  Tests of general relativity with gravitational wave observations from merging
compact binaries continue to confirm Einstein's theory of gravity with
increasing precision. However, these tests have so far only been applied to
signals that were first confidently detected by matched-filter searches
assuming general relativity templates. This raises the question of selection
biases: what is the largest deviation from general relativity that current
searches can detect, and are current constraints on such deviations necessarily
narrow because they are based on signals that were detected by templated
searches in the first place? In this paper, we estimate the impact of selection
effects for tests of the inspiral phase evolution of compact binary signals
with a simplified version of the GstLAL search pipeline. We find that selection
biases affect the search for very large values of the deviation parameters,
much larger than the constraints implied by the detected signals. Therefore,
combined population constraints from confidently detected events are mostly
unaffected by selection biases, with the largest effect being a broadening at
the $\sim10$ % level for the $-1$PN term. These findings suggest that current
population constraints on the inspiral phase are robust without factoring in
selection biases. Our study does not rule out a disjoint, undetectable binary
population with large deviations from general relativity, or stronger selection
effects in other tests or search procedures.
