None
According to the view here developed, it is the weeding out of the sample of elemental abiUties which is specific. The team work is specific, though the players play for several clubs. This would appear to enable a reconciliation to be effected between the almost universal behef in " types " of abiUty (to which Professor Spearman refers) and the experi- mental facts concerning both correlation and transfer. If there be a General Factor at all, it might be the power to shake down rapidly into good team work, in a word, educabiUty. But there seems no objection to assuming that this, instead of being a General Factor, is a property of each elemental factor, varying from factor to factor. 192 COKRELATION [pt. ii, ch. x To sum up this section : if transfer of training really does not occur to any great extent, then it has to be admitted that the Theory of Two Factors readily explains this. But the Samphng Theory can also do so, in a manner which is perhaps not so easy to set forth, but which never- theless appears to be more illuminating and less artificial than the alternative theory. (8) CONCLUSIONS Professor Spearman's Theory of Two Factors, which assumes that abihty in any performance is due to (a) a General Factor and (6) a Specific Factor (Group Factors being absent, or at any rate very narrow in range and mutually exclusive), is based chiefly on the observed fact that correlation coefficients in psychological tests tend to fall into " hierar- chical order." It has been shown, however, that the criterion adopted for evaluating the degree of perfection of hierarchical order present is untrustworthy and has led to over-estimation. Such hierarchical order as is actually present is in fact the natural thing to expect, and it is the absence of such which should occasion surprise. The proof of the Theory of Two Factors which is based on the presence of hierarchical order therefore falls to the ground. The theory remains a possible explanation of the facts but ceases to be the unique explanation. As an alternative theory Thomson has advanced a Samphng Theory of Abihty, in which any performance is considered as being carried out by a sample of Group Factors. This theory is preferred because it makes fewer and less special assumptions, because it is more elastic and wider, and because it is in closer accord with theories in use in biology and in the study of heredity *. ♦ For articles on the General Ability controversy which have appeared while this book was going through the press the reader is referred to the conclusion of the Biblio- graphy, p. 212. APPENDIX T TABLES 1. Fechner's Fundamental Table. 2. Urban's Tables for the Constant Process. 3. Table of Muller-Urban Weights. 4. Reciprocals of 'pq, where p -\- q = 1. 5. Rich's Checking Table for the Constant Process. 1. Fechner's Fundamental Table. p 7 0-0000 1 P 7 i P 1 7 0-50 ! 0-67 0-3111 ! 0-84 0-7031 0-61 0-0177 1 0-68 0-3307 0-85 0-7329 0-52 0-0366 0-69 0-360^ 0-86 0-7639 0-63 00632 0-70 0-3708 0-87 0-7966 0-64 00710 0-71 0-3913 0-88 0-8308 0-65 0-0888 0-72 0-4121 0-89 0-8673 0-56 0-1067 0-73 0-4333 i 0-90 0-9062 0-67 0-1247 0-74 0-4649 0-91 0-9480 0-68 0-1427 0-76 0-4769 0-92 0-9936 0-69 0-1609 ; 0-76 0-4994 0-93 1-0436 0-60 0-1792 , 0-77 0-6224 0-94 1-0993 0-61 01976 0-78 0-5460 0-95 1-1630 0-62 0-2160 0-79 0-6702 0-96 1-2380 0-63 0-2346 0-80 0-6951 0-97 1-3300 0-64 0-2636 0-81 0-6208 0-98 1-4620 0-65 0-2725 0-82 0-6473 0-99 1-6460 0-66 0-2916 1 0-83 0-6747 l-OO cc If p is < 0*5, look in the Table not for p but for I - p, and take y negative. Thus the y f or ^ = 0-25 is - 0-4769. This Table is less generally useful than Sheppard's Tables of the Probability Integral, Tables I and II of Pearson's Tables for Statisticians and Biometricians (Cambridge University Press). Table I there differs from this only by a factor \/2 : but gives many more values and to more decimal places. &T. 13 194 APPENDIX I 2. Urban* s Tables for the Constant Process, From Arckivf. d. ges. Psychol. 1912, xxtv. 240—241*. p w yW 1 2W 2^W 2yW 3W S^W SyW 0-0000 4W ^ZW ^yW 0-50 10000 0-0000 2-0000 4-0000 0-0000 3-0000 90000 40000 16-0000 0-0000 0-51 0-9998 0-0177 1-9996 3-9991 0-0354 2-9993 8-9980 0-0531 3-9991 16-9965 0-0708 0-52 ! 0-9991 0-0355 1-9982 3-9963 0-0709 2-9972 8-9917 0-1064 3-9963 15-9853 0-1419 0-53 1 0-9980 0-0531 i 1-9959 3-9918 0-1062 2-9938 8-9816 0-1593 ! 3-9918 15-9672 0-2124 0-54 0-9964 0-0707 i 1-9928 3-9855 0-1415 2-9891 8-9674 0-2122 3-9855 15-9421 0-2830 0-66 0-9943 00883 ' 1-9886 3-9772 0-1766 2-9829 8-9487 0-2649 3-9772 15-9088 0-3532 0-56 0-9918 0-1058 1 1-9836 3-9671 0-2116 2-9753 8-9260 0-3175 3-9671 15-8685 0-4233 0-57 0-9888 01233 i 1-9776 3-9551 0-2466 2-9663 8-8990 0-3699 3-9551 16-8205 0-4932 0-68 0-9853 0-1406 ! 