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The second generation of gravitational-wave detectors is scheduled to startoperations in 2015. Gravitational-wave signatures of compact binarycoalescences could be used to accurately test the strong-field dynamicalpredictions of general relativity. Computationally expensive data analysispipelines, including TIGER, have been developed to carry out such tests. As ameans to cheaply assess whether a particular deviation from general relativitycan be detected, Cornish et al. and Vallisneri recently proposed an approximatescheme to compute the Bayes factor between a general-relativitygravitational-wave model and a model representing a class of alternativetheories of gravity parametrised by one additional parameter. This approximatescheme is based on only two easy-to-compute quantities: the signal-to-noiseratio of the signal and the fitting factor between the signal and the manifoldof possible waveforms within general relativity. In this work, we compare theprediction from the approximate formula against an exact numerical calculationof the Bayes factor using the lalinference library. We find that, usingfrequency-domain waveforms, the approximate scheme predicts exact results withgood accuracy, providing the correct scaling with the signal-to-noise ratio ata fitting factor value of 0.992 and the correct scaling with the fitting factorat a signal-to-noise ratio of 20, down to a fitting factor of $\sim$ 0.9. Weextend the framework for the approximate calculation of the Bayes factor whichsignificantly increases its range of validity, at least to fitting factors of$\sim$ 0.7 or higher.

Testing general relativity with compact coalescing binaries: comparing exact and predictive methods to compute the Bayes factor