As you can see in the first graphic, the soil helps to insulate a basement so there is more heat lost on the top of the basement than on the bottom. That is why the National Building Code requires a minimum level of insulation in a basement that reaches from the floor boards above your head, down the wall to about two feet below the outside grade level. This does save most of the heat loss from basements, and may be adequate for a storage space. However it does not allow a basement to be warm enough to use as a living space. For full energy savings and livable comfort you will want to insulate totally to the floor.
Research has been carried out by the National Research Council some time ago that proves that you will not create frost problems with the basement walls by insulating to the floor. We can safely say that worry has been put to rest over twenty years ago. It is suprising how long myths can last. For more details follow this link to the research.
To see a complete animation about various basement insulation solutions check out the link: "Basement Insulation"