  A common goal in clinical trials is to conduct tests on estimated treatment
effects adjusted for covariates such as age or sex. Analysis of Covariance
(ANCOVA) is often used in these scenarios to test the global null hypothesis of
no treatment effect using an $F$-test. However, in several samples, the
$F$-test does not provide any information about individual null hypotheses and
has strict assumptions such as variance homoscedasticity. We extend the method
proposed by Konietschke et al. (2021) to a multiple contrast test procedure
(MCTP), which allows us to test arbitrary linear hypotheses and provides
information about the global as well as the individual null hypotheses.
Further, we can calculate compatible simultaneous confidence intervals for the
individual effects. We derive a small sample size approximation of the
distribution of the test statistic via a multivariate t-distribution. As an
alternative, we introduce a Wild-bootstrap method. Extensive simulations show
that our methods are applicable even when sample sizes are small. Their
application is further illustrated within a real data example.
