Do you know of a reference that discusses alternative choices for plotting positions for a normal probability plot? The documentation for qqnorm says it calls ppoints, which returns qnorm((1:m-a)/(m+1-2*a)) with "a" = ifelse(n<=10, 3/8, 1/2)? The help pages for qqnorm and ppoints just refer to Becker, Chambers and Wilks (1988) The New S Language (Wadsworth & Brooks/Cole), and I couldn't find any discussion of this. I seem to recall that this was discussed in 1960 or earlier in a paper by Anscombe, but I can't find a reference and I wonder if someone might suggest something else. I've been asked to comment on specialized software that allows the user to select "a" = +/-0.5, 0, 0.3, and 0.3175 (but not 0.375 = 3/8, curiously). I'd also be interested in any examples of real data sets where the choice of "a" actually made a difference. When I've had so few data points that the choice for "a" might make a difference, a normal probability plot was not very informative, anyway, and I get more information from a simple dot plot. If your experience is different, I'd like to know. Thanks, Spencer Graves
Spencer: I seem to remember that Jim Filliben did some work on this. Try checking the references in this: J. J. Filliben (1975) The Probability Plot Correlation Coefficient Test for Normality Technometrics, Vol. 17, No. 1, pp. 111-117 My experience agrees with yours: if sample sizes are small enough for it to make a difference, then sample sizes are too small to say much useful about the distribution anyway. Heresy: I gave up using normal and half normal plots for screening designs years ago, as they never told me more (nor less) than dot plots. Cheers, Bert -----Original Message----- From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Spencer Graves Sent: Thursday, April 13, 2006 1:21 PM To: R help list Subject: [R] Plotting positions in qqnorm? Do you know of a reference that discusses alternative choices for plotting positions for a normal probability plot? The documentation for qqnorm says it calls ppoints, which returns qnorm((1:m-a)/(m+1-2*a)) with "a" = ifelse(n<=10, 3/8, 1/2)? The help pages for qqnorm and ppoints just refer to Becker, Chambers and Wilks (1988) The New S Language (Wadsworth & Brooks/Cole), and I couldn't find any discussion of this. I seem to recall that this was discussed in 1960 or earlier in a paper by Anscombe, but I can't find a reference and I wonder if someone might suggest something else. I've been asked to comment on specialized software that allows the user to select "a" = +/-0.5, 0, 0.3, and 0.3175 (but not 0.375 = 3/8, curiously). I'd also be interested in any examples of real data sets where the choice of "a" actually made a difference. When I've had so few data points that the choice for "a" might make a difference, a normal probability plot was not very informative, anyway, and I get more information from a simple dot plot. If your experience is different, I'd like to know. Thanks, Spencer Graves ______________________________________________ R-help at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
On Thu, 13 Apr 2006, Spencer Graves wrote:> Do you know of a reference that discusses alternative choices for > plotting positions for a normal probability plot? The documentation for > qqnorm says it calls ppoints, which returns qnorm((1:m-a)/(m+1-2*a)) > with "a" = ifelse(n<=10, 3/8, 1/2)? The help pages for qqnorm and > ppoints just refer to Becker, Chambers and Wilks (1988) The New S > Language (Wadsworth & Brooks/Cole), and I couldn't find any discussion > of this. > > I seem to recall that this was discussed in 1960 or earlier in a > paper by Anscombe, but I can't find a reference and I wonder if someone > might suggest something else. I've been asked to comment on specialized > software that allows the user to select "a" = +/-0.5, 0, 0.3, and 0.3175 > (but not 0.375 = 3/8, curiously). > > I'd also be interested in any examples of real data sets where the > choice of "a" actually made a difference. When I've had so few data > points that the choice for "a" might make a difference, a normal > probability plot was not very informative, anyway, and I get more > information from a simple dot plot. If your experience is different, > I'd like to know. > > Thanks, > Spencer Graves >I suspect that what you are looking for is this paper: Hyndman, Rob J. and Fan, Yanan (1996) Sample quantiles in statistical packages The American Statistician, 50, 361-365 which discusses different definitions of sample quantiles. See also the documentation for quantile. David Scott _________________________________________________________________ David Scott Department of Statistics, Tamaki Campus The University of Auckland, PB 92019 Auckland NEW ZEALAND Phone: +64 9 373 7599 ext 86830 Fax: +64 9 373 7000 Email: d.scott at auckland.ac.nz Graduate Officer, Department of Statistics ASC/NZSA 2006: "Statistical Connections" The joint conference of the Statistical Society of Australia Inc. and the New Zealand Statistical Association, July 3--6, 2006 in Auckland. Go to: http://www.statsnz2006.com/