1-9706 3-9413 0-2812 2-9560 8-8679 0-4218 3-9413 15-7661 0-5624 0-59 0-9814 0-1579 1-9627 3-9254 0-3158 2-9441 8-8322 0-4737 3-9254 15-7018 0G3i() 0-60 0-9768 0-1750 1-9537 3-9074 0-3501 2-9306 8-7916 0-5252 3-9074 15-6296 0-7002 0-61 0-9720 0-1920 1-9440 3-8881 0-3839 2-9161 8-7482 0-5759 3-8881 16-5523 0-7679 0-62 0-9666 0-2088 1-9332 3-8663 0-4176 2-8997 8-6992 0-6263 3-8663 16-4653 0-8351 0-63 0-9607 0-2254 1-9214 3-8429 0-4508 2-8822 8-6465 0-6762 3-8429 15-3716 0-9015 0-64 0-9542 0-2419 1-9084 3-8168 0-4838 2-8626 8-5878 0-7257 3-8168 15-2672 0-9676 0-65 0-9473 0-2581 1-8945 3-7890 0-5163 2-8418 8-5253 0-7744 3-7890 15-1562 1-0325 0-66 0-9398 0-2741 1-8797 3-7594 0-6481 2-8196 8-4586 0-8222 3-7594 15-0376 1-0962 0-67 0-9317 0-2899 1-8634 3-7268 0-5797 2-7951 8-3853 0-8696 3-7268 14-9072 11594 0-68 i 0-9232 0-3053 1-8464 3-6929 0-6106 2-7697 8-3090 0-9159 3-6929 14-7716 1-2212 0-69 0-9140 0-3205 1-8280 3-6561 0-6409 2-7421 8-2262 0-9614 3-6561 14-6243 1-2818 0-70 0-9043 0-3353 1-8085 3-6170 0-6706 2-7128 8-1383 1-0059 3-6170 14-4682 1-3412 0-71. 0-8939 0-3498 1-7878 3-5755 0-6996 2-6816 8-0449 10493 3-5755 14-3021 1-3991 0-72 0-8830 0-3639 17659 3-5318 0-7277 2-6489 7-9466 1-0916 3-5318 14-1274 1-4555 0-73 0-8713 0-3775 1-7426 3-4852 0-7541 2-6139 7-8417 1-1326 3-4852 13-9408 1-6101 0-74 0-8590 0-3908 1-7180 3-4360 0-7815 2-5770 7-7310 1-1723 3-4360 13-7440 1-5630 0-75 0-8460 0-4035 1-6921 3-3842 0-8070 2-5381 7-6144 1-2104 3-3842 13-5366 1-6139 0-76 0-8323 0-4157 1-6646 3-3293 0-8313 2-4970 7-4909 1-2470 3-3293 13-3171 1-6626 0-77 0-8179 0-4273 1-6357 3-2714 0-8545 2-4536 7-3607 1-2818 3-2714 13-0858 1-7090 0-78 0-8025 0-4382 1-6051 3-2102 0-8764 2-4076 7-2229 1-3146 3-2102 12-8406 1-7527 0-79 0-7865 0-4484 1-5729 3-1459 0-8969 2-3594 7-0782 1-3453 3-1459 12-5835 1-7938 0-80 0-7695 0-4579 1-5390 3-0780 0-9159 2-3085 6-9255 1-3738 3-0780 12-3120 1-8317 0-81 0-7515 0-4665 1-5031 3-0061 0-9331 2-2546 6-7638 1-3996 30061 12-0245 1-8602 0-82 0-7327 0-4743 1-4653 2-9307 0-9485 2-1980 6-5940 1-4228 2-9307 11-7227 1-8970 0-83 0-7129 0-4810 1-4257 2-8515 0-9619 2-1386 6-4158 1-4429 2-8515 11-4059 1-9239 0-84 0-6921 0-4866 1-3842 2-7683 0-9732 2-0762 6-2287 1-4598 2-7683 110733 1-9464 0-85 0-6697 0-4908 1-3394 2-6788 0-9816 20091 60273 1-4725 2-6788 10-7152 1-9633 0-86 0-6463 0-4937 1-2927 2-5853 0-9875 1-9390 5-8170 1-4812 2-5853 10-3413 1-9749 0-87 0-6215 0-4950 1-2430 2-4860 0-9900 1-8645 5-5935 1-4851 2-4860 9-9440 19801 0-88 0-5953 0-4946 1-1907 2-3813 0-9892 1-7860 5-3580 1-4838 2-3813 9-5253 1-9784 0-89 0-5673 0-4920 1-1346 2-2692 0-9840 1-7019 5-1056 1-4760 2-2692 9-0766 1-9680 0-90 0-5376 0-4871 1-0751 2-1502 0-9743 1-6126 4-8380 1-4614 2-1602 8-6008 l-948;j 0-91 0-5059 0-4796 1-0118 2-0236 0-9592 1-5177 4-5531 1-4388 2-0236 8-0944 1-9184 0-92 0-4718 0-4687 0-9435 1-8871 0-9374 1 1-4153 4-2459 1-4061 1-8871 7-5483 1-8748 0-93 0-4351 0-4540 0-8702 1-7403 0-9080 ! 1-3052 3-9157 1-3620 1-7403 69613 1-8160 0-94 0-3954 0-4346 0-7907 1-5814 0-8692 , 1-1861 3-5582 1-3039 1-5814 6-3268 1-7385 0-95 0-3519 0-4093 0-7038 1-4076 0-8185 I 1-0557 3-1671 1-2278 1-4076 5-6304 1-6370 0-96 0-3036 0-3759 0-6073 1-2146 0-7518 0-9109 2-7328 1-1277 1-2146 4-8582 l-503( 0-97 0-2469 0-3282 0-4936 0-9871 0-6564 0-7403 2-2210 0-9847 0-9871 3-9486 1-312S 0-98 01881 02732 0-3762 0-7525 0-5463 0-5644 1-6931 0-8195 0-7525 30099 l-092e 0-99 01127 01854 0-2254 0-4508 0-3708 0-3381 1-0142 0-5561 0-4508 1-8030 0-741C * With three corrections, two of which were made by Urban in the Praxis der Kon- stanzmetfiode, and the third by Rich in Amer. Journ. Psychol. 1918, xxix. 121. The last was also rediscovered by the Cambridge Univ. Press proof reader. APPENDIX I 196 2. Urban* s Tables for the Constant Process (contd.). From Archivf. d. ges. Psychol. 1912, xxiv. 240—241. p 5W 5*W 5yW 1 6W 6*W 6yW 1 TW vw TyW 0-50 50000 26-0000 00000 60000 36-0000 0-0000 70000 49-0000 00000 0-61 4-9989 24-9945 0-0885 5-9987 35-9921 0-1062 6-9986 48-9892 0-1239 0-52 4-9954 24-9770 0-1773 i 5-9946 36-9669 0-2128 6-9936 48-9649 0-2483 0-53 4-9898 24-9488 0-2655 5-9877 36-9262 0-3185 6-9866 48-8996 0-3716 0-54 4-9819 24-9095 0-3537 i 6-9783 35-8697 0-4251 6-9747 48-8266 0-4960 0-55 4-9715 24-8575 0-4415 6-9658 35-7948 0-5298 6-9601 48-7207 0-6181 0-56 4-9589 24-7945 0-5291 ' 6-9507 35-7041 0-6349 6-9426 48-6972 0-7408 0-57 4-9439 24-7195 0-6165 6-9327 35-5961 0-7398 6-9215 48-4602 0-8631 0-58 4-9266 24-6330 0-7030 5-9119 35-4715 0-8436 6-8972 48-2807 0-9842 0-59 4-9068 24-5340 0-7895 5-8882 35-3290 0-9474 6-8695 48-0866 1-1063 0-60 4-8842 24-4212 0-8753 5-8611 35-1666 1-0503 6-8380 47-8666 1-2264 0-61 4-8601 24-3005 0-9599 5-8321 34-9927 1-1518 6-8041 47-6290 1-3438 0-62 4-8329 24-1645 10439 5-7995 34-7969 1-2527 6-7661 47-3624 1-4616 0-63 4-8036 24-0180 11269 6-7643 34-5859 1-3523 6-7250 47-0753 1-5777 0-64 1 4-7710 23-8550 1-2094 5-7252 34-3512 1-4513 6-6794 46-7568 1-6932 0-65 ' : 4-7363 23-6815 1-2906 5-6836 34-1014 1-6488 6-6308 46-4167 1-8069 0-66 - 4-6992 23-4962 1-3703 5-6391 33-8346 1-6444 6-5790 46-0526 1-9184 0-67 1 , 4-6585 23-2925 1-4493 5-5902 33-5412 1-7391 6-5219 45-6533 2-0290 0-68 1 4-6161 230805 1-5265 6-5393 33-2359 1-8319 6-4625 45-2378 2-1372 0-69 4-5701 22-8505 1-6023 5-4841 32-9047 1-9227 6-3981 44-7870 2-2432 0-70 1 4-5213 22-6065 1-6765 5-4256 32-5534 20118 6-3298 44-3087 2 3471 0-71- i 4-4694 22-3470 1-7489 5-3633 32-1797 2-0987 6-2672 43-8001 2-4484 