Abstract
The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodnessoffit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position pi = (i – .375)/(n + .25) yields a competitive regression test of fit for normality.
Original language  English (US) 

Pages (fromto)  7579 
Number of pages  5 
Journal  American Statistician 
Volume  39 
Issue number  1 
DOIs 

State  Published  Feb 1985 
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Keywords
 Empirical power comparison
 Filliben test
 Plotting position
 Regression tests of fit
 ShapiroFrancia test
 ShapiroWilk test
ASJC Scopus subject areas
 Statistics and Probability
 Mathematics(all)
 Statistics, Probability and Uncertainty
Cite this
Commentaries : Use of the correlation coefficient with normal probability plots. / Looney, Stephen W.; Gulledge, Thomas R.
In: American Statistician, Vol. 39, No. 1, 02.1985, p. 7579.Research output: Contribution to journal › Comment/debate
}
TY  JOUR
T1  Commentaries
T2  Use of the correlation coefficient with normal probability plots
AU  Looney, Stephen W.
AU  Gulledge, Thomas R.
PY  1985/2
Y1  1985/2
N2  The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodnessoffit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position pi = (i – .375)/(n + .25) yields a competitive regression test of fit for normality.
AB  The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodnessoffit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position pi = (i – .375)/(n + .25) yields a competitive regression test of fit for normality.
KW  Empirical power comparison
KW  Filliben test
KW  Plotting position
KW  Regression tests of fit
KW  ShapiroFrancia test
KW  ShapiroWilk test
UR  http://www.scopus.com/inward/record.url?scp=84952511519&partnerID=8YFLogxK
UR  http://www.scopus.com/inward/citedby.url?scp=84952511519&partnerID=8YFLogxK
U2  10.1080/00031305.1985.10479395
DO  10.1080/00031305.1985.10479395
M3  Comment/debate
AN  SCOPUS:84952511519
VL  39
SP  75
EP  79
JO  American Statistician
JF  American Statistician
SN  00031305
IS  1
ER 