funtimes (version 8.0)

beales: Beale's Estimator and Sample Size

Description

Beale's ratio estimator Beale_1962funtimes 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).

Usage

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 required. By default, length(x) is used.

p

optional argument specifying the required relative error, from 0 to 1, for computing corresponding sample size. For example, p = 0.15 defines a 15% relative error.

d

optional argument specifying the required margin of error for computing 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.

Value

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).

References

See Also

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

Examples

# NOT RUN {
#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)

# }