STATISTICAL TREATMENT 241 



The preceding illustrations have presented methods for treating a 

 series of measurements in a few of the simplest statistical constants, but 

 since we are in general interested in as direct and simple a summary of 

 the observations as possible, these methods will usually be found to be 

 sufficient. In certain cases the measurements may have some more 

 elaborate statistical characteristics, such as skewness or bimodality, that 

 are capable of biological interpretation and are therefore worthy of inves- 

 tigation. These factors will obviously demand more complex treatment, 

 but their development will follow natural extensions of the logic so far 

 employed. 



TREATMENT OF LETHAL DOSE 



Since many forms of radiation destroy living matter if sufficient dosage 

 is used, one of the very common problems encountered in the study of 

 the effect of radiation on organisms is that of the size of dose necessary 

 to kill the organism. It is usually found that if a group of organisms is 

 subjected to a sufficiently smah dosage, none of the forms dies, but that 

 as the dosage is increased, an increasing percentage dies until ultimately 

 a dosage is reached at which all of them are killed. If we plot the per- 

 centage of survivors against dosage an S-shaped curve results running 

 from 100 per cent for small doses down through to zero per cent for large 

 doses. This curve describes the lethal power of the form of radiation 

 used on the particular organism subjected to experimentation. As an 

 abbreviated statement of the lethal power of the radiation on the organ- 

 ism, the term lethal dose has been used. The words lethal dose have 

 not been consistently used by different writers ; some have used the words 

 to indicate the dosage below which all animals would live but at which 

 one or two would begin to die, others have used the words to indicate 

 the minimal dosage at which all the animals would be killed, and still 

 others have called the lethal dose that at which 50 per cent of the animals 

 would die. All three of these definitions are statistical in character and 

 are based on the above described S-shaped curve. The first two defini- 

 tions are dependent on the end points of the range of the curve, while 

 the third definition involves a centering point. Since range is a statistical 

 constant having a high degree of variability, the end points are sta- 

 tistically less stable than the centering point and therefore the third 

 definition is to be preferred and is the one which will be indicated when- 

 ever the words lethal dose are used in this chapter. 



The accurate determination of lethal dose is obviously often a tedious 

 and expensive procedure, for it calls for the determination at a variety 

 of dosages of the percentage of animals killed, and therefore at each 

 dosage enough animals must be used to determine a percentage with a 

 reasonable degree of precision. If the biological form used for experi- 



