Does anyone know of a function or R package that can help me turn z scores into percentile scores? The final goal is to classify or rank a group of respondents into four categories based on the heights of their z scores (20% lowest scores, 30%, 30%, 20% highest scores).

Any ideas? Many thanks in advance!

  • $\begingroup$ With what assumptions on the original scores? How are the values scaled - are the z-scores computed from sample mean and sample std deviation or from some known/assumed values? $\endgroup$
    – Glen_b
    Commented Apr 14, 2013 at 10:13
  • $\begingroup$ The original scores are raw test scores before i normalized them by using scale(x) $\endgroup$ Commented Apr 14, 2013 at 10:17
  • $\begingroup$ Related: Computing percentile rank in R. $\endgroup$
    – chl
    Commented Apr 14, 2013 at 10:37
  • $\begingroup$ chl, thanks! I initially missed that ont, but it turned out to be very helpful. $\endgroup$ Commented Apr 22, 2013 at 18:21

1 Answer 1


pnorm(z) will do it.

> pnorm(1.96)
[1] 0.9750021
> pnorm(0)
[1] 0.5
> pnorm(-1)
[1] 0.1586553

Or if you insist on a percentile, boom. Then try

  • 1
    $\begingroup$ The usual 95% confidence interval is given by pnorm(1.96) - pnorm(-1.96) with result 0.9500042 $\endgroup$
    – PatrickT
    Commented Nov 14, 2017 at 14:50

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