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Jun 23, 2011

Confidence Interval for a Quantile (Percentile)

Sometimes you want to determine the quintile for a population, such as the median (0.5 or 50% quantile). You might also want the interval estimate. This script will compute the point estimate and the interval estimate for you.

I will use the Big Class data table to demonstrate how to use this script. I will first estimate the 95% confidence interval for the median of the height of students and then estimate the 80% confidence interval for the 75% percentile of the weight of students.

  • Open your data table with the data column containing the sample.
  • Open and run the script.
  • I desire a 95% confidence interval for the median, so enter 0.5 for the quantile (default) and 0.95 for the confidence (default).
  • Select height and click Response.


  • Click OK.


You see the additional information at the bottom of the platform. Note that the actual confidence is reported with the interval.

Repeating this demonstration for the other case,

  • Run the script.
  • Enter 0.75 for the quantile and 0.8 for the confidence.
  • Select weight and click Response.


  • Click OK.



Confidence Intervals for Percentiles and Medians


Thanks, Mark.

I also wanted to let JMP users know that in versions of JMP 10 or higher, you can also get these quantiles and confidence intervals within the distribution platform. Using the same data table as Mark, you could get these reports for height and weight by selecting Display Options > Custom Quantiles.  You enter the quantiles you would like to calculate in the entry column and then set the confidence level.  Here is what I enter for height:


Here are the JMP results:


Here is what I enter for weight:


Here are the JMP results:


Note that I am using JMP 12 for this example.  The "Compute smoothed empirical likelihood quantiles" check box is a new option for JMP 12.  In JMP 10 and 11 the empirical likelihood quantiles and confidence intervals are always computed in this report.

If you are interested in reading a little more about the Custom Quantiles option you can ready the blog I wrote for JMP 10.



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