0-72 4-4148 22-0740 1-8193 5-2978 31-7866 2-1832 6-1807 43-2650 2-5471 0-73 4-3565 21-7825 1-8877 5-2278 31-3668 2-2652 6-0991 42-6937 2-6427 0-74 4-2950 21-4750 1-9538 51540 30-9240 2-3446 6-0130 42-0910 2-7353 0-75 1 4-2302 21-1510 2-0174 5-0762 30-4574 2-4209 6-9223 41-4560 2-8243 0-76 1 4-1616 20-8080 20783 4-9939 29-9635 2-4940 6-8262 40-7837 2-9096 0-77 1 4-0893 20-4465 21363 4-9072 29-4430 2-6635 6-7250 40-0751 2-9908 0-78 40127 20-0635 2-1909 4-8152 28-8914 2-6291 6-6178 39-3245 3-0673 0-79 3-9324 19-6618 2-2422 4-7188 28-3129 2-6907 6-5053 38-5370 3-1391 0-80 3-8475 19-2375 2-2896 4-6170 27-7020 2-7476 5-3865 37-7055 3-2055 0-81 3-7576 18-7882 2-3327 4-5092 27-0551 2-7993 6-2607 36-8250 3-2658 0-82 3-6634 18-3168 2-3713 4-3960 26-3761 2-8455 6-1287 35-9008 3-3198 0-83 3-5644 17-8218 2-4049 4-2772 25-6631 2-8858 4-9901 34-9306 3-3668 0-84 3-4604 17-3020 2-4330 4-1525 24-9149 2-9196 4-8447 33-9119 3-4062 0-85 3-3485 16-7425 2-4541 4-0182 24-1092 2-9449 4-6879 32-8153 3-4358 0-86 3-2316 16-1582 2-4687 3-8780 23-2679 2-9624 4-5243 31-6702 3-4561 0-87 3-1075 15-5375 2-4751 3-7290 22-3740 2-9701 4-3505 30-4535 3-4652 0-88 2-9766 14-8832 2-4730 3-5720 21-4319 2-9676 4-1673 29-1712 3-4622 0-89 2-8364 141822 2-4600 3-4037 20-4222 2-9521 3-9710 27-7972 3-4441 0-90 2-6878 13-4388 2-435() 3-2253 19-3518 2-9228 3-7628 26-3400 3-4099 0-91 2-5295 12-6475 2-3980 30354 18-2124 2-8776 3-5413 24-7891 3-3572 0-92 2-3588 11-7942 2-3435 2-8306 16-9837 2-8122 3-3024 23-1167 3-2809 0-93 2-1754 10-8770 2-2700 2-6105 15-6629 2-7240 3-0466 21-3189 3-1780 0-94 1-9768 9-8840 2-1731 2-3722 14-2330 2-6077 2-7675 19-3726 3-0423 0-95 1-7595 8-7975 2-0463 2-1114 12-6684 2-4566 2-4633 17-2431 2-8648 0-96 1-5182 7-5910 1-8795 1-8218 10-9310 2-2564 ( 2-1255 14-8784 2-6313 0-97 1-2339 61695 1-6411 1 1-4807 8-8841 1-9693 1-7275 12-0922 2-2976 0-98 0-9406 4-7030 1-3658 1 1-1287 6-7723 1-6389 1 1-3168 9-2179 1-9121 0-99 0-5634 2-7172 0-9269 1 0-6761 3-9668 1-1123 i 0-7888 6-4218 1-2976 196 APPENDIX I 3. p W P W P W 0-50 1000 0-67 0-932 0-84 0-694 0-51 1-000 0-68 0-923 0-86 0-670 0-62 0-999 i 0-69 0-914 0-86 0-646 0-53 0-998 i 0-70 0-904 0-87 0-621 0-54 0-996 1 0-71 0-894 0-88 0-595 0-55 0-996 0-72 0-883 0-89 0-567 0-66 0-992 1 0-73 0-871 0-90 0-538 0-57 0-989 1 0-74 0-859 0-91 0-506 0-58 0-985 1 0-75 0-846 0-92 0-472 069 0-981 i 0-76 0-832 0-93 0-435 0-60 0-977 0-77 0-818 0-94 0-396 0-61 0-972 0-78 0-803 0-96 0-352 0-62 0-967 0-79 0-787 0-96 0-304 0-63 0-960 0-80 0-770 0-97 0-249 0-64 0-954 1 0-81 0-752 0-98 0-187 0-66 0-947 0-82 0-733 0-99 0-112 0-66 0-940 0-83 0-713 1-00 0-000 The weight of a ^ which is less than 0*5 is the same as the weight of a p which exceeds 0-5 by the same amount. Thus the weights of jo = 0-25 and of ^ = 0-75 are both alike, = 0-846. ♦ The table is quoted from F. M. Urban, "The Method of CJonstant Stimuli and its Generalisations," Psychological Beview, 1910, xvn, p. 253. See also "Die psychophysischen Masamethoden als Grundlagen empirischer Messungen," by the same author, Archiv f. d. ges. Psychologie, xv. and xvi. 4. Reciprocals of pq, where p + q = 1. 1 1 1 povq pq povq pq porq pq -50 4-0 •67 4-5 •84 7-5 •51 4-0 •68 46 1 •85 7-9 -52 4-0 •69 4^7 1 •86 8-3 •53 4-0 •70 4-8 •87 8-8 •54 4-0 •71 4-9 •88 9-4 •55 4-1 •72 50 •89 10-2 •56 41 •73 51 •90 111 -57 4-1 •74 52 •91 122 -58 41 •76 63 •92 136 •59 41 •76 54 •93 154 •60 4-2 •77 56 •94 17^7 •61 4-2 •78 5^8 •95 210 •62 4-3 •79 60 •96 260 •63 43 •80 62 •97 344 •64 44 •81 6-5 •98 510 •65 44 •82 6^8 •99 101 •66 45 •83 71 100 00 APPENDIX I 197 5. Rich* 8 Checking Table for the Constant Method. Published from the Laboratory of Cornell University, in Amer. Joum. Psychol. 1918, xxix. 120. An example will best explain the use of this Table. Consider the example worked on p. 73. If we form for each line the totals of the five quantities W -\-yW + 8W + sm + syW we get the results 8 V Totals -6 •00 •0000 -5 •10 13-2371 -4 •14 9-8835 -3 •40 7-1880 -2 •65 2-5836 0 •80 1-2274 2 ■87 5-8356 4 •96 8-2559 6 1-00 0-0000 48-2110 These totals however will all be found in Rich's Table entered with the proper 5 (Rich's x) and p, and can thus be checked. The grand total 48-2110 ought to agree with the sum of the last row of the table (4) on p. 73, i.e. with 4-8026 + 0-4311 - 7-6406 + 43-7049 + 6-9130. 198 APPENDIX I Riches Checking Table. Jo J -00 Jo 4 ./ -00 ^ D= I zh-'^'dz = i, I = zero. Jo J -<x> T? r n z^^ 1.3.5...(n-l)V^. , ^' 2.2.2.2...2 ^^ ^^^^• 6? ' ^^ =A P C082 ^ - 2ii COS ^ sin ^ + g sin2 6 V{PQ - R^) ' but I is no^ ^. H=r .-<-P+^^«^d^ = :^ e-'^ , but f " is not f. \iPQ>R\ hut rr isnot^. Jo Jo 4 A = e ' ^ ' zrfz = V- ^ <? » but is wo« -jr J -00 O* /o 2 <?' APPENDIX n 203 L^r r e-<''^^»««^0^> ^dxdy^ T^ . if Pg > ft., but I IB not -r ' Jo Jo 4 0 if J -00 2Q* ^= /- Jl ^-^'"^^-•^^^.