With the scales in use in this country the Binet year units are not equivalent in the sense in which they are usually spoken of as equivalent. We should recognize this and emphasize it. Even if the norms at each age marked off the same proportion of the individuals, as shown in A and B of Fig. 4, unless we knew that the forms of distribution were always alike, we should not know that the distance between successive age norms was the same on any sort of objective scale other than average age increments. Moreover, we would not have an objective scale of equal units applicable to measuring the deviation of children of any one age. The average annual increments would not necessarily represent the same proportion of the total distance from the lowest to the highest ability at different ages even if the distributions were all normal. With normal distributions it would also be necessary to demonstrate empirically that the annual average growth increment between successive ages always bore a constant relation to the deviations at these adjacent ages as shown in B of Fig. 4 where the increment is equal to 1 S. D. at each age. This could not possibly hold when the increment lessened near maturity. [Illustration: FIG. 4. _The Question of Equivalence of Year Units._] If the distributions of ability were variously skewed, the year units of excess or deficiency would not be shown to be equivalent at the different ages even if the proportion of individuals one year accelerated was equal to the number one year retarded, two years accelerated equal to those two years retarded, etc., at each age and the norm at each age shut out the same proportions of the age group. This is shown in C of Fig. 4 in which the year units are clearly not equal steps from lowest to highest ability even for the same age and yet the usual criteria which have been suggested for discovering the equivalence of the units are fulfilled. Whether the actual distribution of ability is skewed or normal cannot be determined by the Binet scale, of course, on account of the uncertain and probably varying size of its year units in measuring deviations at any age. With the empirical evidence against the equivalence of the year units and the impossibility of determining their equivalence unless we first know that ability is distributed normally at each age, it is certainly hazardous to assume that individual deviations measured in terms of year units are equivalent at different ages. It may be noted that it is quite as hazardous to suppose that the units of the Point scale are equivalent in any theoretical or practical sense. This question will be discussed later in Chap. XIII, B, (b). (c) IS TESTED CAPACITY DISTRIBUTED NORMALLY?