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propTestN(p.or.p1, p0.or.p2, alpha = 0.05, power = 0.95,
sample.type = "one.sample", alternative = "two.sided",
ratio = 1, approx = TRUE,
correct = sample.type == "two.sample",
round.up = TRUE, warn = TRUE, return.exact.list = TRUE,
n.min = 2, n.max = 10000, tol.alpha = 0.1 * alpha,
tol = 1e-7, maxiter = 1000)sample.type="one.sample", this argument denotes the
true value of $p$, the probability of dQuote{success}.
When sample.type="two.sample", this argument denotes the value of $p_1$,
thsample.type="one.sample",
this argument denotes the hypothesized value of $p$, the probability of dQuote{success}.
When sample.type="two.sample", this argument denotes the value of $palpha=0.05.power=0.95.sample.type="one.sample", the computed sample size is based
on a hypothesis test for a single proportion.
When "two.sided" (the default), "less", and
"greater".ratio=1.
All values of ratio must be greater than or equal to 1.
This argument is ignored ifapprox=TRUE.
Currently, the exact method (approx=FALSE) is only availableapprox=TRUE. The default value is approx=TRUE when
sample.type="two.sample" and approx=FALSE when
sample.type="one.sampleround.up=TRUE.warn=TRUE. When approx=TRUE (sample size based on the normal approximation)
and warn=T, a warning is issued for cases when the normal approx=FALSE
(i.e., when the power is based on the exact test). This argument indicates whether
to return a list containing extra information about the exact test in addition to
the power 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.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.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
approx=FALSE
(i.e., when the power is based on the exact test). This argument is passed to the
uniroot function and indicates the tolerance to approx=FALSE
(i.e., when the power is based on the exact test). This argument is passed to the
uniroot function and indicates the maximum number of itapprox=TRUE).
When sample.type="one.sample", or sample.type="two.sample"
and ratio=1 (i.e., equal sample sizes for each group), propTestN
returns a numeric vector of sample sizes. When
sample.type="two.sample" and at least one element of ratio is
greater than 1, propTestN returns a list with two components called
n1 and n2, specifying the sample sizes for each group.
Exact Test (approx=FALSE).
If return.exact.list=FALSE, propTestN returns a numeric vector of sample sizes.
If return.exact.list=TRUE, propTestN returns a list with the following components:alpha.alternative="greater".)alternative="less".)p.or.p1, p0.or.p2, alpha, power, ratio,
and tol.alpha are not all the same length, they are replicated to be the same length
as the length of the longest argument.
The computed sample size is based on the difference p.or.p1 - p0.or.p2.
One-Sample Case (sample.type="one.sample").
[object Object],[object Object]
Two-Sample Case (sample.type="two.sample").
When sample.type="two.sample", sample size is computed based on the test that uses the
normal approximation to the binomial distribution;
see the help file for prop.test.
The formula for this test and its associated power is presented in standard statistics texts,
including Zar (2010, pp. 549-550, 552-553) and
Millard and Neerchal (2001, pp. 443-445, 508-510).
These equations can be inverted to solve for the sample size, given a specified power,
significance level, true proportions, and ratio of sample size in group 2 to sample size in
group 1.propTestPower, propTestMdd, plotPropTestDesign,
prop.test, binom.test.# Look at how the required sample size of the one-sample
# proportion test with a two-sided alternative and Type I error
# set to 5\% increases with increasing power:
seq(0.5, 0.9, by = 0.1)
#[1] 0.5 0.6 0.7 0.8 0.9
propTestN(p.or.p1 = 0.7, p0.or.p2 = 0.5,
power = seq(0.5, 0.9, by = 0.1))