^y = ^-^^, . if Pg> ft.. Note. In the above integrals P and Q do not, as often, represent constants whose sum is unity. i2 is not a correlation coefficient, although it is closely connected therewith. APPENDIX III NOTATION A simple, consistent, and easily remembered notation is an essential in any mathematical treatment. The chief difficulty in the way of obtaining consistency in a work like the present is the desire naturally felt to keep any piece of research in the notation used by its originator. But a great effort has been made to attain a notation which could be used throughout the book without too seriously altering the appearance of any well-known formula. Most of the symbols in the following Table have been used by several important writers with the meaning here indicated. They are either always used with this meaning: or if there be any exception it is hoped that the context will make clear what is meant. The greatest difficulty has been felt over the choice of a symbol for a stimulus value. The commonest symbols hitherto used have been R and S for stimulus and sensation intensity respectively, and r has been used instead of R by at least one very important writer. But there is still greater unanimity of usage in employing r and R for correla- tion coefficients. In adopting small s for stimulus, we realise that there is some danger of confusion with great S used in the past, by writers on Weber's Law, for sensation intensity. But some of the same writers also use S for a standard stimulus (as we do) : and after the first chapter we have no necessity to speak of sensation-intensities at all, it is frankly physical stimuli which are measured. In the first chapter itself ambiguity or misunderstanding is avoided by printing the words at full length. It is hoped that this list of symbols may assist in obtaining unanimity and consistency in the notation of the subject and serve as a convenient reference. APPENDIX III 205 Symbols Used Symbol Meaning a a mean, m is also used for a mean, and any quantity with a bar, as S, is a A a true value. aj, a,, a, readings of which a is the mean. b a coefficient of regression. Usually suffixes are added. c and C constants, k is also used in this sense. Oj, Cj, and 4> contingency symbols. 8 a deviation: also used for a finite increment, d indicating an infin't^""^* increment, e an error. h modulus of precision in one notation of the Gaussian or Normal Curve of Error. k a constant. Also c and C. See also n. 2 see n. m a mean. See also n. M Miiller's weights. See w. H and V moments. N see n. n a number (of experiments, or the like). Wh6re necessary, JV, and also it, i, m, are used in this sense, m more commonly is used for a mean. p a mathematical measure of probability. P same as p. Q same as p. Usually Q is 1 -P: also used, usually with a suffix, for a quartile. q same as p. Usually g is \ -p. r a correlation coefficient. R a correlation coefficient. ri a correlation ratio. 8 a stimulus value. jS is a standard stimulus, V a variable, a is also on one occasion used for a standard deviation. <r a standard deviation. Also S is used, and on one occasion «. 2 a standard deviation. Would also be used for a summation of any kind other than that for which 8 is used in this book; but no such occasion arises in the present work. 8 a sum over the distribution, e.g. S (e) is the sum of the errors. 5 is also used for a standard stimulus, see small a and also the remarks preceding this table. t t, with Xf y and z, is used as a variable of integration. T Thresholds, both absolute and difference. Sometimes with suffixes as T^ and Ti for upper and lower difference thresholds or limina. u u and v "residuals" in observation equations. V see u. V variable stimulus, see s. Also coefficient of variation. w "weight" of a reading or an equation. Also W, and M^ the latter for Miiller's weights only. W see w. X in connection with goodness of fit. X Xfy,z and t are used as variables of integration. y see x. BIBLIOGRAPHY In view of the excellence of the annual Psychological Index (Princeton, N.J.), and the annual General Reviews, in the Psychological Bulletin, on Correlation, and on Psychological Measurement Methods, it is unnecessary and undesirable to attempt to make this bibhography complete. Some General Works Mexjmann, E. Vorlesungen zur Einfiihrung in die ezperimentelle Pddagogik und ihre psychologischen Grundlugen. 2nd edition. Leipzig. Myers, C. S. A Textbook of Experimental Psychology. 2nd edit. Cambridge, 1911. Pearson, K. The Chrammar of Science. 2nd edition. London, A. and C. Black. Thorndike, E. L. An Introduction to the Theory of Mental arid Social Measurements. New York, Teachers' College, Columbia University. TiTCHENER, E. B. Experimental Psychology. New York, 1905. Whipple, G. M. A Manual of Mental and Physical Tests. 2nd edition. Baltimore. Yule, G. U. An Introduction to the Theory of Statistics. London, Charles Grifl&n, 1911. Chapter I. Mental Measurement Ament, W. Ueber das Verhfiltnis der ebenmerklichen zu den iibermerklichen Unterschieden bei Licht- und Schall-intensitaten. Phil. Studien, 1900, xvi. 135 ff. Delboetjf, J. Elements de psychophysique, g^ndrale et spdciale. Paris, Germer, Bailli^re et Cie, 1883. Ebbinghaus, H. Ueber den Grand der Abweichungen von dem Weber'schen Gesetz bei Lichtempfindungen. Pfliiger's Arch. 1889, Bd. 54, 113 ff. Fechner, G. T. Elemente der Psychophysik [I860]. 