binPower {binGroup}R Documentation

Power to reject a hypothesis using confidence intervals in binomial testing

Description

Closed calculation of the Power to reject a hypothesis using confidence intervals for a single binomial proportion, for specified sample size n, conf.level and an assumed absolute difference to the threshold parameter under the null hypothesis. Can be applied for the confidence interval methods given in binCI().

Usage

binPower(n, delta, p.hyp, conf.level = 0.95, 
alternative = "two.sided", method = "CP")

Arguments

n number of trials n in the binomial experiment, specify as a single integer
delta assumed absolute difference of the true proportion to the threshold proportion under the null hypothesis
p.hyp threshold proportion under the null hypothesis
conf.level nominal confidence level of the interval
alternative character string, defining the alternative hypothesis, either 'two.sided', 'less' or 'greater' where 'less' calculates the 'power of the upper confidence limit' for a true proportion p.hyp-delta, 'greater' calculates the 'power of the lower confidece limit' for a true proportion of p.hyp+delta. 'two.sided' calculates min(power(p.hyp-delta, p.hyp+delta)) for a two.sided CI, thus can result in much lower power. Note that coverage probability and power are not necessarily symmetric for upper and lower bound of binomial CI, especially for Wald, Wilson Score and Agresti-Coull CI.
method Character string, specifying the confidence interval method (see ?bin.CI) to be used

Details

The power of a confidence interval here is defined as the probability that a confidence interval or limit excludes the threshold parameter (p.hyp) of the null hypothesis. F.e. the null hypothesis H0: p>= 0.005 can be rejected, if an upper confidence limit for p does not contain p.hyp=0.005. In case that a delta of 0.002 shall be detectable, this function calculates the probability, that an interval of a given method will exclude p.hyp=0.005 if the true proportion = 0.003. Due to discreteness, the power does not increase monotone for increasing sample size (number of trials or indivoiduals under observation) n , but exhibits local maxima and minima, depending on n, conf.level and p.hyp. The power can be identical for different methods, depending on the particular combination of n, p.hyp, conf.level.

Value

A list containing

power the power which is achieved for tzhe specified parameters and method

See Also

binDesign for iteration of a sample size n for which a specified power is reached

Examples


# What is the probability to reject the null hypothesis
# H0: p >= 0.02 in order to show that the alternative
# hypothesis HA: p < 0.02 is very likely in the first
# example of if 200 seeds are taken from a seed lot and
# are checked for the proportion of defectives.
# We assume a true proportion under the alternative:
# p = 0.01, i.e. a absolute difference delta = 0.01 
# to the threshold proportion p.hyp=0.02.
# We can reject the null hypothesis if the threshold
# p.hyp=0.02 is excluded by an 95 percent upper bound of the 
# Clopper-Pearson CI. How big is power?

binPower(n=200, delta=0.01, p.hyp=0.02,
 alternative="less", method="CP")

# May be we assume a lower true proportion (we are
# satisfied also with the situation that we can only reject H0
# in case that the seed lot has a very high purity, e.g.
# only a proportion of 0.001 defectives )

binPower(n=200, delta=0.019, p.hyp=0.02,
 alternative="less", method="CP")

# Or we have to use a higher sample size:

binPower(n=600, delta=0.01, p.hyp=0.02,
 alternative="less", method="CP")


[Package binGroup version 0.3-2 Index]