This paper describes a speech-in-noise test which is suitable for testing both human and machine speech recognition in noise. The test uses spoken digit triplets, presented in a range of babble backgrounds and signal-to-noise ratios (SNRs). The performance of a normal hearing (NH) and hearing impaired (HI) listener have been assessed using the test. Both listeners show a fall in performance with decreasing SNR, as well as a decrease in performance with an increase in the number of talkers in the babble background. A physiologically accurate computational auditory model has been tuned to match the NH and HI listeners, allowing their performance in the test to be modelled using a missing data-based automatic speech recognition (ASR) system. For the NH model we show a good match to the behaviour of the human listener. However, the computer model underestimates the digit test performance of the specific HI listener considered here.