2 vols. Leipzig, Breitkopf und Hartel, 1889. Frobes, J. Ein Beitrag iiber die sogenannten Vergleichungen iibermerklicher Empfindungsunterschiede. Zeitschr. fiir Psychol. 1904, xxxvi. 241 ff., 344 ff. Galtgn.F. Statistics bylntercomparison. Philosophical Magazine, 1875, xlix. 33 — 46. James, W. Principles of Psychology, i. Ch. xiii. London, Macmillan and Co. 1901. Steinach, E. Elektromotorische Erscheinungen an Hautsinnesnerven bei adaquater Reizung. Pfluger's Arch. 1896, Bd. 63, 495 ff. Waller, A. D. Points relating to the Weber-Fechner Law. Brain, 1895, xvin. 200 ff. Weber, E. H. Der Tastsinn und das Gemeingefiihl [1846]. Offprint from R. Wagner's Handworterhuch der Physiologic, 1851. WuNDT, W. Grundzuge der physiologischen Psychologic, i. 493 ff. Leipzig, 1902. See also a symposium on " Are the Intensity Differences of Sensation Quantitative?" in the Brit. Journ. Psychol. 1913, vi. 137—190, by C. S. Myers, G. Dawes Hicks, H. J. Watt, and William Brown. Chapter II. The Elementary Theory of Probability Bruns, H. Wahrscheinlichkeitsrechnung und Kollektivmasslehre. Leipzig, 1906. Cztjber, E. Die Entwickelung der Wahrscheinlichkeitstheorie und ihre Anwendung. Jahreshericht der deutschen Mathematikervereinigung, 1899, vn. Laplace, P. S. de. Thiorie analytigue des Probabilit^s. Merriman, M. a Textbook of the Method of Least Squares. New York, 1907. Pearson, K. Tables for Statisticians and Biometricians (with an important introduc- tion). Cambridge, 1914. Westergaard, H. Statistikens Teori i Qrundrids. 2nd edition. Copenhagen, 1915. Useful for Scandinavian references. BIBLIOGRAPHY 207 Chapter III. The Psychophysical Methods Anqkll, F. On Judgments of Like. Am. Joum. Psychol. 1907, xvm. 263. Boring, E. G. Urban's Tables. Amer. Joum. Psychol. 1917, xxvra. 280, and other papers. Ebbinghaus, H. Orundziige der Psychologic. Leipzig, Veit and Co. 1906. Febnberger, S. W. On the Relation of the Methods of Just Perceptible DiflFerenooi and Constant Stimuli. Psychol. Monog., Psychol. Rev. publications, 1913, xiv. 4, whole number 61. Also other papers in America. Lipps, G. F. Grundriss der Psychophysik. 1899. Also in German journals. Maxfield, F. N. Some Mathematical Aspects of the Binet-Simon Tests. Joum, Educ. Psychol. 1918, ix. 1—12. McDouQALL, W. The Method of Serial Groups. Bep. Cambridge Anthrop. Kxped, n. 190—193. Cambridge, 1903. MuLLER, G. E. Ueber die Maassbestimmungen des Ortssinnes der Uaut mittels der Methode der richtigen und falschen Falle. Pfliiger^s Archiv, 1879, xix. 191. Die Gesichtspunkte und die Tatsachen der psychophysischen Methodik. Wiesbaden, 1904. Rich, G. J. Checking Tables. Amer. Joum. Psychol. 1918, xxix. 120. Spearman, C. The Method of Right and Wrong Cases (Constant Stimuli) without Gauss's Formulae. Brit. Joum. Psychol. 1908, n. 227. Stratton, G. M. The Method of Serial Groups. Psychol. Bev. 1902, ix. 444. Thomson, Godfrey H. Comparison of Psychophysical Methods. Brit. Joum, Psychol. 1912, V. 203. Inquiry into the Best Form of the Method of Serial Groups. Ibid. 1913, v. 398. Probable Error of Urban's Formula. Ibid. 1913, vi. 217. Changes in the Spatial Threshold duiing a Sitting. Ihid. 1914, vi. 432. The Accuracy of the Phi-gamma Process. Ibid. 1914, vn. 44. A Direct Deduction of the Constant Process, used in the Method of Right and Wrong Cases. Psychol. Bev. 1919, xxvi. 454. Urban, F. M. On the Method of Just Perceptible Differences. Psychol. Bev. 1907, XIV. 244. Die psychophysischen Massmethoden als Grundlagen empirischer Messungen. Archiv f. d. ges. Psychol. 1909, xv. and xvi. 261 — 415. The Application of Statistical Methods to Psychophysics. Philadelphia, 1908. Ueber die Methode der mehrfachen Falle. Archiv f. d. ges. Psychol. 1910, xvn. 367. The Method of Constant Stimuli and its Generalisations. Psychol. Bev. 1910, xvn. 229. Die Praxis der Konstanzmethode. Leipzig, 1912. Various other articles mainly in German journals in controversy with Wirth, Lipps, etc. Wirth, W. Die mathematischen Grundlagen der sogenannten unmittelbaren Behand- lung psychophysischer Resultate. Wundt's Psychol. Studien, 1910, vi. 141, 262, and 430. Ein einheitliches Prazisionsmass der Urteilsleistung bei der Methode der drei Hauptfalle und seine Beziehung zum mittleren Schatzungswerth. Archiv f. d. ges. Psychol. 1912, xxiv. 141. Other articles, ibid. Psychophysik. Leipzig, 1912. Chapter IV. Skewness and Heterogeneity in Psychophysical Data Charlier, C. V. L. Researches into the Theory of Probability. Lutids Universitels Arsskrift, 1905, N. F. Afd. 2, Bd. i. No. 5. This article describes curves other than Pearson's, though not unconnected, and gives further references. A method of dissecting into two normal curves is given. Eldbrton, W. Palin. Frequency Curves and Correlation. London, 1906. 208 BIBLIOGRAPHY Greenwood, M. (Junr.) On Errors of Random Sampling in certain Cases not suitable for the Application of a Normal Curve of Error. Biometrika, 1913, IX. 69. IssERLis, L. On the Conditions under which the Probable Errors of Frequency Constants have a real Significance. Proc. Roy. 8oc. 1915, xcn. A, 23. Lipps, G. F. Die psychischen Massmethoden. 