We investigate the spatial clustering of galaxies in the PSCz galaxy redshift survey, as revealed by the two-point correlation function, the luminosity mark correlations and the moments of counts-in-cells. We construct volume-limited subsamples at different depths and search for a luminosity dependence of the clustering pattern. We find no statistically significant effect in either the two-point correlation function or the mark correlations and so we take each subsample (of different characteristic luminosity) as representing the same statistical process. We then carry out a counts-in-cells analysis of the volume-limited subsamples, including a rigorous error calculation based on the recent theory of Szapudi, Colombi & Bernardeau. In this way, we derive the best estimates to date of the skewness and kurtosis of IRAS galaxies in redshift space. Our results agree well with previous measurements in both the parent angular catalogue and the derived redshift surveys. This is in contrast with smaller, optically selected surveys, where there is a discrepancy between the redshift space and projected measurements. Predictions from cold dark matter theory, obtained using the recent semi-analytical model of galaxy formation of Benson et al., provide an excellent description of our clustering data.