We study the relationship between the gas column density () and the star formation rate surface density (ΣSFR) for a sample of extremely small (MB∼−13, ΔV50∼ 30 km s−1) dwarf irregular galaxies. We find a clear stochasticity in the relation between the gas column density and star formation. All gas with M⊙ pc−2 has some ongoing star formation, but the fraction of the gas with ongoing star formation decreases as the gas column density decreases and falls to about 50 per cent at M⊙ pc−2. Further, even for the most dense gas, the star formation efficiency is at least a factor of ∼2 smaller than typical of star-forming regions in spirals. We also find that the ratio of Hα emission to far-ultraviolet emission increases with the increasing gas column density. This is unlikely to be due to increasing dust extinction because the required dust-to-gas ratios are too high. We suggest instead that this correlation arises because massive (i.e. Hα-producing) stars are formed preferentially in regions with high gas density.