1906. Mentions Pearson's curves only to reject them. Pearson, K. On the Dissection of Frequency Curves. Phil. Trans. Roy. Soc. 1894. (No. I of Contributions to the Mathematical Theory of Evolution.) Skew Variation in Homogeneous Material. Phil. Trans. 1895, clxxxvi. A, 343. On the Criterion that a given System of Deviations from the Probable in the Case of a correlated System of Variables is such that it can reasonably be supposed to have arisen from Random Sampling. Phil. Mag. 1900, l. 157. On the systematic Fitting of Curves to Observations and Measurements. Biometrika, 1901, i. 265, and 1903, ii. 1. On a General Theory of the Method of False Position. Phil. Mag. 1903, (6), v. 658. A method of curve fitting applicable when neither least squares nor moments can be employed. On an elementary Proof of Sheppard's Formula for correcting Raw Moments. Biometrika, 1904, ra. 308. On the Curves which are most suitable for describing the Frequency of Random Samples of a Population. Biometrika, 1906, v. 172. On the Probable Errors of Frequency Constants. Biometrika, ii. 273, and ix. 1. On the Influence of Past Experience on Future Expectation. Phil. Mag. 1907, (6), xm. 365. On a brief Proof of the Fundamental Formula for Testing the Goodness of Fit of Frequency Distributions, and on the Probable Error of "P." Phil. Mag. 1916, (6), XXXI.* 369. Sheppard, W. F. On the Calculation of the most Probable Values of Frequency Constants, for Data arranged according to Equidistant Divisions of a Scale. Proc. Lond. Math. Soc. xxix. 353. Thomson, Godfrey H. The Criterion of Goodness of Fit of Psychophysical Curves. Biometrika, 1919, xn. 216. Chapter V. Introduction to Correlation Galton, F. Correlations and their Measurement, chiefly from Anthropometric Data. Proc. Roy. Soc. Lond. 1888, xlv. 135. Natural Inheritance. London, 1889. Mill, J. S. A System of Logic, Bk. in. Chapter vm. Thomson, G. H. Mathematics and the Inductive Methods of Logic. Proc. Univ. DurJiam Phil. Soc. 1913, v. 76. Chapter VI. The Mathematical Theory of Correlation Blakeman, J. On Tests for Linearity of Regression in Frequency Distributions. Biamelrika, 1905, iv. 332. and Pearson, K. On the Probable Error of Mean Square Contingencv. Bio- metrika, 1906, V. 191. Bravais, a. Analyse math^matique sur les probabilit^s des erreurs de situation d'un point. Acad, des Sciences, Memoires prisentds par divers savants {Memoires de Vlnstitut de France), 1846, 2ieme S6rie, ix. 266. The first paper on Correlation as we now understand it. Edgbworth, F. Y. Various articles on Correlation, the chief being perhaps that on Correlated Averages. Phil. Mag. 1892, (5), xxxiv. 190. Harms, J. A. A Short Method of Calculating the Coefficient of Correlation in the Case of Integral Variates. Biometrika, 1909, vn. 214. On Inter-class and Intra-clasa Correlations. Biomeirika, 1913, ix. 446. BIBLIOGRAPHY 209 LlPPS,G.F. TheoriederColleciivgegenaUinde. 1902. Engelmann, Leipzig, and in Wundt's Phil Sttid. xvn. Gives methods of curve fitting and of fitting correlation surfaces: but they are very cumbersome. Uses summation methods for momenU. Peaeson, K. Regression, Heredity and Panmixia. Phil. Trans. Roy. Soc. 1896, CLXXXvn. A, 253. A very important memoir. Definee various terms, gives a concise history of correlation, develops a general theory of correlation f<Mr n organs assuming normal distribution, and proves that the product-moment formula is the best. with Beamley-Moore, L., Filon, L. N. G. and Lee, Alice. On the Correlation of Characters not quantitatively Measurable. Phil. Trans, Boy. Soc. 1900, oxcv. A, pp. 1 — 47. Develops the Fourfold Table. On the Mathematical Theory of Errors of Judgment, with special reference to the Personal Equation. Phil. Trans, cxcvni. A, 236. On the Theory of Contingency and its Relation to Association and Normal Cor- relation. Drapers' Company Research Memoirs, Biom&tnc^GneB, I. 1904. London. On the Theory of Skew-correlation and Non-linear regression. Draper$' Company Research Memoirs, Biometric Series, n. 1905. On the Relationship of Intelligence to Size and Shape of Head and to other Physical and Mental Characters, Biometrika, 1906, v. 105. On Further Methods of Determining Correlation. Drapers' Company Research Memoirs, Biometric Series, rv. 1907. On a New Method of Determining Correlation between a Measured Character A and a Character B of which only the percentage of cases wherein B exceeds (or falls short of) a given Intensity is recorded for each Grade of A. Biomelrika, 1909, vn. 96. On a New Method of Determining Correlation when one Variable is given by Alternative and the other by Multiple Categories. Biometrika, 1910, vn. 248. On the Probable Error of a Coefficient of CoiTelation as found from a Fourfold Table. Biometrika, 1913, ix. 22. On the Measurement of the Influence of Broad Categories on Correlation. Biometrika, 1913, ix. 116. On an Extension of the Method of Correlation by Grades or Ranks. Biom.etrika, 1914, X. 416. On the Probable Error of a Coefficient of Mean Square Contingency. Biometrika, 1915, X. 570. and Heeon, D. On Theories of Association. Biometrika, 1913, ix. 159. and YoTJNO, A. W. On the Probable Error of a Coefficient of Contingency without Approximations. Biometrika, 1916, xi. 215. RuML, B, The Measurement of the Efficiency of Mental Tests. Psychol. Rev. 1916, xxin. 501. Coefficients of Diagnostic Value. J. of Phil., Psychol, and Set. Meihs. 