eqValBound: p-value Through Relaxation on Number of Batches Without...
In elec.strat: Functions for election audits using stratified random samples

Description Usage Arguments Author(s) References See Also Examples

eqValBound and withReplaceBound find a p-value by changing the original constraint (that the total difference is greater than the margin), instead placing a restriction on the number of batches with error no larger than t.

eqValBound finds an exact solution with this restriction, whereas withReplaceBound finds a more conservative bound. See Stark for more details about withReplaceBound.

	eqValBound(Z, t = NULL, asTaint = FALSE, asNumber = FALSE, 
		M = NULL, takeOutZeroMMB=TRUE, bound.col = "e.max", 
		 calc.e_p=calc.pairwise.e_p, w_p = weight.function("no.weight"))
	withReplaceBound(Z, t = NULL, asTaint = FALSE, asNumber = FALSE, 
		M = NULL, takeOutZeroMMB = TRUE, bound.col = "e.max",  	
		calc.e_p=calc.pairwise.e_p, w_p = weight.function("no.weight"))

`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.
`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.
`bound.col, calc.e_p, w_p`	Arguments used to compute `t` from audit data, instead of passing `t` directly. These arguments are ignored if `t` is not NULL. See `compute.stark.t` for details.

Mike Higgins, Hua Yang

P.B. Stark. Conservative Statistical Post-Election Audits. Annals of Applied Statistics, 2:2. 550-581.

See LKPBound for finding a p-value through a continuous relaxation. See BaB for finding an exact p-value through solving a 0-1 knapsack problem. See compute.stark.t for computing t through audit data.

	data(MN_Senate_2006)
	eqValBound(MN_Senate_2006.strat, takeOutZeroMMB = FALSE)
	withReplaceBound(MN_Senate_2006.strat, t = 2, asNumber = TRUE, 
		takeOutZeroMMB = FALSE)