Boschloo's exact unconditional test (method = "boschloo") for a 2 x 2 table whose rows are two independent
binomial samples. Equivalent to Exact::exact.test() in R.
The rows are the groups and column 1 counts the events: [[x1, n1 - x1], [x2, n2 - x2]]. The statistic is Fisher's
exact p-value of each possible table (one-sided, or two-sided for tsmethod: "square"), and the p-value is the
largest probability, over the common proportion pi under the null hypothesis, of the tables whose statistic is at
most the observed one (Boschloo 1970). alternative: "less" means pi1 < pi2 (Exact's orientation; exact2x2's
boschloo() uses the opposite one). "central" doubles the one-sided p-value in the direction of the data.
The p-value is the true supremum, from a fine grid and a refinement of every candidate maximum; Exact maximises
over 100 points refined by optimise and rounds to 12 digits (about 1e-9 relative off), and its two-sided
"square" region can contain tables that do not belong there (docs/differences-from-r.md). statistic is the
observed Fisher p-value (one-sided in the direction tested, or two-sided for "square"), estimate the difference
of the proportions x1/n1 - x2/n2, and nuisanceParameter the pi at which the supremum is attained.
A table with more than 2^24 possible outcomes ((n1 + 1)(n2 + 1)) is a RangeError, as is one whose grid would take
more than about 10 seconds.
Boschloo's exact unconditional test (
method = "boschloo") for a 2 x 2 table whose rows are two independent binomial samples. Equivalent toExact::exact.test()in R.The rows are the groups and column 1 counts the events:
[[x1, n1 - x1], [x2, n2 - x2]]. The statistic is Fisher's exact p-value of each possible table (one-sided, or two-sided fortsmethod: "square"), and the p-value is the largest probability, over the common proportion pi under the null hypothesis, of the tables whose statistic is at most the observed one (Boschloo 1970).alternative: "less"means pi1 < pi2 (Exact's orientation; exact2x2'sboschloo()uses the opposite one)."central"doubles the one-sided p-value in the direction of the data.The p-value is the true supremum, from a fine grid and a refinement of every candidate maximum; Exact maximises over 100 points refined by
optimiseand rounds to 12 digits (about 1e-9 relative off), and its two-sided"square"region can contain tables that do not belong there (docs/differences-from-r.md).statisticis the observed Fisher p-value (one-sided in the direction tested, or two-sided for"square"),estimatethe difference of the proportions x1/n1 - x2/n2, andnuisanceParameterthe pi at which the supremum is attained.A table with more than 2^24 possible outcomes ((n1 + 1)(n2 + 1)) is a RangeError, as is one whose grid would take more than about 10 seconds.