get.first.r.samp: Obtain a Vector of Sample Sizes Given Constraint on p-Value
In elec.strat: Functions for election audits using stratified random samples

Description Usage Arguments Details Author(s) References See Also Examples

get.first.r.samp, get.next.r.samp, and get.prop.samp obtain sample sizes so that, if a maximum observed overstatement of t or less is observed, the sample will produce a p-value less than alpha.

get.first.r.samp uses the first.r algorithm to obtain the sample, get.next.r.samp uses the next.r algorithm to obtain the sample, and get.prop.samp finds a vector of sample sizes that is proportional to stratum sizes.

For details about the first.r and the next.r algorithms, and for a description on how to produce a sample that will ensure that the p-value is less than alpha when no overstatement greater than t is uncovered, see Higgins, Rivest, Stark.

	get.first.r.samp(Z, alpha, t, bal=TRUE, numSamp = TRUE, initn = 1, 
		asTaint = FALSE, asNumber = FALSE, M = NULL, 
		takeOutZeroMMB=TRUE)
	get.next.r.samp(Z, alpha, t, bal=TRUE, numSamp = TRUE, initn = 1, 
		asTaint = FALSE, asNumber = FALSE, M = NULL, 
		takeOutZeroMMB=TRUE)
	get.prop.samp(Z, alpha, t, bal=TRUE, numSamp = TRUE, initn = 1, 
		asTaint = FALSE, asNumber = FALSE, M = NULL, 
		takeOutZeroMMB=TRUE)

`Z`	A `strat.elec.data` object.
`t`	Value of the observed maximum, either as the MRO, as taint, or as the overstatement of the margin in votes.
`alpha`	Threshold for the p-value. If an audit does not uncover an overstatement less than `t`, the sample obtained will ensure that the p-value is less than `alpha`.
`bal`	If `bal = TRUE`, the output will include the expected number of audited ballots for the sample.
`numSamp`	If `numSamp = TRUE`, the output will include the total number of audited batches.
`initn`	The first sample size checked by algorithm will have a total of `initn` samples. If this first sample will not produce a p-value less than alpha, the algorithm will increment the number of samples until such a vector of sample sizes is found. `initn` may be adjusted to dramatically decrease the runtime of algorithms.
`asTaint`	Set `asTaint = TRUE` if `t` is the maximum observed taint.
`asNumber`	Set `asNumber` if `t` is the maximum observed overstatement of the margin in votes.
`M`	A priori margin. If NULL, `M` defaults to 1.
`takeOutZeroMMB`	Setting `takeOutZeroMMB = TRUE` will consider batches with a `maximumMarginBound` of zero as having no chance of being sampled.

Sample sizes from get.first.r.samp and get.next.r.samp are obtained by repeatedly calling first.r and next.r, respectively, while incrementing the total number of samples n. The algorithm stops when the sample produced will ensure a p-value less than alpha.

Mike Higgins

M. Higgins, R. L. Rivest, P. B. Stark. Sharper p-Values for Stratified Election Audits

See first.r, next.r and propSizes for finding sample sizes given constraints on the p-value and the largest observed overstatement. Also, see first.r and next.r for a brief description of the first.r and next.r algorithms. See optStrat for finding optimal sample sizes so that, if a maximum observed overstatement of t or less is observed, the sample will produce a p-value less than alpha. Optimal sample sizes will minimize the number of batches required for audit.

	data(CA_House_2008)
	get.first.r.samp(CA_House_2008.strat[[3]], alpha = .1, t = .01, asTaint = TRUE)
	get.next.r.samp(CA_House_2008.strat[[3]], alpha = .1, t = .01, asTaint = TRUE)
	get.prop.samp(CA_House_2008.strat[[3]], alpha = .1, t = .01, asTaint = TRUE)