ABSTRACT We describe how to implement the spectral kurtosis method of interference removal (zapping) on a digitized signal of averaged power values. Spectral kurtosis is a hypothesis test, analogous to the t-test, with a null hypothesis that the amplitudes from which power is formed belong to a ‘good’ distribution – typically Gaussian with zero mean – where power values are zapped if the hypothesis is rejected at a specified confidence level. We derive signal-to-noise ratios (SNRs) as a function of amount of zapping for folded radio pulsar observations consisting of a sum of signals from multiple telescopes in independent radio-frequency interference environments, comparing four methods to compensate for lost data with coherent (tied-array) and incoherent summation. For coherently summed amplitudes, scaling amplitudes from non-zapped telescopes achieves a higher SNR than replacing zapped amplitudes with artificial noise. For incoherently summed power values, the highest SNR is given by scaling power from non-zapped telescopes to maintain a constant mean. We use spectral kurtosis to clean a tied-array radio pulsar observation by the Large European Array for Pulsars: the signal from one telescope is zapped with time and frequency resolutions of $6.25\, \mathrm{ms}$ and $0.16\, \mathrm{MHz}$, removing interference, along with 0.27 per cent of ‘good’ data, giving an uncertainty of $0.25\, \mathrm{\mu \mathrm{ s}}$ in pulse time of arrival (TOA) for PSR J1022+1001. We use a single-telescope observation to demonstrate recovery of the pulse profile shape, with 0.6 per cent of data zapped and a reduction from 1.22 to $0.70\, \mathrm{\mu \mathrm{ s}}$ in TOA uncertainty.