nContOpt {PracTools}

Compute the sample size required to estimate the mean of a continuous variable by optimizing the numbers of take-alls and non-take-all units selected by probability sampling

Description

Compute a sample size required to achieve a precision target for an estimated mean, \hat{\bar{y}}_s, based on splitting the sample between take-alls and non-take-alls. The sample design for non-take-alls can be either simple random sampling or probability proportional to size sampling.

Usage

nContOpt(X, Y = NULL, CV0 = NULL, V0 = NULL, design = NULL)

Arguments

X

population variable used for determining take-all cutoff and for selecting a probability proportional to size sample if design = "PPS". X is a vector that contains a value for every unit in the population.

Y

variable used for computing a population variance; required if design = "PPS". Y is ignored if design = "SRS". X is a vector that contains a value for every unit in the population and is the same length as Y.

CV0

target value of coefficient of variation of \hat{\bar{y}}_s

V0

target value of variance of \hat{\bar{y}}_s

design

Sample design to be used for non-take-alls; must be either "SRS" or "PPS".

Details

Compute a sample size based on splitting the sample between take-alls and non-take-alls in a way that achieves either a target coefficient of variation or a target variance for an estimated mean. The function sorts the file in descending order by X and then systematically designates units as take-alls (certainty selections) starting from largest to smallest, and computes the sample size of non-take-alls needed to achieve the precision target. Initially, no unit in the ordered list is a certainty, and if design = "SRS", the first value in nContOpt.curve is the same as nCont produces under identical inputs. In each pass, the algorithm increases the number of certainties. In the second pass, the first value is taken as a certainty and the non-take-all sample size is based on units 2:N, where N is the population size. On the third pass, the first two values are taken as certainties and the non-take-all sample size is based on units 3:N. The function cycles through units 1:(N-1) with take-alls increasing by 1 each cycle, and determines the minimum total sample size needed to achieve the specified precision target. The optimum sample size nContOpt.n combines certainties and non-certainties for its value.

The sample design can be either simple random sampling or probability proportional to size sampling. When design = "SRS", calculations are based only on X. The SRS variance formula is for without replacement sampling so that a finite population correction factor (fpc) is included. When design = "PPS", X is used for the measure of size and Y is the variable for computing the variance used to determine the sample size. The PPS variance is computed for a with-replacement design, but an ad hoc fpc is included. Either CV0 or V0 must be provided but not both.

Value

A list with five components:

nContOpt.Curve

The sample size for the given inputs based on the number of take-alls incrementing from 1 to N-1

Take.alls

A TRUE/FALSE vector for whether the element in the X vector is a take-all

nContOpt.n

The minimum sample size (take-alls + non-take-alls) required for the given inputs, rounded to 4 decimal places

Min.Takeall.Val

The minimum value of X for the take-alls

n.Take.all

The number of take-all units in the optimal sample

Author(s)

George Zipf, Richard Valliant

See Also

nCont, nContMoe

Examples

nContOpt(X = TPV$Total.Pot.Value, CV0 = 0.05, design = "SRS")
nContOpt(X = TPV$Total.Pot.Value, V0  = 5e+14, design = "SRS")
g <- nContOpt(X = TPV$Total.Pot.Value, CV0 = 0.05, design = "SRS")
plot(g$nContOpt.Curve,
     type = "o",
     main = "Sample Size Curve",
     xlab = "Take-all / Sample Split Starting Value",
     ylab = "Total sample size (take-alls + non-tale-alls)" )
nContOpt(X = TPV$Total.Pot.Value, Y = TPV$Y, CV0 = 0.05, design = "PPS")