1917, XIV. 633. The Rank Tangential Coefficient. Psychol. Monogs. xxiv. No. 105. Reliability of Mental Tests in the Division of an Academic Group. Psychol. Monogs. 1917, xxiv. No. 4. SoPEE, H. E. On the Probable Error of the Correlation Coefficient to a Second Approximation. Biometrika, 1913, ix. 91. On the Probable Error of the Biserial Expression for the Correlation Coefficient. Biomelrika, 1914, x. 384. with Young, A. W., Cave, B. M., Lee, A. and Peaeson, K. On the Distribution of the Correlation Coefficient in Small Samples. Biometrika, 1917, xi. 329. Speaeman, C. Foot-rule for Measuring Correlation. Brit. Joum. Psychol. 1906, n. 89. "Student." The Correction to be made to the Correlation Ratio for Grouping. Biometrika, 1913, ix. 316. The Probable Error of a Coefficient of Correlation. Biometrika, 1908, vi. 302. Thoendike, E. L. Empirical Studies in the Theory of Measurement. Archives of Psychol. 1907. New York. Thuestone, L. L. a Method of Calculating the Pearson Correlation Coefficient without the Use of Deviations. Psychol Bull 1917, xiv. 28. B. & T. 14 210 BIBLIOGRAPHY Chapter VII. The Influence of Selection Anderson, von O. Nochmals ueber "The Elimination of Spurious Correlation due to Position in Space or Time." Biometrika, 1914, x. 269. Cave, B. M. and Pearson, K. Numerical Illustrations of the Variate DiflFerence Correlation Method. Biometrika, 1914, x. 340. Galton, F. Spurious Correlation due to Indices. Proc. Boy. Soc. 1897, lx. 498. Readable by non-mathematicians. Harris, J. A. On Spurious Values of Intra-class Correlation Coefficients arising from Disorderly Differentiation within the Classes. Biometrika, 1914, x. 412. Heron, D. A Second Study of Extreme Alcoholism in Adults. Eugenics Laboratory Memoirs, 1912, xvn. Shows importance of partial correlation methods. Isseblis, L. On the Partial Correlation Ratio. Biometrika, 1914, x. 391, and 1915, XI. 50. The Variation of the Multiple Correlation Coefficient in Samples drawn from an Infinite Population. Phil. Mag. 1917, (6), xxxiv. 205. Kapteyn, J. C. Definition of the Correlation Coefficient. Monthly Notices of the Astronomical Society, 1912, lxxii. 518. Kelley, T. L. Educational Guidance, an experimental study in the analysis and prediction of ability of high school pupils. Columbia Contributions to Education, 1914, No. 71. Applies the partial regression equation extensively. Tables to Facilitate the Calculation of Partial Coefficients of Correlation and Regression Equations. Bull, of the Univ. of Texas, 1916. MooRE, C. N. On the Coefficient of Correlation as a Measure of Relationship. Science, 1915, XLH. 575. Pearson, K. On a Form of Spiuious Correlation which may arise when Indices are used. Proc. Boy. Soc. Lond. 1897, lx. 489. with FiLON, L. N. G. On the Probable Errors of Frequency Constants. Phil. Trans. 1898, cxci. A, 229. Probably the most important article for this chapter. On the Influence of Natural Selection on the Variabilitv and Correlation of Organs. Phil. Trans. 1902, cc. A, 1. On the General Theory of the Influence of Selection on Correlation and Varia- tion. Biometrika, 1912, vin. 437. On the Partial Correlation Ratio. Proc. Boy. Soc. Tjond. 1915, xci. A, 492. Novel Properties of Partial and Multiple Conelation. Biometrika, 1916, xi. 231 . Relations between multiple and partial correlation coefficients are properties of spheropolyhedra in multiple space. RrrcHiE-ScoTT, A. Note on the Probable Error of the Coefficient of Correlation in the Variate Difference Correlation Method. Biometrika, 1915, xi. 136. RosENOW, C. The Analysis of Mental Functions. Psychol. Monoqs. 1917, xxiv. "Student." The Elimination of Spurious Correlation due to Position in Time or Space. Biometrika, 1914, x. 179. Weldon, W. F. R. Inheritance in Animals and Plants. In Lectures on the Method of Science, edited by T. B. Strong. Clarendon Press, 1 906. Yule, G. U. The Significance of Bravais' Formulae in the Case of Skew Correlation. Proc. Boy. Soc. Lond. 1896, lx. 477. On the Theory of Correlation for any Number of Variables treated by a New System of Notation. Proc. Boy. Soc. 1907, lxxix. A, 182. These two articles are of primary importance. Chapter VIII. The Correction of Raw Correlation Coefficients Betz, W. Ueber Korrelatioc. Beiheft iii. zur Zeitschrift filr angew. Psychol, u. Psych)- logische Sammelforschung. 1911. Controversy with Spearman. Zeitschrift f, angew. Psychol. 1912. Several articles and notes. Brown, W. The Effects of Observational Errors and other Factors upon Correlation. Coefficients in Psychology. Brit. Journ. Psychol. 