Talk:Q–Q plot

message: This page is incomplete. It only discusses quantile normal plots; there are also quantile quantile plots, where the quantiles of two different distributions (e.g. the weights of adult human males and the weights of adult human females) are plotted against each other.
I am very new here (this is my first time writing anything!) This would be complicated to edit, with formulas, charts, etc.  I have no idea how to do it, but someone should (see, e.g. William S. Cleveland's Visualizing Data).  What do I do?  thanks! —The preceding unsigned comment was added by Plf515 (talk • contribs) .
:Hmm, I am not sure what other kind of QQ plot you're talking about.  QQ Plots, at least I had thought, were short for quantile-quantile plots.  If you plot one data set against another, is it to compare two distributions.  Do the data sets have to be the same size?  Is there a discription on a website, by any chance?  I'm certainly happy to help with editing, and am quite curious to add this bit of stat knowledge to my learning.  Thanks, --TeaDrinker 02:09, 23 November 2006 (UTC)
replies: text: Ahh some googling does seem to show what you're talking about.  Mathworld seems to discuss it as comparison of two data sets .  --TeaDrinker 02:12, 23 November 2006 (UTC)

text: Curiosuly, I don't see the edit in the history (you can check the past history by clicking the history tab at the top of the screen).  Did you get a note saying either "edit conflict" or "database locked?"  The former would have looked like an edit window, the latter would look like the talk page, with red writing across the top saying something about it being a preview.  (Database errors are relatively rare, but it looks like the databased was momentarily locked a few minutes ago).  --TeaDrinker 02:26, 23 November 2006 (UTC)

text: I think it got loast. I did see a database locked, but then it went away.  Oh well, perhaps when I thought I hit save I hit preview.  Here's what I had to say, more or less.
The plots shown in the diagram are very useful (e.g. to check that the residuals from a linear regression are normally distributed), and correct (they look nice, too; what software did you use?).  But they are only part of what can be done with these types of plots.  As another example, suppose you are interested in comparing the weights of adult human males vs. adult human females. Clearly, males are heavier (on average), but are there differences in the shapes of the distributions?  One way to check is to have a QQ plot where one axis has quantiles of the distribution for men, the other for women.  
That's a trivial example; one place where some controversy has arisen is in whether the distributions of male and feamle IQs are equal - they have the same mean and sd, but some claim that male IQs have a different distribution than females, with more in the extreme ends.  This isn't the palce for a lengthy discussion of that, though; it's just to give you the idea.  Plf515 02:34, 23 November 2006 (UTC)

text: Just working it out in my head, if two data sets come from exactly the same distribution, the quantiles should probably fall roughly in a line.  Likewise, if two data sets came from different normal distributions (ie different mean and variance), they should both fall in a line.  The same would be true of most distributions which are location-scale families in their parameters.  I think, however, that other distributions which dramatically change shape with different parameters (gamma for instance), would not form a line for most parameter values.  Is there a source which makes this explicit?  --TeaDrinker 02:59, 23 November 2006 (UTC)

text: One source is William S. Cleveland's book Visualizing Data (a worthwhile purchase for anyone who likes statistics).  There's also discussion in the R help pages for qqnorm and qqplot.  I don't recall distributions like gamma, particularly.  It would be pretty easy to try it out and simulate data from gammas with different parameters.  My intuition is that you are right.  But, for what I am talking about, the issue is not so much which theoretical distribution is best, but how well the two distributions match.  
1. Are they different at the median? 
2. Are they different at various other quantiles?
3. Are these difference constant across the distribution (e.g. Is the difference between a man in the 1st percentile and a woman in the 1st percentile the same as between a man at the median and a woman at the median?) If not, how does the difference change across the distribution?
I gotta go, but will check in over the weekend.  Thanks for your warm welcome, happy thanksgiving  Plf515 03:13, 23 November 2006 (UTC)
thread_title: Incomplete

message: I have added a section about plotting positions today, with some references. DFH 18:43, 29 January 2007 (UTC)
thread_title:  Plotting positions 

message: That the Weibull expression m/(N+1) is the only correct choice for the plotting position has now been mathematically proven from the first principles of the probability theory. Please read Makkonen, L., Pajari, M. and Tikanmäki, M. (2013). Closure to "Problems in the extreme value analysis". Structural Safety 40,65-70.
(LasseMakkonen (talk) 19:37, 4 January 2013 (UTC)
thread_title:  The unique plotting position proven

message: I think that adding a gallery of normal Q-Q plots of all major distributions (at least gamma, Cauchy, beta, possibly more) would be a good idea. I haven't found such a resource in the Internet. And it would be a very good resource for finding what distribution data fit best. Tomato86 (talk) 15:12, 26 September 2010 (UTC)
thread_title:  Gallery 

message: I think the existing caption is incorrect: 
"that the July distribution is skewed to the left compared to the March distribution"
Instead, it should say "to the right" --- add the intuition that "July has warmer temperatures on average."  — Preceding unsigned comment added by Gforman44 (talk • contribs) 16:59, 12 September 2018 (UTC)
thread_title:  Bug in caption?! 

message: The graph of opening/closing dates of SR20 doesn't look like a Q-Q plot. The horizontal axis is indeed a quantile scale, but the vertical axis has units of days, so I don't think this is a Q-Q plot. --Macrakis (talk) 20:02, 1 April 2024 (UTC)
replies: text: @Macrakis It’s been 15 years, so I’d need to think to see what was going on; I was probably rearranging existing content. From a quick look, this is a Q–Q plot comparing against the theoretical normal distribution (vertical axis is the difference from mean/median, think standard deviations; horizontal axis is quantile). See the last paragraph in this section, beginning “Another common use of Q–Q plots is to compare the distribution of a sample to a theoretical distribution ”. Does this help? The caption certainly needs clarification! —Nils von Barth (nbarth) (talk) 21:30, 1 April 2024 (UTC)
replies: text:  Maybe I'm misunderstanding, but the vertical axis seems to be in absolute units (days), not in distributional units (quantiles). --Macrakis (talk) 21:37, 1 April 2024 (UTC)

text: Even if it were in SDs, that doesn't reflect the empirical distribution. --Macrakis (talk) 21:39, 1 April 2024 (UTC)
replies: text: @Macrakis You’re definitely right that it’s not a Q–Q plot on absolute axes! OTOH, it certainly looks like some kind of normal probability plot – it would be a straight line if the distribution were normal. I think it’s a rankit plot – the horizontal values are quantiles of the assumed normal distribution (the graphs and descriptions seem to correspond). In any case, this is complicated and confusing (and graphs two series too!), and shouldn't be the primary example! I’ll move the example to the rankit page, fix the image description and caption, and just have a link from Q–Q plot to Rankit, giving that as a more complicated example. WDYT? —Nils von Barth (nbarth) (talk) 23:16, 1 April 2024 (UTC)
replies: text: Sounds good! Macrakis (talk) 15:39, 2 April 2024 (UTC)
thread_title: Opening/closing dates of SR 20