The Data
The source of the data used to help answer the above questions is some six thousand test papers gathered from twenty-six representative school systems. Copies of the tests may be found in Part I, pages 10 and 11; as may also a statement of conditions under which the tests were personally given by the author, page 13; and the method of scoring, pages 15 to 18.
The achievements are considered from two standpoints—(1) the scores and mistakes of the systems as systems, (2) the scores of individual pupils as individuals.
Table III gives the scores made in reasoning by each of the twenty-six systems, counting all the problems that were solved, and weighting them according to the last column of table II. The Roman numerals used in the left-hand column to designate the systems are those that fell to each system by lot. As seen by the column headed scores made, the systems are arranged according to number of scores, i.e. system XXIII made three hundred fifty-six points, the lowest score, and is placed first in the table; system XXIV made four hundred twenty-nine points, and is placed second, etc. System V, having made the highest score, is placed last in the table.
ACHIEVEMENTS OF THE SYSTEMS AS SYSTEMS
Measured by Scores Made
TABLE III[34] TABLE IV
| Scores of the Twenty-six Systems in Reasoning with Deviations from the Median. Scores from all Problems | Scores of the Twenty-six Systems in Fundamentals with Deviations from the Median. Scores from all Problems | ||||||
| M[35] = 551 | M = 3111 | ||||||
| Systems in Order of Achieve- ment | Scores Made[36] | Devia- tions from the Median | Devia- tions in Per Cent of the Median | Systems in Order of Achieve- ment | Scores Made | Devia- tions from the Median | Devia- tions in Per Cent of the Median |
| XXIII | 356 | -195 | -35 | XXIII | 1841 | -1270 | -41 |
| XXIV | 429 | -122 | -22 | XXV | 2167 | -944 | -30 |
| XVII | 444 | -107 | -19 | XX | 2168 | -943 | -30 |
| IV | 464 | -87 | -16 | XXII | 2311 | -800 | -26 |
| XXV | 464 | -87 | -16 | VIII | 2747 | -364 | -12 |
| XXII | 468 | -83 | -15 | X | 2749 | -362 | -12 |
| XVI | 469 | -82 | -15 | XV | 2779 | -332 | -11 |
| XX | 491 | -60 | -11 | III | 2845 | -266 | -8 |
| XVIII | 509 | -42 | -8 | I | 2935 | -176 | -6 |
| XV | 532 | -19 | -3 | XXI | 2951 | -160 | -5 |
| III | 533 | -18 | -3 | II | 2958 | -153 | -5 |
| VIII | 538 | -13 | -2 | XVII | 3042 | -69 | -2 |
| VI | 550 | -1 | -2 | XIII | 3049 | -62 | -2 |
| I | 552 | 1 | 2 | VI | 3173 | 62 | 2 |
| X | 601 | 50 | 9 | XI | 3261 | 150 | 5 |
| II | 615 | 64 | 12 | IX | 3404 | 293 | 9 |
| XXI | 627 | 76 | 14 | XII | 3410 | 299 | 10 |
| XIII | 636 | 85 | 15 | XXIV | 3513 | 402 | 13 |
| XIV | 661 | 110 | 19 | XIV | 3561 | 450 | 14 |
| IX | 691 | 140 | 20 | IV | 3563 | 452 | 14 |
| VII | 734 | 183 | 33 | V | 3569 | 458 | 15 |
| XII | 736 | 185 | 34 | XXVI | 3682 | 571 | 18 |
| XI | 759 | 208 | 38 | XVI | 3707 | 596 | 19 |
| XXVI | 791 | 240 | 44 | XVIII | 3758 | 647 | 21 |
| XIX | 848 | 297 | 54 | VII | 3782 | 671 | 22 |
| V | 914 | 363 | 66 | XIX | 4099 | 988 | 31 |
The middle column gives the deviations from the median, which is that measure above and below which one half the cases lie. In this table the median is five hundred fifty-one. These deviations serve to show the differences in scores made; and they are also employed in computing the measures of variability and relationship. The third column is the deviations in per cent of the median. It affords another expression of the difference in size of scores made by the systems.