  The width (W), root mean squared amplitude (Rs) of lower and upper kHz
quasi-periodic oscillations (QPOs) from accreting neutron stars vary with
frequency. Similarly, the QPO frequency varies with the source count rate (S).
Hence, the significance of a QPO, scaling as S x Rs^2/W^(1/2) will also depend
on frequency. In addition, the significance also scales up with the square root
of the integration time of the Fourier power density spectrum (T).
Consequently, depending on the way data are considered, kHz QPOs may be
detected only over a limited range of their frequency spans or detected
predominantly at some frequencies, leading potentially to biases in the
observed distributions of frequencies or frequency ratios. Although subject of
much controversy, an observed clustering of QPO frequency ratios around 3/2 in
Sco X-1, also seen in other sources, has been previously used as an argument
supporting resonance based models of neutron star QPOs. In this paper, we
measure how the statistical significance of both kHz QPOs vary with frequency
for three prototype neutron star kHz QPO sources, namely 4U1636-536, 4U0614+091
and Sco X-1. As the significance of QPO detection depends on frequency, we show
that in sensitivity-limited observations (as in the case of the RXTE/PCA), a
simultaneous detection of both the lower and upper kHz QPOs can only be
achieved over limited frequency ranges. As a result, even a uniform
distribution of QPO frequencies will lead to peaks (in particular around 3/2)
in the histogram of frequency ratios. This implies that the observed clustering
of ratios does not provide any evidence for intrinsically preferred frequency
ratios, thus weakening the case for a resonance mechanism at the origin of
neutron star kHz QPOs.
