MSPRT (version 2.1)

overshoot.oneProp: Error summary of the truncated Wald's SPRT in one-sample proportion tests

Description

MSPRT is designed on the assumption that we can afford at most, say, N samples. This function calculates a summary of the Type 1 or Type 2 error committed by the Wald's SPRT when it is simply truncated at N in one-sample proportion tests. This is done using parallel computation.

It is worth a mention that a case may remain inconclusive due to the truncation. The required sample size for reaching that decision is N.

Usage

overshoot.oneProp(error.type, batch.seq, null, gen.par, alt.LR, alt.psi,
                  up, low, N, R, core.no, return.n = T)

Arguments

error.type

a character; specifies which of the 2 types of errors need to be accounted for.

"type1" for Type 1 error.

"type2" for Type 2 error.

batch.seq

a numeric vector; an increasing sequence of values until N. Denotes the sequence of sample sizes where a user will observe data sequentially.

Last element should equal to N.

null

a numeric in (0,1); the hypothesized value of proportion under the simple null hypothesis.

gen.par

a numeric; the value of proportion from which the data needs to be generated from.

alt.LR

a numeric vector of lenth 2; this consists of the 2 UMPBT alternative points. The sequence of weighted likelihood ratios (\(L_n\)) is computed in favour of this alternative.

This is same with the output u from umpbt.oneProp().

alt.psi

a numeric in (0,1); the mixing probability corresponding to the first component of alt.LR in the UMPBT alternative.

This is same with the output psi from umpbt.oneProp().

up

a numeric; value of a constant rejection threshold. Should be greater than low.

low

a numeric; value of a constant acceptance threshold. Should be smaller than up.

N

a positive numeric (integer); number of samples where truncation of Wald's SPRT is required.

In a MSPRT, this is the maximum available sample size.

R

a positive numeric (integer); number of replications desired in the Monte Carlo study.

At least 1e+5 is required.

core.no

a numeric; number of cores this function can use for carrying out the Monte Carlo study using the parallel computing.

return.n

logical; if TRUE, this returns a vector of sample sizes required for reaching a decision in each of the R replications.

Value

If return.n = TRUE, a list with following components is returned:

count

a numeric; number of errors of error.type those are committed out of R replications.

inconclusive.vec

a numeric vector; a vector containing the likelihood ratio values at N which remained inconclusive at the last stage.

n.vec

a numeric vector; a vector of the required number of samples in each replications. This vector has length R.

If return.n = FALSE, the same list except n.vec is returned.

References

Wald, A., Sequential Tests of Statistical Hypotheses. Ann. of Math. Statist., vol. 16, no. 2, 1945, 117-186.

Examples

# NOT RUN {
N.max = 30
#overshoot.oneProp( error.type= "type1", batch.seq= 1:N.max, null= 0.5,
#                   gen.par= 0.5, alt.LR= c(0.5,0.55), alt.psi= 0.4,
#                   up= 160, low= 0.2, N= N.max, R= 1e+6,
#                   core.no= 2, return.n = T)
               
#overshoot.oneProp( error.type= "type2", batch.seq= 1:N.max, null= 0.5,
#                   gen.par= 0.7, alt.LR= c(0.5,0.55), alt.psi= 0.4,
#                   up= 160, low= 0.2, N= N.max, R= 1e+6, 
#                   core.no= 2, return.n = T)

# }