Quantiles and confidence intervals

Calculates an estimate for a quantile and confidence intervals for a vector of discrete or continuous values

quantileCI(
  x,
  tau = 0.5,
  level = 0.95,
  method = "binomial",
  type = 3,
  digits = 3,
  ...
)

Arguments

x

The vector of observations. Can be an ordered factor as long as type is 1 or 3.

tau

The quantile to use, e.g. 0.5 for median, 0.25 for 25th percentile.

level

The confidence interval to use, e.g. 0.95 for 95 percent confidence interval.

method

If "binomial", uses the binomial distribution the confidence limits. If "normal", uses the normal approximation to the binomial distribution.

type

The type value passed to the quantile function.

digits

The number of significant figures to use in output.

...

Other arguments, ignored.

Value

A data frame of summary statistics, quantile estimate, and confidence limits.

Details

Conover recommends the "binomial" method for sample sizes less than or equal to 20. With the current implementation, this method can be used also for larger sample sizes.

References

https://rcompanion.org/handbook/E_04.html

Conover, W.J., Practical Nonparametric Statistics, 3rd.

See also

groupwisePercentile, groupwiseMedian

Author

Salvatore Mangiafico, mangiafico@njaes.rutgers.edu

Examples

### From Conover, Practical Nonparametric Statistics, 3rd
Hours = c(46.9, 47.2, 49.1, 56.5, 56.8, 59.2, 59.9, 63.2,
          63.3, 63.4, 63.7, 64.1, 67.1, 67.7, 73.3, 78.5)
quantileCI(Hours)
#>  tau  n Quantile Nominal.level Actual.level Lower.ci Upper.ci
#>  0.5 16     63.2          0.95        0.951     56.5     64.1

### Example with ordered factor
set.seed(12345)
Pool = factor(c("smallest", "small", "medium", "large", "largest"),
             ordered=TRUE, 
             levels=c("smallest", "small", "medium", "large", "largest"))
Sample = sample(Pool, 24, replace=TRUE)
quantileCI(Sample)
#>  tau  n Quantile Nominal.level Actual.level Lower.ci Upper.ci
#>  0.5 24   medium          0.95        0.957    small    large