first.r: Obtain a Vector of Sample Sizes with Total Number of Samples...
In elec.strat: Functions for election audits using stratified random samples

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

first.r, next.r, and propSizes obtain sample sizes so that the total number of samples is fixed. first.r uses the first.r algorithm, next.r uses the next.r algorithm, and propSizes finds a vector of sample sizes that is proportional to stratum sizes.

See Higgins, Rivest, Stark for details about the first.r and the next.r algorithms.

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	first.r(Z, n, t = 0, asTaint = FALSE, asNumber = FALSE, M = NULL, initSamp = NULL)
	next.r(Z, n, t = 0, asTaint = FALSE, asNumber = FALSE, M = NULL, initSamp = NULL)
	propSizes(Z, n)

`Z`	A `strat.elec.data` object.
`n`	The fixed number of samples. When `initSamp` is provided, `first.r` and `next.r` will run for `n` iterations, adding samples iteratively to `initSamp`; `first.r` and `next.r` will produce a vector of sample sizes with a total of `sum(initSamp) + n)` samples.
`t`	Value of the observed maximum, either as the MRO, as taint, or as the overstatement of the margin in votes.
`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.
`initSamp`	An initial choice of sample sizes. Used in call of `get.first.r.samp` and `get.next.r.samp` to reduce computational time.

The arguments t, asTaint, asNumber, M are used in first.r and next.r in the call of getEbsMargin. The getQ function is bypassed to increase efficiency.

propStrat obtains a vector of sample sizes that has exactly n samples. It obtains such a sample by sorting values of k*sum(Z$strat$n)/Z$strat$n, where k = 0, 1, ..., in increasing order and allocating a sample to the strata corresponding to the first n values. Ties are broken by choosing the strata with the largest number of batches. See Higgins, Rivest, Stark for details.

Mike Higgins, Hua Yang

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

See get.first.r.samp, get.next.r.samp, and get.prop.samp for finding sample sizes given constraints on the p-value and the largest observed overstatement.

	data(MN_Senate_2006)
	MN_Senate_2006.strat$strat$audit <- first.r(MN_Senate_2006.strat, n = 150)
	BaB(MN_Senate_2006.strat)
	MN_Senate_2006.strat$strat$audit  <- next.r(MN_Senate_2006.strat, n = 150)
	BaB(MN_Senate_2006.strat)
	MN_Senate_2006.strat$strat$audit  <- propSizes(MN_Senate_2006.strat, n = 150)
	BaB(MN_Senate_2006.strat)