  Gravitational-wave backgrounds are expected to arise from the superposition
of gravitational wave signals from a large number of unresolved sources and
also from the stochastic processes that occurred in the Early universe. So far,
we have not detected any gravitational wave background, but with the
improvements in the detectors' sensitivities, such detection is expected in the
near future. The detection and inferences we draw from the search for a
gravitational-wave background will depend on the source model, the type of
search pipeline used, and the data generation in the gravitational-wave
detectors. In this work, we focus on the effect of the data generation process,
specifically the calibration of the detectors' digital output into strain data
used by the search pipelines. Using the calibration model of the current LIGO
detectors as an example, we show that for power-law source models and
calibration uncertainties $\lesssim 10 \%$, the detection of isotropic
gravitational wave background is not significantly affected. We also show that
the source parameter estimation and upper limits calculations get biased. For
calibration uncertainties of $\lesssim 5 \%$, the biases are not significant
($\lesssim 2 \%$), but for larger calibration uncertainties, they might become
significant, especially when trying to differentiate between different models
of isotropic gravitational-wave backgrounds.
