EnvStats (version 2.3.1)

plotPredIntNormTestPowerCurve: Power Curves for Sampling Design for Test Based on Prediction Interval for Normal Distribution

Description

Plot power vs. \(\Delta/\sigma\) (scaled minimal detectable difference) for a sampling design for a test based on a prediction interval for a normal distribution.

Usage

plotPredIntNormTestPowerCurve(n = 8, df = n - 1, n.mean = 1, k = 1, 
    range.delta.over.sigma = c(0, 5), pi.type = "upper", conf.level = 0.95, 
    plot.it = TRUE, add = FALSE, n.points = 20, plot.col = "black", 
    plot.lwd = 3 * par("cex"), plot.lty = 1, digits = .Options$digits, ..., 
    main = NULL, xlab = NULL, ylab = NULL, type = "l")

Arguments

n

positive integer greater than 2 indicating the sample size upon which the prediction interval is based. The default is value is n=8.

df

positive integer indicating the degrees of freedom associated with the sample size. The default value is df=n-1.

n.mean

positive integer specifying the sample size associated with the future average(s). The default value is n.mean=1 (i.e., individual observations). Note that all future averages must be based on the same sample size.

k

positive integer specifying the number of future observations that the prediction interval should contain with confidence level conf.level. The default value is k=1.

range.delta.over.sigma

numeric vector of length 2 indicating the range of the x-variable to use for the plot. The default value is range.delta.over.sigma=c(0,5).

pi.type

character string indicating what kind of prediction interval to compute. The possible values are pi.type="upper" (the default), and pi.type="lower".

conf.level

numeric scalar between 0 and 1 indicating the confidence level of the prediction interval. The default value is conf.level=0.95.

plot.it

a logical scalar indicating whether to create a plot or add to the existing plot (see explanation of the argument add below) on the current graphics device. If plot.it=FALSE, no plot is produced, but a list of (x,y) values is returned (see the section 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").

main, xlab, ylab, type, …

additional graphical parameters (see par).

Value

plotPredIntNormTestPowerCurve invisibly returns a list with components:

x.var

x-coordinates of points that have been or would have been plotted.

y.var

y-coordinates of points that have been or would have been plotted.

Details

See the help file for predIntNormTestPower for information on how to compute the power of a hypothesis test for the difference between two means of normal distributions based on a prediction interval for a normal distribution.

References

See the help files for predIntNorm and predIntNormSimultaneous.

See Also

predIntNorm, predIntNormK, predIntNormTestPower, predIntNormSimultaneous, predIntNormSimultaneousK, predIntNormSimultaneousTestPower, Prediction Intervals, Normal.

Examples

# NOT RUN {
  # Pages 6-16 to 6-17 of USEPA (2009) present EPA Reference Power Curves (ERPC)
  # for groundwater monitoring:
  #
  # "Since effect sizes discussed in the next section often cannot or have not been 
  # quantified, the Unified Guidance recommends using the ERPC as a suitable basis 
  # of comparison for proposed testing procedures.  Each reference power curve 
  # corresponds to one of three typical yearly statistical evaluation schedules - 
  # quarterly, semi-annual, or annual - and represents the cumulative power 
  # achievable during a single year at one well-constituent pair by a 99% upper 
  # (normal) prediction limit based on n = 10 background measurements and one new 
  # measurement from the compliance well.
  #
  # Here we will reproduce Figure 6-3 on page 6-17.

  dev.new()
  plotPredIntNormTestPowerCurve(n = 10, k = 1, conf.level = 0.99, 
    ylim = c(0, 1), main="")

  plotPredIntNormTestPowerCurve(n = 10, k = 2, conf.level = 0.99, 
    add = TRUE, plot.col = "red", plot.lty = 2)

  plotPredIntNormTestPowerCurve(n = 10, k = 4, conf.level = 0.99, 
    add = TRUE, plot.col = "blue", plot.lty = 3)

  legend("topleft", c("Quarterly", "Semi-Annual", "Annual"), lty = 3:1, 
    lwd = 3 * par("cex"), col = c("blue", "red", "black"), bty = "n") 

  title(main = paste("Power vs. Delta/Sigma for Upper Prediction Interval with",
    "n=10, Confidence=99%, and Various Sampling Frequencies", sep="\n"))

  #==========
# }
# NOT RUN {
  # Plot power vs. scaled minimal detectable difference for various sample sizes 
  # using a 5<!-- % significance level. -->

  dev.new()
  plotPredIntNormTestPowerCurve(n = 8, k = 1, ylim = c(0, 1), main="") 

  plotPredIntNormTestPowerCurve(n = 16, k = 1, add = TRUE, plot.col = "red") 

  plotPredIntNormTestPowerCurve(n = 32, k = 1, add = TRUE, plot.col = "blue") 

  legend("bottomright", c("n=32", "n=16", "n=8"), lty = 1, lwd = 3 * par("cex"), 
    col = c("blue", "red", "black"), bty = "n") 

  title(main = paste("Power vs. Delta/Sigma for Upper Prediction Interval with",
    "k=1, Confidence=95%, and Various Sample Sizes", sep="\n"))

  #==========

  # Clean up
  #---------
  graphics.off()
# }