Pearson is, of course, a more precise measure of relation within the special conditions for which it is designed (two normal distributions); and the least-square procedure is useful in fitting a straight line or other curve to a set of figures; but the T-method seems worth using as a measure of relation whose reliability (unlike least-squares) 2 can always be readily found; and which, though less refined than the product-moment r, is far more widely applicable.

REFERENCES

I. BORING, E. G. Is there a generalized psychometric function? Amer. J. of Psychol., 1924, 35, 75.

2. BROWN, WARNER. The judgment of difference, etc. Univ. Calif. Publ. Psychol., 1910, I, I.

3. BROWN, W., & THOMSON, G. H. Essentials of mental measurement. Cambridge: University Press, 1921.

4. CULLER, ELMER. Thermal discrimination and Weber's law, with a theory on the nature and function of sensory adaptation. Arch. of Psychol., 1926, no. 81. 5. CULLER, ELMER. Studies in psychometric theory (I-X). Psychol. Monog., (Illinois studies), 1926, 35, no. 163.

6. Fernberger, S. W. Approximation of actual data to the phi-gamma hypothesis. Amer. J. of Psychol., 1923, 34, 498.

7. HOISINGTON, L. B. Example of fractionation of data, etc. Amer. J. of Psychol., 1917, 28, 588.

8. RICH, G. J. Measure of approximation of data to the phi-gamma hypothesis. Amer. J. of Psychol., 1925, 36, 615.

9. THOMSON, G. H. Criterion of goodness of fit of psychophysical curves. Biometrika, 1919, 12, 216.

10. URBAN, F. M. Messungen.

11. URBAN, F. M.

Die psychophysischen Massmethoden als Grundlagen empirischer
Arch. f. d. ges. Psychol., 1909, 15, 261; 16, 168.

Der Einfluss der Übung bei Gewichtsversuchen. Arch. f. d. ges.
Psychol., 1913, 29, 271.

12. URBAN, F. M. Approximation of actual data to the phi-gamma hypothesis. Amer. J. of Psychol., 1923, 34, 496.

2 In fact, the writer is not aware of any procedure, generally usable, for determining the reliability of the slope of a fitted line.

SPECIFIC SERIAL LEARNING; A STUDY OF

BACKWARD ASSOCIATION

BY HULSEY CASON

Syracuse University

PRELIMINARY STATEMENT

Theory of remote associations.-For some years it has been assumed that when associations are formed in a series from item 1 to item 2, from 2 to 3, from 3 to 4, etc., certain remote associations are also formed; so that item 2, for example, becomes connected with all of the other items in the series, in both the forward and backward directions. Ebbinghaus carried out the original experiments on which this theory of remote associations was based; and he claimed that the remote associations are stronger in the forward than in the backward direction, and that the strength of the associations decreases with the number of intervening items. About two years ago the writer suggested some of the difficulties with this theory expecially as it relates to backward associations.2 The present paper describes experiments in which the problem of backward association is for the first time submitted to a systematic experimental investigation.3

1 H. Ebbinghaus, Memory, a contribution to experimental psychology, 1885, 90-117 (Tr. by Ruger and Bussenius). See also G. E. Müller & F. Schumann, Experimentelle Beiträge zur Untersuchungen des Gedächtnisses, Zsch. f. Psychol. u. Physiol. d. Sinnesorgane, 1894, 6, 81-190, 257–339; G. E. Müller & A. Pilzecker, Experimentelle Beiträge zur Lehre vom Gedächtniss, Zsch. f. Psychol. u. Physiol. d. Sinnesorgane, Ergänzungsband I. (1900), pp. 1–288; A. Wohlgemuth, Ueber die Richtung der Assoziationen, Ber. über d. V. Kongress f. exper. Psychol., 1912, 284-287, and On memory and the direction of associations, Brit. J. Psychol., 1913, 5, 447-465; A. Michotte & F. Fransen, Note sur l'analyse des facteurs de la mémorisation et sur l'inhibition associative, Ann. de l'institut sup. de philos. (Université de Louvain), 1914, 3, 503-549; H. A. Carr & A. S. Freeman, Time relationships in the formation of associations, Psychol. Rev., 1919, 26, 465-473.

H. Cason, The concept of backward association, Amer. J. Psychol., 1924, 35,

217-221.

