Sequential Probability Ratio Test — sprt • sequential.pops

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)

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.

Value

An object of class "SPRT".

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
#> 
#> Sequential Probability Ratio Test - Stop lines
#> Family: negative binomial
#> H0: mu = 2
#> H1: mu = 4 
#> 
#> Upper line coefficients:
#> Intercept =  5.128255
#> Slope =  2.841808
#> Lower line coefficients:
#> Intercept =  -5.128255
#> Slope =  2.841808
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.
#> 
#> Sequential Probability Ratio Test
#> Family: negative binomial
#> H0: mu = 2
#> H1: mu = 4 
#> 
#> Recommendation based on provided criteria: accept H1
#> Number of sampling bouts processed:  5

## End (Not run)