Hi there!
Thanks for coming to car-seat.org to ask your question.
As tempting as it may be to install your car seats directly on the vehicle floor, it's definitely a no-go. Car seats are intended to be installed
only on vehicle seats (and
only on forward-facing vehicle seats at that). This information is included in your car seat manual, probably in the first 1/4 or so of the manual. (Your vehicle manual should address child restraint installation as well.)
In addition to it being "against the manual," your car seats simply haven't been tested that way, as Sceason mentioned. There's no way for us to know how they would work in a crash - how they would protect your children in a crash. The only way to know for sure how it will work is to test it in an actual crash - and by then it would be too late.
Is there a particular reason that you've asked this question? Do you have a cargo van, for instance, with no vehicle seats? Let us know your situation and we may be able to help you find a solution.
I hope that answers your question. Please let us know if you have other questions.