80 per cent of such families are independent of the child’s wages.  But Holley concludes,[27] from a study of certain towns in Illinois, that “there is a high correlation between the economic, educational, and social advantages of a home and the number of years of school which its children receive.”  It will hardly be denied that even aside from the relation of the family means to the school persistence, the economic needs may have a direct influence on the failing of the children in their school work, either because home conditions may be decidedly unfavorable for required home study, or because of the larger portion of time that must be given to outside employment, with its consequent reduction of the normal vitality of the individual or of his readiness to study.  But, in spite of the possible interrelationship of these factors, it still appears that the school entrance age of pupils will serve as a valuable sort of educational compass to foretell in part the probable direction of their later accomplishment.

3.  THE AMOUNT OF FAILURE AT EACH AGE AND ITS RELATION TO THE POSSIBILITY OF FAILING FOR THAT AGE

We have considered at some length the prognostic value of the age at entrance.  Here we shall briefly consider the prognostic value of age in reference to the time when failures occur and the amount of failure for such age.  If we were to total all the failures for a given age, as shown in Table I, what part will that form of the total subjects taken by these pupils at the time the failures occur?  In other words, what are the percentages formed by the total failures on the possibility of failing, for the same pupils and the same semesters, considered by age groups?  The summary line of Table I gives the total failures according to the ages at which they occurred.  The number of pupils sharing in each group of these failures is also known by a separate tabulation.  Then the full number of subjects per pupil is taken as 41/2, since approximately 50 per cent of the pupils take five or more subjects each semester and the other 50 per cent take four or less (see p. 61).  With the number of pupils given, and with a schedule of 41/2 subjects per pupil, we are able to compute the percentages which the failures form of the total subjects for these failing pupils at the time.  These percentages are given below.

  THE PERCENTAGES FORMED BY FAILURES AT EACH AGE ON THE POSSIBILITIES OF
  FAILING AT THAT AGE AND TIME, FOR THE SAME PUPILS

  Ages 13 14 15 16 17 18 19 20 21

  % 36.6 38.0 37.9 40.9 40.8 41.2 41.3 42.0 42.7

  [Footnote:  These percentages are computed from the data secured in
  Table I, as noted above.]