A simple statistical test is used in cyclostratigraphy to discover candidate orbital frequencies in power spectra of climate proxy data-series. In published studies at least, this test never fails to find multiple frequencies, at high levels of statistical significance (e.g. p<0.01). However, the same method finds similarly high statistical significance at similar numbers of frequencies in random, simulated datasets. The problem lies with the standardised application of the test, which is linked to MTM spectral analysis in a one-step procedure that is readily accessible through specialist software packages. This procedure presents confidence limits as if they were context-free, but statistical tests are necessarily tied to specific (null) hypotheses. The test as used in cyclostratigraphy is calibrated for application at a single frequency, but it is routinely used as if applicable at all frequencies, a practice that invokes the statistical multiple comparisons problem and which largely explains the inadvertent conversion of noise to signal when applied to random datasets. This general problem is addressed here with reference to a specific recently published case.