Fragmentation measures how complete a fossil is.  For this study fragmentation was measured from 1 to 5.  A number closer to 1 means that it is fossil is complete or almost all there.  A number closer to 5 means that the fossil is very broken.

Fossils tend to break or fragment when they are moved around a lot. If you have ever been to a beach you have probably noticed that that there are many broken shells, especially those that are thin. Shells get broken when they are tossed around in the waves. If you were to swim out deeper where the waves were not breaking, chances are you would find fewer broken shells.

What does this tell us?  Assuming waves are the main cause of breakage, the more fragmented the shells in a sample (closer to 5), the shallower the water.  Less fragmented shells (closer to 1) tend to be found in deeper water.

This is a good rule of thumb, but it is not always the case. For instance, smaller fossils may not break apart as easily as larger fossils. There could be a scenario where shells from a little deeper may be larger and were more apt to break than smaller shells from shallow water. Because of this, it is good to use multiple forms of evidence when reconstructing past environments.