  The detection of gravitational waves from coalescing compact binaries would
be a computationally intensive process if a single bank of template wave forms
(i.e., a one step search) is used. In an earlier paper we had presented a
detection strategy, called a two step search}, that utilizes a hierarchy of
template banks. It was shown that in the simple case of a family of Newtonian
signals, an on-line two step search was about 8 times faster than an on-line
one step search (for initial LIGO). In this paper we extend the two step search
to the more realistic case of zero spin 1.5 post-Newtonian wave forms. We also
present formulas for detection and false alarm probabilities which take
statistical correlations into account. We find that for the case of a 1.5
post-Newtonian family of templates and signals, an on-line two step search
requires about 1/21 the computing power that would be required for the
corresponding on-line one step search. This reduction is achieved when signals
having strength S = 10.34 are required to be detected with a probability of
0.95, at an average of one false event per year, and the noise power spectral
density used is that of advanced LIGO. For initial LIGO, the reduction achieved
in computing power is about 1/27 for S = 9.98 and the same probabilities for
detection and false alarm as above.
