  Gravitational-wave observations of binary black holes allow new tests of
general relativity to be performed on strong, dynamical gravitational fields.
These tests require accurate waveform models of the gravitational-wave signal,
otherwise waveform errors can erroneously suggest evidence for new physics.
Existing waveforms are generally thought to be accurate enough for current
observations, and each of the events observed to date appears to be
individually consistent with general relativity. In the near future, with
larger gravitational-wave catalogs, it will be possible to perform more
stringent tests of gravity by analyzing large numbers of events together.
However, there is a danger that waveform errors can accumulate among events:
even if the waveform model is accurate enough for each individual event, it can
still yield erroneous evidence for new physics when applied to a large catalog.
This paper presents a simple linearised analysis, in the style of a Fisher
matrix calculation, that reveals the conditions under which the apparent
evidence for new physics due to waveform errors grows as the catalog size
increases. We estimate that, in the worst-case scenario, evidence for a
deviation from general relativity might appear in some tests using a catalog
containing as few as 10-30 events above a signal-to-noise ratio of 20. This is
close to the size of current catalogs and highlights the need for caution when
performing these sorts of experiments.
