There are tons of false statements and awkward explanations out there when it comes to the influence of Cropped Size sensors on the Depth Of Field (DOF) on an image. Sometimes it seems to be a war out there when I read the comment sections.
In fact the whole thing is much easier to understand than some people make it to be. I hope this less than five minute video makes things clear for you and if you don't want to take my word for granted (what totally is up to you) you can have a look at the explantions of engineers who actually design high-end cameras http://www.red.com/learn/red-101/sensor-crop-factors
Of course I know that there will always be some people who know everything better while they don't even have a profile picture, lol.