Woody ['16] has constructed his well-known tests on this principle, though he uses only one example at each step of difficulty instead of eight or ten as suggested above. His test, so far as addition of integers goes, is:-- SERIES A. ADDITION SCALE (in part) By Clifford Woody (1) (2) (3) (4) (5) (6) (7) (8) (9) 2 2 17 53 72 60 3 + 1 = 2 + 5 + 1 = 20 3 4 2 45 26 37 10 -- 3 -- -- -- -- 2 -- 30 25 -- (10) (11) (12) (13) (14) (15) (16) (17) (18) 21 32 43 23 25 + 42 = 100 9 199 2563 33 59 1 25 33 24 194 1387 35 17 2 16 45 12 295 4954 -- -- 13 -- 201 15 156 2065 -- 46 19 --- ---- --- -- (19) (20) (21) (22) $ .75 $12.50 $8.00 547 1.25 16.75 5.75 197 .49 15.75 2.33 685 ----- ------ 4.16 678 .94 456 6.32 393 ----- 525 240 152 --- In his original report, Woody gives no scheme for scoring an individual, wisely assuming that, with so few samples at each degree of difficulty, a pupil's score would be too unreliable for individual diagnosis. The test is reliable for a class; and for a class Woody used the degree of difficulty such that a stated fraction of the class can do the work correctly, if twenty minutes is allowed for the thirty-eight examples of the entire test. The measurement of even so simple a matter as the efficiency of a pupil's responses to these tests in adding integers is really rather complex. There is first of all the problem of combining speed and accuracy into some single estimate. Stone gives no credit for a column unless it is correctly added. Courtis evades the difficulty by reporting both number done and number correct. The author's scheme, which gives specified weights to speed and accuracy at each step of the series, involves a rather intricate computation.