  This paper derives accuracy standards for model gravitational waveforms
required to ensure proper use of the Allen $\chi^2$ discriminator in
gravitational wave (GW) data analysis. These standards are different from
previously established requirements for detection and waveform parameter
measurement based on signal-to-noise optimization. We present convenient
formulae for evaluating and interpreting the contribution of model errors to
measured values of this $\chi^2$ statistic. The new accuracy standards derived
here are needed to ensure the reliability of measured values of the Allen
$\chi^2$ statistic, both in their traditional role as vetoes and in their
current role as elements in evaluating the significance of candidate
detections.