#[1] 25 31 38 47 62
#----------
# Repeat the last example, but compute the sample size based on
# the exact test instead of the approximation. Note that because
# we require the actual Type I error (alpha) to be within
# 10\% of the supplied value of alpha (which is 0.05 by default),
# due to the discrete nature of the exact binomial test
# we end up with more power then we specified.
n.list <- propTestN(p.or.p1 = 0.7, p0.or.p2 = 0.5,
power = seq(0.5, 0.9, by = 0.1), approx = FALSE)
lapply(n.list, round, 3)
#$n
#[1] 37 37 44 51 65
#
#$power
#[1] 0.698 0.698 0.778 0.836 0.910
#
#$alpha
#[1] 0.047 0.047 0.049 0.049 0.046
#
#$q.critical.lower
#[1] 12 12 15 18 24
#
#$q.critical.upper
#[1] 24 24 28 32 40
#----------
# Using the example above, see how the sample size changes
# if we allow the Type I error to deviate by more than 10 percent
# of the value of alpha (i.e., by more than 0.005).
n.list <- propTestN(p.or.p1 = 0.7, p0.or.p2 = 0.5,
power = seq(0.5, 0.9, by = 0.1), approx = FALSE, tol.alpha = 0.01)
lapply(n.list, round, 3)
#$n
#[1] 25 35 42 49 65
#
#$power
#[1] 0.512 0.652 0.743 0.810 0.910
#
#$alpha
#[1] 0.043 0.041 0.044 0.044 0.046
#
#$q.critical.lower
#[1] 7 11 14 17 24
#
#$q.critical.upper
#[1] 17 23 27 31 40
#----------
# Clean up
#---------
rm(n.list)
#==========
# Look at how the required sample size for the two-sample
# proportion test decreases with increasing difference between
# the two population proportions:
seq(0.4, 0.1, by = -0.1)
#[1] 0.4 0.3 0.2 0.1
propTestN(p.or.p1 = seq(0.4, 0.1, by = -0.1),
p0.or.p2 = 0.5, sample.type = "two")
#[1] 661 163 70 36
#Warning message:
#In propTestN(p.or.p1 = seq(0.4, 0.1, by = -0.1), p0.or.p2 = 0.5, :
# The computed sample sizes 'n1' and 'n2' are too small,
# relative to the given values of 'p1' and 'p2', for the normal
# approximation to work well for the following element indices:
# 4
#----------
# Look at how the required sample size for the two-sample
# proportion test decreases with increasing values of Type I error:
propTestN(p.or.p1 = 0.7, p0.or.p2 = 0.5,
sample.type = "two",
alpha = c(0.001, 0.01, 0.05, 0.1))
#[1] 299 221 163 137
#==========
# Modifying the example on pages 8-5 to 8-7 of USEPA (1989b),
# determine the required sample size to detect a difference in the
# proportion of detects of cadmium between the background and
# compliance wells. Set the complicance well to "group 1" and
# the backgound well to "group 2". Assume the true probability
# of a "detect" at the background well is 1/3, set the probability
# of a "detect" at the compliance well to 0.4 and 0.5, use a 5%
# significance level and 95% power, and use the upper
# one-sided alternative (probability of a "detect" at the compliance
# well is greater than the probability of a "detect" at the background
# well). (The original data are stored in EPA.89b.cadmium.df.)
#
# Note that the required sample size decreases from about
# 1160 at each well to about 200 at each well as the difference in
# proportions changes from (0.4 - 1/3) to (0.5 - 1/3), but both of
# these sample sizes are enormous compared to the number of samples
# usually collected in the field.
EPA.89b.cadmium.df
# Cadmium.orig Cadmium Censored Well.type
#1 0.1 0.100 FALSE Background
#2 0.12 0.120 FALSE Background
#3 BDL 0.000 TRUE Background
# ..........................................
#86 BDL 0.000 TRUE Compliance
#87 BDL 0.000 TRUE Compliance
#88 BDL 0.000 TRUE Compliance
p.hat.back <- with(EPA.89b.cadmium.df,
mean(!Censored[Well.type=="Background"]))
p.hat.back
#[1] 0.3333333
p.hat.comp <- with(EPA.89b.cadmium.df,
mean(!Censored[Well.type=="Compliance"]))
p.hat.comp
#[1] 0.375
n.back <- with(EPA.89b.cadmium.df,
sum(Well.type == "Background"))
n.back
#[1] 24
n.comp <- with(EPA.89b.cadmium.df,
sum(Well.type == "Compliance"))
n.comp
#[1] 64
propTestN(p.or.p1 = c(0.4, 0.50), p0.or.p2 = p.hat.back,
alt="greater", sample.type="two")
#[1] 1159 199
#----------
# Clean up
#---------
rm(p.hat.back, p.hat.comp, n.back, n.comp)Run the code above in your browser using DataLab