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EnvStats

plotPropTestDesign

Plots for Sampling Design Based on One- or Two-Sample Proportion Test

Description

Create plots involving sample size, power, difference, and significance level for a one- or two-sample proportion test.

Usage

plotPropTestDesign(x.var = "n", y.var = "power", 
    range.x.var = NULL, n.or.n1 = 25, n2 = n.or.n1, ratio = 1, 
     p.or.p1 = switch(alternative, greater = 0.6, less = 0.4, 
       two.sided = ifelse(two.sided.direction == "greater", 0.6, 0.4)), 
    p0.or.p2 = 0.5, alpha = 0.05, power = 0.95, 
    sample.type = ifelse(!missing(n2) || !missing(ratio), "two.sample", "one.sample"), 
    alternative = "two.sided", two.sided.direction = "greater", 
    approx = TRUE, correct = sample.type == "two.sample", round.up = FALSE, 
    warn = TRUE, n.min = 2, n.max = 10000, tol.alpha = 0.1 * alpha, 
    tol = 1e-07, maxiter = 1000, plot.it = TRUE, add = FALSE, n.points = 50, 
    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), "delta" (minimal detectable difference), "power" (power of the test), and "alpha" (significance level of the test).

y.var

character string indicating what variable to use for the y-axis. Possible values are "power" (power of the test; the default), "delta" (minimal detectable difference), 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(20,400). When x.var="delta" and alternative="greater" or alternative="two.sided" and two.sided.direction="greater", the default value is c(0.05, 0.2). When x.var="delta" and alternative="less" or alternative="two.sided" and two.sided.direction="less", the default value is -c(0.2, 0.05). When x.var="power" the default value is
c(alpha + .Machine$double.eps, 0.95). When x.var="alpha", the default value is c(0.01, 0.2).

n.or.n1

numeric scalar indicating the sample size. The default value is n.or.n1=25. When sample.type="one.sample", n.or.n1 denotes the number of observations in the single sample. When sample.type="two.sample", n.or.n1 denotes the number of observations from group 1. 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".

n2

numeric scalar indicating the sample size for group 2. The default value is the value of n.or.n1. Missing (NA), undefined (NaN), and infinite (Inf, -Inf) values are not allowed. This argument is ignored when sample.type="one.sample".

ratio

numeric vector indicating the ratio of sample size in group 2 to sample size in group 1 n_2/n_1. The default value is ratio=1. All values of ratio must be greater than or equal to 1. This argument is only used when x.var="n" or y.var="n" and sample.type="two.sample".

p.or.p1

numeric vector of proportions. When sample.type="one.sample", p.or.p1 denotes the true value of p, the probability of “success”. When
sample.type="two.sample", p.or.p1 denotes the value of p_1, the probability of “success” in group 1. When alternative="greater" or
alternative="two.sided" and two.sided.direction="greater", the default value is p.or.p1=0.6. When alternative="less" or
alternative="two.sided" and two.sided.direction="less", the default value is p.or.p1=0.4. Missing (NA), undefined (NaN), and infinite (Inf, -Inf) values are not allowed. This argument is ignored when x.var="delta" or y.var="delta".

p0.or.p2

numeric vector of proportions. When sample.type="one.sample", p0.or.p2 denotes the hypothesized value of p, the probability of “success”. When
sample.type="two.sample", p0.or.p2 denotes the value of p_2, the probability of “success” in group 2. The default value is p0.or.p2=0.5. Missing (NA), undefined (NaN), and infinite (Inf, -Inf) values are not allowed.

alpha

numeric scalar between 0 and 1 indicating the Type I error level associated with the hypothesis test. The default value is alpha=0.05. This argument is ignored when x.var="alpha".

power

numeric scalar between 0 and 1 indicating the power associated with the hypothesis test. The default value is power=0.95. This argument is ignored when x.var="power" or y.var="power".

sample.type

character string indicating whether the design is based on a one-sample or two-sample proportion test. When sample.type="one.sample", the computations for the plot are based on a one-sample proportion test. When
sample.type="two.sample", the computations for the plot are based on a two-sample proportion test. The default value is sample.type="one.sample".

alternative

character string indicating the kind of alternative hypothesis. The possible values are "two.sided" (the default), "less", and "greater".

two.sided.direction

character string indicating the direction (positive or negative) for the minimal detectable difference when alternative="two.sided". When
two.sided.direction="greater" (the default), the minimal detectable difference is positive. When two.sided.direction="less", the minimal detectable difference is negative. This argument is ignored unless
alternative="two.sided" and either x.var="delta" or y.var="delta".

approx

logical scalar indicating whether to compute the power, sample size, or minimal detectable difference based on the normal approximation to the binomial distribution. The default value is approx=TRUE. Currently, the exact method (approx=FALSE) is only available for the one-sample case (i.e.,
sample.type="one.sample").

correct

logical scalar indicating whether to use the continuity correction when
approx=TRUE. The default value is correct=TRUE when
sample.type="two.sample" and correct=FALSE when
sample.type="one.sample". This argument is ignored when approx=FALSE.

round.up

logical scalar indicating whether to round up the values of the computed sample size(s) to the next smallest integer. The default value is round.up=FALSE. This argument is ignored unless y.var="n".

