Quantile plots: New planks in an old campaign

Quantile plots show ordered values (raw data, estimates, residuals, whatever) against rank or cumulative probability or a one-to-one function of the same. Even in a strict sense, they are almost 200 years old. In Stata, quantile, qqplot, and qnorm go back to 1985 and 1986. So why any fuss? The presentation is built on a long-considered view that quantile plots are the best single plot for univariate distributions. No other kind of plot shows so many features so well across a range of sample sizes with so few arbitrary decisions. Both official and user-written programs appear in a review that includes side-by-side and superimposed comparisons of quantiles for different groups and comparable variables. Emphasis is on newer, previously unpublished work, with focus on the compatibility of quantiles with transformations; fitting and testing of brand-name distributions; quantile-box plots as proposed by Emanuel Parzen (1929–2016); equivalents for ordinal categorical data; and the question of which graphics best support paired and two-sample t and other tests. Commands mentioned include distplot, multqplot, and qplot (Stata Journal) and mylabels, stripplot, and hdquantile (SSC).