All of the special T statistics are based on the assumption that the samples being compared are independent of each other. However, in levels data, there is normally a relationship between the lower levels and the higher levels, which means that cases at the lower level are not independent of each other. For example, you would not expect the voting patterns of the members of a household to be totally independent of each other, nor would you expect the various journeys or shopping trips made by an individual to be unrelated to each other. These relationships mean that the underlying assumptions required for the special T statistics are almost never satisfied when you run the tests on lower level data.