beales function

Beale's Estimator and Sample Size

Beale's ratio estimator if(!exists(".Rdpack.currefs")) .Rdpack.currefs <-new.env();Rdpack::insert_citeOnly(keys="Beale_1962",package="funtimes",cached_env=.Rdpack.currefs)

for estimating population total and confidence intervals, with an option of calculating sample size for a required relative error (p) or margin of error (d).

beales(x, y, level = 0.95, N = NULL, p = NULL, d = NULL, verbose = TRUE)

Arguments

• x: a numeric vector with quantities of interest, such as river discharge per month. Missing values (NA) are allowed.
• y: a numeric vector with quantities of interest for which the total shall be estimated, such as total nutrient loads per month. Missing values (NA) are allowed. Lengths of x and y mush be the same.
• level: confidence level, from 0 to 1. Default is 0.95, that is, 95% confidence.
• N: population size for which the estimate of the total y is required. By default, length(x) is used.
• p: optional argument specifying the required relative error, from 0 to 1, for computing the corresponding sample size. For example, p = 0.15 defines a 15% relative error.
• d: optional argument specifying the required margin of error for computing the corresponding sample size. If both p and d are specified, only p is used.
• verbose: logical value defining whether the output should be printed out in words. Default is set to TRUE to give such output.

Returns

A list with the following components: - estimate: Beale's estimate of the population total for the variable y.

• se: standard error of the estimate.

• CI: a vector of length 2 with a confidence interval (lower and upper value) for the estimate.

• level: confidence level for the interval.

• N: population size.

• n: the actual sample size.

• p: the relative error used for sample size calculations. Reported only if p was specified in the input.

• d: the margin of error used for sample size calculations. Reported only if d was specified and p was not specified in the input.

• nhat: estimated sample size for the given level and error (p or d).

Examples

#Some hypothetical data for monthly river discharge 
#and corresponding nutrient loads:
discharge <- c(NA, 50, 90, 100, 80, 90, 100, 90, 80, 70, NA, NA)
loads <- c(33, 22, 44, 48, NA, 44, 49, NA, NA, 36, NA, NA)

#Example 1:
#Estimate total annual load (12 months), 
#with 90% confidence intervals
beales(discharge, loads, level = 0.9)

#Example 2:
#Calculate sample size required for 90% confidence intervals 
#with a margin of error 30 units
beales(discharge, loads, level = 0.9, d = 30)

References

if(!exists(".Rdpack.currefs")) .Rdpack.currefs <-new.env();Rdpack::insert_all_ref(.Rdpack.currefs)

See Also

vignette("beales", package = "funtimes")

Author(s)

Vyacheslav Lyubchich, thanks to Dave Lorenz for pointing out an error in version 7 and below of the package