Experimental evidence shows that if the probability of biological response is plotted against the absorbed dose from ionizing radiation, and if both dose and response are determined at the same level of biological organization (e.g., cell or organ-organism) the result appears as a sigmoid, medical-toxicological type of "dose-response" function when plotted using linear coordinates. However, if the biological response expressed at the cellular level is similarly plotted against the average absorbed dose expressed at the organ-organism level, a linearly proportional, "non-threshold" function is obtained. To explain this marked difference in curve shape, the absorbed dose at the organ level in terms of its meaning at the cellular level was examined, and both dose and response were put on the latter level. The result is consistent with the conclusion that absorbed dose at the organ-organism level can be treated, at the cellular level, as the product of two quantities: 1) the mean energy concentration or dose in a cell from a deposition event, i.e., "hit size" (the frequency-averaged specific energy in a reference cell target), and 2) the number of deposition events, or "hits," on the exposed cells. When the mean hit size for a given radiation remains constant, and the number of hits is increased, the total number of responses follows a linearly proportional "hit number response function." However, if the hit number is held constant or normalized to a given value, and the hit size is varied, the resulting probability of cell response again plots as the apparently sigmoid curve mentioned above, which has been termed the "hit size effectiveness function." With decreasing hit size, the probability of a cellular response appears to decrease asymptotically, and become indistinguishable from zero before zero dose is reached. It follows from this inherent relationship between the two kinds of functions that a sufficiently extensive set of data on a population of cells permits either type of function to be produced at will. These findings bear on the interpretation of the "linear, non threshold" hypothesis.