# Two-Stage Tests in R

A two-stage test can be viewed as a family of decreasing functions
f[c](p1) in the unit square. Each of these functions is a conditional
error function, specifying the type I error conditional on the
p-value p1 of the first stage. For example, f[c](p1) = min(1, c/p1)
corresponds to Fisher's combination test. Based on this function
family, the test can be put into practice by specifying the desired
overall level alpha, stopping bounds alpha1 LE alpha0 and a parameter
alpha2. After computing p1, the test stops with or without rejection
of the null hypothesis if p1 LE alpha1 or p1 GT alpha0,
respectively. Otherwise, the null hypothesis is rejected if and only
if p2 LE f[c](p1), where c is such that the local level of this
latter test is alpha2.

The four parameters alpha, alpha0, alpha1 and alpha2 are
interdependent, and the form of their functional relationship
depends on the test under consideration. For example, for
Fisher's combination test, alpha = alpha1 + c(alpha2) *
(ln(alpha0) - ln(alpha1)). This program provides functions that
calculate any of the four parameters based on the remaining
ones. Currently, this is done for the following four tests:
Bauer/Koehne 1994, Lehmacher/Wassmer 1999, Vandemeulebroecke
2006, and the horizontal conditional error function.

The functions are part of the package **adaptTest**.
The package and further informations about the package and the author can be found via **CRAN**.

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Last modified: Mon Oct 19 16:42:15 (MEZ) Mitteleuropäische Sommerzeit 2009