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Rapidity of Learning Series of Syllables

47

In order to make the number of repetitions comparable it is necessary, so to speak, to reduce them to a common denominator and to divide them each time by the number of the series. In this way it is found out how many repetitions relatively were necessary to learn by heart the single series, which differ from each other only in the number of syllables, and which each time had been taken together with as many others of the same kind as would make the duration of the whole test from fifteen to thirty minutes.^[1]

However, a conclusion can be drawn from the figures from the standpoint of decrease in number of syllables. The question can he asked: What number of syllables can be correctly recited after only one reading? For me the number is usually seven. Indeed I have often succeeded in reproducing eight syllables, but this has happened only at the beginning of the tests and in a decided minority of the cases. In the case of six syllables on the other hand a mistake almost never occurs; with them, therefore, a single attentive reading involves an unnecessarily large expenditure of energy for an immediately following reproduction.

If this latter pair of values is added, the required division made, and the last faultless reproduction subtracted as not necessary for the learning, then the following table results.

Number of syllables in a series	Number of repetitions necessary for first errorless reproduction (exclusive of it)	Probable error
7	1
12	16.6	± 1.1
16	30.0	± 0.4
24	44.0	± 1.7
36	55.0	± 2.8

↑ The objection might be made that, by means of this division, recourse made directly to the averages for the memorising of the single series, and that in this way the result of the Fourth Chapter is disregarded. For, according to that, the averages of the numbers obtained from groups of series could indeed be used for investigation into relations of dependence, but the averages obtained from separate series could not be so used. I do not claim, however, that the above numbers, thus obtained by division, form the correct average for the numbers belonging to the separate series, i.e., that the latter group themselves according to the law of errors. But the numbers are to be considered as averages for groups of series, and, for the sake of a better comparison with others—a condition which in the nature of the case could not be everywhere the same—is made the same by division. The probable error, the measure of their accuracy, has not been calculated from the numbers for the separate series but from those for the groups of series.

[1] The objection might be made that, by means of this division, recourse made directly to the averages for the memorising of the single series, and that in this way the result of the Fourth Chapter is disregarded. For, according to that, the averages of the numbers obtained from groups of series could indeed be used for investigation into relations of dependence, but the averages obtained from separate series could not be so used. I do not claim, however, that the above numbers, thus obtained by division, form the correct average for the numbers belonging to the separate series, i.e., that the latter group themselves according to the law of errors. But the numbers are to be considered as averages for groups of series, and, for the sake of a better comparison with others—a condition which in the nature of the case could not be everywhere the same—is made the same by division. The probable error, the measure of their accuracy, has not been calculated from the numbers for the separate series but from those for the groups of series.

[1]