We present probability density functions and higher order (skewness and kurtosis) analyses of the galaxy-wide and spatially resolved distributions of H i column density in the LITTLE THINGS sample of dwarf irregular galaxies. This analysis follows that of Burkhart et al. for the Small Magellanic Cloud (SMC). About 60% of our sample have galaxy-wide values of kurtosis that are similar to that found for the SMC, with a range up to much higher values, and kurtosis increases with integrated star formation rate. Kurtosis and skewness were calculated for radial annuli and for a grid of 32 pixel ×32 pixel kernels across each galaxy. For most galaxies, kurtosis correlates with skewness. For about half of the galaxies, there is a trend of increasing kurtosis with radius. The range of kurtosis and skewness values is modeled by small variations in the Mach number close to the sonic limit and by conversion of H i to molecules at high column density. The maximum H i column densities decrease with increasing radius in a way that suggests molecules are forming in the weak-field limit, where H2 formation balances photodissociation in optically thin gas at the edges of clouds.