coleen, no you don't have to have concrete floors, in the sense of a slab on grade or a mud bed, but you do need a substrate that won't move much, either by flexion or with moisture content. Your ok as long as your sub-floor meets the minimum standard standard for rigidity of L/360 deflection or less. Usually this is achived by at least 5/8" (3/4" preferable) plywood over 16" oc joists.