You have to keep in mind that any day is no more than 7 days from either a new or full moon, of course.
It's very easy to do a statistical study, and it's been done, and there's no statistical relationship of large earthquakes and moon phases at all, especially on land.
However there ARE some lunar effects on earthquakes; small quakes in volcanic areas do increase with tides (the daily tides, not monthly phases) and there's some limited effect on moderate sized underwater quakes.
The more recent news is indicating an upgrade in magnitude and very regrettably, scores of injuries resulting from this latest earthquake for the people of eastern Japan's main island.