sequential.pops (version 0.1.1)

sprt: Sequential Probability Ratio Test

Description

Runs a Sequential Probability Ratio Test for hypotheses about population densities of the form \(H_{0}:\mu = \psi_{0}\) vs. \(H_{1}:\mu < \psi_{1}\), where \(\psi_{0} < \psi_{1}\). Data is treated in a sequential framework.

Usage

sprt(data = NA, mu0, mu1, density_func, overdispersion, alpha, beta)

Value

An object of class "SPRT".

Arguments

data

Optional vector of count data (NAs not allowed). Each value is considered a sampling bout over time. Can't process group sequential data. If not provided (NA), returns a "SPRT" object that can be used to plot a chart with stop lines or to return stop lines coefficients. If provided, returns a "SPRT" object that can be used to plot a chart with stop lines and data or to return test summary.

mu0

Single non-negative number with the value for the low hypothesized population density, \(\psi_{0}\).

mu1

Single non-negative number with the value for the high hypothesized population density, \(\psi_{1}\).

density_func

Kernel probability density function for the data. See details.

overdispersion

A number specifying the overdispersion parameter. Only required when using "negative binomial" as kernel density. See details.

alpha

Single number indicating tolerable type I error rate.

beta

Single number indicating tolerable type II error rate.

Details

The density_func argument should be specified as character string. Acceptable options are "poisson", "negative binomial", and "binomial". As far as we know, no one has ever calculated and published stop lines for the beta-binomial family. The overdispersion parameter should only be specified as a constant. In contrast to the STBP, SPRT is only use overdispersion to calculate stop lines, so the estimate for the threshold population density should be used (e.g., at \(\psi_{0} < \psi < \psi_{1}\)).

References

Binns, M.R., Nyrop, J.P. & Werf, W.v.d. (2000) Sampling and monitoring in crop protection: the theoretical basis for developing practical decision guides. CABI Pub., Wallingford, Oxon, UK; New York, N.Y.

Wald, A. (1945) Sequential Tests of Statistical Hypotheses. The Annals of Mathematical Statistics 16(2): 117-186.

Examples

# If no data is provided, an object of class "SPRT" is returned from which a
# chart with stop lines or a summary of the test with coefficients for stop lines
# can be extracted.

test00 <- sprt(mu0 = 2,
                mu1 = 4,
                density_func = "negative binomial",
                overdispersion = 4.6,
                alpha = 0.1,
                beta = 0.1)

test00 # returns test specification and stop lines coefficients
plot(test00) # returns a chart with stop lines


# If data is provided, an object of class "SPRT" is returned with test results.

counts <- c(2, 5, 6, 2, 7)

test11 <- sprt(data = counts,
                mu0 = 2,
                mu1 = 4,
                density_func = "negative binomial",
                overdispersion = 4.6,
                alpha = 0.1,
                beta = 0.1)
test11 # returns "accept H1" after 5 sampling bouts processed.

## End (Not run)