  We propose and study a new global test, namely the $F_{\max}$-test, for the
one-way ANOVA problem in functional data analysis. The test statistic is taken
as the maximum value of the usual pointwise $F$-test statistics over the
interval the functional responses are observed. A nonparametric bootstrap
method is employed to approximate the null distribution of the test statistic
and to obtain an estimated critical value for the test. The asymptotic random
expression of the test statistic is derived and the asymptotic power is
studied. In particular, under mild conditions, the $F_{\max}$-test
asymptotically has the correct level and is root-$n$ consistent in detecting
local alternatives. Via some simulation studies, it is found that in terms of
both level accuracy and power, the $F_{\max}$-test outperforms the Globalized
Pointwise F (GPF) test of \cite{Zhang_Liang:2013} when the functional data are
highly or moderately correlated, and its performance is comparable with the
latter otherwise. An application to an ischemic heart real dataset suggests
that, after proper manipulation, resting electrocardiogram (ECG) signals can be
used as an effective tool in clinical ischemic heart screening, without the
need of further stress tests as in the current standard procedure.