"I wish to make a grateful acknowledgment to my wife, Eloise Boeker Cason, for much valuable assistance in carrying out the experiments and in the preparation of the manuscript, and to all those students at Syracuse University who, as subjects, gave so generously of their time and interest.

Problem. If the series 1-2-3-4-5, etc., is learned so that the items can be reproduced in the proper order, does this learning result in the formation of backward associations and so facilitate the later learning of the items in the order 5-4-3-2-1? When one individual learns the items in the order 1-2-3-4-5 this learning is of course in the forward direction; and when another individual, or the same individual at a different time, learns the same items written in the order 5-4-3-2-1 this learning is likewise in the forward direction. It follows that if there is some practice in the order 5-4-3-2-1, while the principal task of learning the series in the order 1-2-3-4-5 is in progress, then both kinds of learning are really forward in nature. The theory of backward associations assumes that when associations are formed in the order 1-2-3-4-5, associations are at the same time established in the order 5-4-3-2-1. No serious attempts have been made to explain just how or why these backward associations are formed, although the question is of special significance for the psychology of learning.

PART I. TESTS WITH ROTE MATERIAL
INTRODUCTION

Suggested test with the letters of the alphabet.—We thought at first that the letters of the alphabet might be used as learning material. The subjects have already established strong forward associations between these items, and the proposed test might be made as follows. Derive 2 lists from the letters of the alphabet, one list being made up of the adjacent letters arranged in the backward direction, and the other list being made up of the same letters arranged in a mixed order. The theory of backward association might be tested by comparing the relative difficulty of learning the derived backward list and the derived mixed list. The superiority of the backward list would indicate the presence of backward associations, etc. On second thought, however, it seems that such results would not be conclusive, on account of several complicating factors which may be described as follows.

Standards of comparison for backward association.-A subject who is familiar with the letters of the alphabet has already established a variety of associations among the pairs and groups of letters; and a derived mixed list would not necessarily represent zero learning at the beginning of a new learning period. The situation affords the following possibilities. (1) The mixed list might include some strong forward associations between the pairs of letters, which would give it a place above zero at the beginning of a new learning period. (2) The mixed list might include some associations which would interfere with the new learning of the same material, and this circumstance would give it a place below zero at the beginning of a new learning period. (3) It is also possible that the facilitating and inhibiting associations in the mixed list might just balance each other, and in such an event the later learning of the letters in the mixed order would begin at a zero level. In the simple procedure with the letters of the alphabet, it is not known whether the new learning of the mixed list begins above zero, below zero, or at zero, and a comparison between the mixed list and the backward list would in no way indicate the presence or the absence of backward associations.

The best type of material for the purposes of the present experiment seems to be that which contains very few associations between the separate pairs or groups of items. There should be a large number of items, and they should be practically equal in difficulty. Series of letters are unsatisfactory as material because of the small number of letters in the alphabet. The same objection applies to the use of digits. Most of the difficulties suggested above can be satisfactorily met or avoided by a general plan which is outlined in the following paragraphs.

Procedure with forward, backward, and separated lists.Let us suppose that each of the figures in Table I represents a different nonsense syllable. The following plan and procedure can then be used.

(a) Each of the 12 horizontal rows of syllables constitutes a practice list, and each practice list is typewritten on a separate

card. The subject is required to learn these lists singly. The learning is limited as far as possible to the formation of associations in the forward direction, and each list is learned to as nearly the same degree of proficiency as possible. The lists are rotated from time to time for a group of subjects, so that each list has the same advantages on account of its position in the whole set of material.

(b) The 48 syllables represented in Table I also constitute a different set of 12 lists, which will be referred to as the test lists. The test lists are of 3 kinds: 4 forward lists, 4 backward lists, and 4 separated lists. The forward lists are made up of the syllables in the rows directly to the right of the 'F's' in the table, the items being arranged in the order shown, as 1-2-3-4, 31-32-33-34, etc. The backward lists are made up of the syllables in the rows directly to the left of the 'B's' in the table, the items being arranged and written in the reverse order, as 14-13-12-11, 44-43-42-41, etc. The separated lists are made up of the syllables in the columns above the 'S's,' and these items are represented by the italicized numbers, and are arranged from bottom to top, as 111-81-51-21, 112-8252-22, etc.

(c) The 12 test lists derived from the syllables represented in Table I also constitute 4 groups of 3 test lists each. Each