warn

logical scalar indicating whether to issue a warning. The default value is
warn=TRUE. When approx=TRUE (test based on the normal approximation) and warn=TRUE, a warning is issued for cases when the normal approximation to the binomial distribution probably is not accurate. When approx=FALSE (exact test) and warn=TRUE, a warning is issued when the user-supplied sample size is too small to yield a significance level less than or equal to the user-supplied value of alpha.

n.min

integer relevant to the case when y.var="n" and approx=FALSE (i.e., when the power is based on the exact test). This argument indicates the minimum allowed value for n to use in the search algorithm. The default value is n.min=2.

n.max

integer relevant to the case when y.var="n" and approx=FALSE (i.e., when the power is based on the exact test). This argument indicates the maximum allowed value for n to use in the search algorithm. The default value is n.max=10000.

tol.alpha

numeric vector relevant to the case when y.var="n" and approx=FALSE (i.e., when the power is based on the exact test). This argument indicates the tolerance on alpha to use in the search algorithm (i.e., how close the actual Type I error level is to the value prescribed by the argument alpha). The default value is tol.alpha=0.1*alpha.

tol

numeric scalar relevant to the case when y.var="n" and approx=FALSE (i.e., when the power is based on the exact test), or when y.var="delta". This argument is passed to the uniroot function and indicates the tolerance to use in the search algorithm. The default value is tol=1e-7.

maxiter

integer relevant to the case when y.var="n" and approx=FALSE (i.e., when the power is based on the exact test), or when y.var="delta". This argument is passed to the uniroot function and indicates the maximum number of iterations to use in the search algorithm. The default value is maxiter=1000.

plot.it

a logical scalar indicating whether to create a new 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 propTestPower, propTestN, and propTestMdd for information on how to compute the power, sample size, or minimal detectable difference for a one- or two-sample proportion test.

Value

plotPropTestDesign 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 files for propTestPower, propTestN, and propTestMdd.

Author(s)

Steven P. Millard (EnvStats@ProbStatInfo.com)

References

See the help files for propTestPower, propTestN, and propTestMdd.

See Also

Examples

# Look at the relationship between power and sample size for a 
  # one-sample proportion test, assuming the true proportion is 0.6, the 
  # hypothesized proportion is 0.5, and a 5% significance level.  
  # Compute the power based on the normal approximation to the binomial 
  # distribution.

  dev.new()
  plotPropTestDesign()

  #----------

  # For a two-sample proportion test, plot sample size vs. the minimal detectable 
  # difference for various levels of power, using a 5% significance level and a 
  # two-sided alternative:

  dev.new()
  plotPropTestDesign(x.var = "delta", y.var = "n", sample.type = "two", 
    ylim = c(0, 2800), main="") 

  plotPropTestDesign(x.var = "delta", y.var = "n", sample.type = "two", 
    power = 0.9, add = TRUE, plot.col = "red") 

  plotPropTestDesign(x.var = "delta", y.var = "n", sample.type = "two", 
    power = 0.8, add = TRUE, plot.col = "blue") 

  legend("topright", c("95%", "90%", "80%"), lty = 1, 
    lwd = 3 * par("cex"), col = c("black", "red", "blue"), bty = "n") 

  title(main = paste("Sample Size vs. Minimal Detectable Difference for Two-Sample", 
    "Proportion Test with p2=0.5, Alpha=0.05 and Various Powers", sep = "\n"))

  #==========

  # Example 22-3 on page 22-20 of USEPA (2009) involves determining whether more than 
  # 10% of chlorine gas containers are stored at pressures above a compliance limit.  
  # We want to test the one-sided null hypothesis that 10% or fewer of the containers 
  # are stored at pressures greater than the compliance limit versus the alternative 
  # that more than 10% are stored at pressures greater than the compliance limit.  
  # We want to have at least 90% power of detecting a true proportion of 30% or 
  # greater, using a 5% Type I error level.

  # Here we will modify this example and create a plot of power versus 
  # sample size for various assumed minimal detactable differences, 
  # using a 5% Type I error level.


  dev.new()
  plotPropTestDesign(x.var = "n", y.var = "power", 
    sample.type = "one", alternative = "greater", 
    p0.or.p2 = 0.1, p.or.p1 = 0.25, 
    range.x.var = c(20, 50), ylim = c(0.6, 1), main = "")

  plotPropTestDesign(x.var = "n", y.var = "power", 
    sample.type = "one", alternative = "greater", 
    p0.or.p2 = 0.1, p.or.p1 = 0.3, 
    range.x.var = c(20, 50), add = TRUE, plot.col = "red") 

  plotPropTestDesign(x.var = "n", y.var = "power", 
    sample.type = "one", alternative = "greater", 
    p0.or.p2 = 0.1, p.or.p1 = 0.35, 
    range.x.var = c(20, 50), add = TRUE, plot.col = "blue") 

  legend("bottomright", c("p=0.35", "p=0.3", "p=0.25"), lty = 1, 
    lwd = 3 * par("cex"), col = c("blue", "red", "black"), bty = "n") 

  title(main = paste("Power vs. Sample Size for One-Sided One-Sample Proportion",
    "Test with p0=0.1, Alpha=0.05 and Various Detectable Differences", 
    sep = "\n"))

  #==========

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

Package for Environmental Statistics, Including US EPA Guidance

v2.4.0
GPL (>= 3)
Authors
Steven P. Millard [aut], Alexander Kowarik [ctb, cre] (<https://orcid.org/0000-0001-8598-4130>)
Initial release
2020-10-20

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