Plotting position (source code)

= Plotting position
{title2=$p_i=(i-1/2)/n$}

A <plotting position> assigns a <probability> level to an <order statistic> for a <Q-Q plot>. The displayed formula is one convention, not a universal definition. R's `ppoints` uses $p_i=(i-a)/(n+1-2a)$, with $a=1/2$ by default for $n>10$, which gives our choice at $n=19$; for $n\leq10$ its default is $a=3/8$. NIST's <normal probability plot> instead describes an approximation to <uniform distribution> <order statistic> medians. State the convention when comparing plots, especially their extreme <quantiles>. https://stat.ethz.ch/R-manual/R-devel/library/stats/html/ppoints.html[R stats documentation, ppoints]{ref}https://www.itl.nist.gov/div898/handbook/eda/section3/normprpl.htm[NIST/SEMATECH, Normal Probability Plot, definition]{ref}