# plotCiNparDesign: Plots for Sampling Design Based on Nonparametric Confidence...

### Description

Create plots involving sample size, quantile, and confidence level for a nonparametric confidence interval for a quantile.

### Usage

 ```1 2 3 4 5 6 7 8``` ``` plotCiNparDesign(x.var = "n", y.var = "conf.level", range.x.var = NULL, n = 25, p = 0.5, conf.level = 0.95, ci.type = "two.sided", lcl.rank = ifelse(ci.type == "upper", 0, 1), n.plus.one.minus.ucl.rank = ifelse(ci.type == "lower", 0, 1), plot.it = TRUE, add = FALSE, n.points = 100, plot.col = "black", plot.lwd = 3 * par("cex"), plot.lty = 1, digits = .Options\$digits, cex.main = par("cex"), ..., main = NULL, xlab = NULL, ylab = NULL, type = "l") ```

### Arguments

 `x.var` character string indicating what variable to use for the x-axis. Possible values are `"n"` (sample size; the default), `"p"` (quantile), and `"conf.level"` (the confidence level). `y.var` character string indicating what variable to use for the y-axis. Possible values are `conf.level` (confidence level; the default), and `"n"` (sample size). `range.x.var` numeric vector of length 2 indicating the range of the x-variable to use for the plot. The default value depends on the value of `x.var`. When `x.var="n"` the default value is `c(2,50)`. When `x.var="p"` the default value is `c(0.5, 0.99)`. When `x.var="conf.level"`, the default value is `c(0.5, 0.99)`. `n` numeric scalar indicating the sample size. The default value is `n=25`. Missing (`NA`), undefined (`NaN`), and infinite (`Inf`, `-Inf`) values are not allowed. This argument is ignored if either `x.var="n"` or `y.var="n"`. `p` numeric scalar specifying the quantile. The value of this argument must be between 0 and 1. The default value is `p=0.5`. The argument is ignored if `x.var="p"`. `conf.level` a scalar between 0 and 1 indicating the confidence level associated with the confidence interval. The default value is `conf.level=0.95`. This argument is ignored if `x.var="conf.level"` or `y.var="conf.level"`. `ci.type` character string indicating what kind of confidence interval to compute. The possible values are `"two-sided"` (the default), `"lower"`, and `"upper"`. `lcl.rank, n.plus.one.minus.ucl.rank` numeric vectors of non-negative integers indicating the ranks of the order statistics that are used for the lower and upper bounds of the confidence interval for the specified quantile(s). When `lcl.rank=1` that means use the smallest value as the lower bound, when `lcl.rank=2` that means use the second to smallest value as the lower bound, etc. When `n.plus.one.minus.ucl.rank=1` that means use the largest value as the upper bound, when `n.plus.one.minus.ucl.rank=2` that means use the second to largest value as the upper bound, etc. A value of `0` for `lcl.rank` indicates no lower bound (i.e., -Inf) and a value of `0` for `n.plus.one.minus.ucl.rank` indicates no upper bound (i.e., `Inf`). When `ci.type="upper"` then `lcl.rank` is set to `0` by default, otherwise it is set to `1` by default. When `ci.type="lower"` then `n.plus.one.minus.ucl.rank` is set to `0` by default, otherwise it is set to `1` by default. `plot.it` a logical scalar indicating whether to create a plot or add to the existing plot (see `add`) on the current graphics device. If `plot.it=FALSE`, no plot is produced, but a list of (x,y) values is returned (see VALUE). The default value is `plot.it=TRUE`. `add` a logical scalar indicating whether to add the design plot to the existing plot (`add=TRUE`), or to create a plot from scratch (`add=FALSE`). The default value is `add=FALSE`. This argument is ignored if `plot.it=FALSE`. `n.points` a numeric scalar specifying how many (x,y) pairs to use to produce the plot. There are `n.points` x-values evenly spaced between `range.x.var[1]` and `range.x.var[2]`. The default value is `n.points=100`. `plot.col` a numeric scalar or character string determining the color of the plotted line or points. The default value is `plot.col="black"`. See the entry for `col` in the help file for `par` for more information. `plot.lwd` a numeric scalar determining the width of the plotted line. The default value is `3*par("cex")`. See the entry for `lwd` in the help file for `par` for more information. `plot.lty` a numeric scalar determining the line type of the plotted line. The default value is `plot.lty=1`. See the entry for `lty` in the help file for `par` for more information. `digits` a scalar indicating how many significant digits to print out on the plot. The default value is the current setting of `options("digits")`. `cex.main, main, xlab, ylab, type, ...` additional graphical parameters (see `par`).

### Details

See the help files for `eqnpar`, `ciNparConfLevel`, and `ciNparN` for information on how to compute a nonparametric confidence interval for a quantile, how the confidence level is computed when other quantities are fixed, and how the sample size is computed when other quantities are fixed.

### Value

`plotCiNparDesign` invisibly returns a list with components `x.var` and `y.var`, giving coordinates of the points that have been or would have been plotted.

### Note

See the help file for `eqnpar`.

### Author(s)

Steven P. Millard (EnvStats@ProbStatInfo.com)

### References

See the help file for `eqnpar`.

`eqnpar`, `ciNparConfLevel`, `ciNparN`.

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32``` ``` # Look at the relationship between confidence level and sample size for # a two-sided nonparametric confidence interval for the 90'th percentile. dev.new() plotCiNparDesign(p = 0.9) #---------- # Plot sample size vs. quantile for various levels of confidence: dev.new() plotCiNparDesign(x.var = "p", y.var = "n", range.x.var = c(0.8, 0.95), ylim = c(0, 60), main = "") plotCiNparDesign(x.var = "p", y.var = "n", conf.level = 0.9, add = TRUE, plot.col = 2, plot.lty = 2) plotCiNparDesign(x.var = "p", y.var = "n", conf.level = 0.8, add = TRUE, plot.col = 3, plot.lty = 3) legend("topleft", c("95%", "90%", "80%"), lty = 1:3, col = 1:3, lwd = 3 * par('cex'), bty = 'n') title(main = paste("Sample Size vs. Quantile for ", "Nonparametric CI for \nQuantile, with ", "Various Confidence Levels", sep="")) #========== # Clean up #--------- graphics.off() ```

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