The probability of incorrect reception of a transmitted bit under hostile propagation conditions is commonly estimated from bit error ratio measurements performed in the presence of additive white noise and interference. The paper stresses the effects of the finite crest factor of realisable noise sources on the theoretical error probability of digital radio systems. Formulas are presented for calculating this under given combinations of noise, interference and crest factor for common modulation schemes, and are suitable for simple numerical integration on desk-top calculators. Some implications for test equipment design are highlighted. The residual error rate of digital radio systems is so low that it is not practical to measure it directly. However, an estimate can be made by adding sinusoidal interference to produce the carrier/interference ratio (CIR) required to establish a specific error rate, dependent on the amount of residual noise present around the phase states in the constellation employed.