Two dwarf irregular galaxies, DDO 187 and NGC 3738, exhibit a striking pattern of star formation: intense star formation is taking place in a large region occupying roughly half of the inner part of the optical galaxy. We use data on the H i distribution and kinematics and stellar images and colors to examine the properties of the environment in the high star formation rate (HSF) halves of the galaxies in comparison with the low star formation rate halves. We find that the pressure and gas density are higher on the HSF sides by 30%-70%. In addition we find in both galaxies that the H i velocity fields exhibit significant deviations from ordered rotation and there are large regions of high-velocity dispersion and multiple velocity components in the gas beyond the inner regions of the galaxies. The conditions in the HSF regions are likely the result of large-scale external processes affecting the internal environment of the galaxies and enabling the current star formation there.