This paper describes how the ASSR is expected to be useful for the objective, frequency-specific assessment of hearing thresholds in small children. To detect ASSR close to the hearing threshold, a powerful statistical test in the frequency domain has to be applied. Hitherto so-called one-sample tests are used, which only evaluate the phase, or the phase and amplitude, of the first harmonic frequency (the fundamental). It is shown that higher harmonics with significant amplitudes are also contained in the ASSR spectrum. For this reason, statistical tests that only consider the first harmonic ignore a significant portion of the available information. The use of a q-sample test, which, in addition to the fundamental frequency, also includes higher harmonics in the detection algorithm leads to a better detection performance in normal-hearing and hearing impaired subjects (N = 57). The evaluation of test performance uses both detection rate and detection time.