/2008,-0.0654939600771254
> "CHILD HATS, WIGS & MASKS",2/1/2008,0.279247739913908
> "CHILD HATS, WIGS & MASKS",3/1/2008,0.167606602923418
> "CHILD HATS, WIGS & MASKS",4/1/2008,0.189533097427477
> "CHILD HATS, WIGS & MASKS",5/1/2008,0.402062194225847
> "CHILD HATS, WIGS & MASKS",6/1/2008,1.97150984262995
> "CHILD HATS, WIGS & MASKS",7/1/2008,-2.27538477532968
> "CHILD HATS, WIGS & MASKS",8/1/2008,1.89091792097945
> "CHILD HATS, WIGS & MASKS",9/1/2008,0.0251732151287081
> "CHILD HATS, WIGS & MASKS",10/1/2008,-0.2349741808124
> "CHILD HATS, WIGS & MASKS",11/1/2008,-0.659332058368173
> "CHILD HATS, WIGS & MASKS",12/1/2008,0.127284768034285
> "CHILD HATS, WIGS & MASKS",1/1/2009,-1.42838560676513
> "CHILD HATS, WIGS & MASKS",2/1/2009,0.617689775286461
> "CHILD HATS, WIGS & MASKS",3/1/2009,-0.034243005247084
> "CHILD HATS, WIGS & MASKS",4/1/2009,-0.304574261133836
> "CHILD HATS, WIGS & MASKS",5/1/2009,0.128679369916751
> "CHILD HATS, WIGS & MASKS",6/1/2009,-0.657479389968652
> "CHILD HATS, WIGS & MASKS",7/1/2009,0.608766068692517
> "CHILD HATS, WIGS & MASKS",8/1/2009,1.92814770869400
> "CHILD HATS, WIGS & MASKS",9/1/2009,-0.172644961366165
> "CHILD HATS, WIGS & MASKS",10/1/2009,-0.453255508263169
> "CHILD HATS, WIGS & MASKS",11/1/2009,-1.09903330959344
> 
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