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106
Mermory

so that the first experiments gave results which were somewhat too high; and the second, results that were somewhat too low. It is allowable, under this hypothesis, to put the two sets of figures together so that the contrasting errors may compensate each other. In this way there was finally obtained out of the 85 double tests the following table.


Number of
intermediate
syllabes skipped
in the formation
of the
derived series
Time for
learning
the
original
series
Time for
learning
the
derived
series
Saving of
work in
learning
the derived
series
Probable
error of
saving
of work[* 1]
Saving of
work in %
of original
learning
time
(The numbers of the four middle columns denote seconds)
0 (1266) (844) (422) (33.3)
1 1275 1138 137 ±16 10.8
2 1260 1171 89 ±18 7.0
3 1260 1186 73 ±13 5.8
7 1268 1227 42 ± 7 3.3
permutation
of syllables
1261 1255 6 ±13 0.5
  1. The probable errors are calculated from the separate values for savings of work, while the latter, which were actually obtained by subtraction, are considered as the results of direct observation. (see p. 67, note.)


Section 39. Discussion of Results

In the foregoing table an especial interest, it seems to me, is connected with the last, and also with the next to the last, row of numbers. When there was complete identity of all the syllables and the initial and end terms were left in their places, the average saving of time for 17 tests dealing with the learning of the derived series was so slight that it was hardly to be determined. It fell within half of its probable error. The syllables were, therefore, in themselves, outside of their connection, so familiar to me that they did not become noticeably more familiar after being repeated 32 times. On the contrary when a related series was repeated the same number of times, each syllable became so firmly bound to the syllable which followed 8 places beyond that 24 hours later the influence of this connection could be determined in no doubtful fashion. It attains a value 6 times the probable error. Its existence, therefore, must be considered to be fully proved although naturally we cannot be so sure that its size is exactly what it was found