1913, vi. 223. BIBLIOGRAPHY 211 Grove, C. C. Mathematics and Psychology. Mathematics Teacher, 1916, vni. 176, and IX. 3 and 103. Spearman, C. The Proof and Measurement of AssociRtion between Two Things. Am. Joum. Psychol. 1904, xv. 72. Demonstration of Formulae for True Measurement of Correlation. Am. Joum. Psychol. 1907, xvm. 161. Correlation Calculated from Faulty Data. Brit. Joum. Psychol. 1910, m. 271. Die praktische Elimination des Ei'nflusses der zufAlUgen Fehler von dem Kor- relationskoefficient. Zsch. f. angew. Psychol. 1912, vi. 565. Correlation of Sums or Differences. Brit. Joum. Psychol. 1913, v. 417. WissLER, Clark. The Correlation of Mental and Physical Tests. Psyched. Reo, Movog. Supp. 1901, in. No. 16. The Spearman Correlation Formula. Science, 1905, N.S. xxn. 309. Chapter IX. The Theory of General Ability Abelson, a. R. The Measurement of the Mental Ability of Backward Children. Brit. Joum. Psychol. 1911, iv. 208. BONSER, F. G. The Reasoning Ability of Children of the Fourth, Fifth and Sixth School Grades. New York, Teachers' College, Columbia University, 1910. Burt, C. Experimental Tests of General Intel^gence. Brit. Joum. Psychol. 1909, m. 94. Collins, E. R. The Correlation of Secondary School Grades with Certain Standard Mental Tests as Evidence of General Intelligence. Bull, of the State Normal School, Moorhead, Minn. 1914, x. No. 4. Damm, H. Korrelative Beziehungen zwischen elementaren Vergleichsleistungen. Beih. z. Zsch. f. angew. Psychol. 1914, ix. Garnett, J. C. Maxweu.. General Ability, Cleverness and Purpose. Brit. Joum. PsycJwl. 1919, IX. 345. On Certain Independent Factors in Mental Measurement. Proc. Boy. Soc. 1919, xcvi. A, 91. GiESE, F. Korrelationen psychischer Functionen. Eine experimentelle Untersuchnng. Zsch. f angew. Psychol. 1915, x. 193. Peterson, A. Correlation of Certain Mental Traits in Normal School Students. Psychol. Rev. 1908, xv. 323. Spearman, C. General Intelligence objectively determined and measured. Am Joum. Psychol. 1904, xv. 201. and Krueger, F. Die Korrelation zwischen verschiedenen geistigen Leistungs- ffthigkeiten. Zeitsch. f. Psychologie, 1906, xliv. 50. and Hart, B. General Ability, its Existence and Nature. Brit. Joum. Psychol. 1912, V. 51. Mental Tests of Dementia. J. of Abnormal Psychol. 1914, ix. 217. The Theory of Two Factors. Psychol. Rev. 1914, xxr. 101. The Heredity of Abilities. Eugenics Rev. 1914, vi. 219. Starch, D. Correlations among Abilities in School Studies. J. of Educ. Psychol. 1913, IV. 415. Webb, E. Character and Intelligence. Brit. Joum. Psychol. Monog. Supp. No. 3, 1916. Wyatt, S. The Quantitative Investigation of Higher Mental Processes. Brit. Joum. Psychol. 1913, vr. 109. Chapter X. A Sampling Theory of Ability AiKENS, H. A. and Thorndike, E. L. (with Hubbell). Correlations among Per- ceptive and Associative Processes. Psychol. Rev. 1902, ix. 374. Bateson, W. and Punnett, R. C. On the Inter-relation of Genetic Factors. Proc Roy. Soc. 1911, Lxxxiv. B, 3. See also other papers and text- books by these authors. BiCKERSTETH, M. E. The Application of Mental Tests to Children of Various Ages. Brit. Joum. Psychol. 1917, ix. 23. 212 BIBLIOGRAl>HY Brown, William. Some Experimental Results in Correlation. Comptes Rendita du Vlme Congrks International de Psychologic. Geneve, Librairie Kiindig, 1910. The Psychologist in the Secondary School. Joum. of Phil, Psychol, and Set. Methods, 1910, vn. Jan. Note on a Quantitative Analysis of Mathematical Intelligence. Ibid. 1910, vn. Sept. Correlation of Mental Abilities. Brit. Joum. Psychol. 1910, in. 296. BuKT, C. General and Specific Factors underlying the Primary Emotions. Brit. Association Beport of the 1915 {Manchester) Meeting. Section I, Physiology. Carey, N. Factors in the Mental Processes of School Children. Brit. Joum. Psychol. 1915, vn. 453; 1915, vm. 70; and 1916, vin. 170. Heymans, G. and Brugmans, H. J. T. W, Intelligenzpriifungen mit Studierenden. Zsch.f. angew. Psychol. 1913, vn. 317. McCall, W. a. Correlation of some Psychological and Educational Measurements with Special Attention to the Measurement of Mental Ability. School and Society, 1917, V. 24. Mendel, Gregor. Experiments in Plant-hybridisation. Verh. naturf. Ver. in BriinUy Abhandlungen, iv. 1865. Trans, in MendeVs Principles of Heredity, W. Bateson. Cambridge, 1909. Reaney, M. J. The Correlation between General Intelligence and Play Ability as shown in Organised Group Games. Brit. Joum. Psychol. 1914, vn. 226. Simpson, B. R. Correlations of Mental Abilities. New York, Teachers' College, Columbia Univ. 1912. Stern, W. The Psychological Methods of Testing Intelligence. Trs. by G. M. Whipple, Educ. Psychol. Monogs. 1914, No. 3. Thomson, Godfrey H. A Hierarchy without a General Factor. Brit. Joum. Psychol. 1916, vin. 271. Spearman's comments follow. The Proof or Disproof of the Existence of General Ability. Brit. Joum. Psychol. 1919, IX. 321. The Hierarchy of Abilities. Ibid. 1919, ix. 337. with Garnett, J. C. M. Joint Note on the above article. Ibid. 345. On the Cause of Hierarchical Order among the Correlation Coefficients of a Number of Variates taken in Pairs. Proc. Roy. Soc. Lond. 1919, xcv. A, 400. On the Degree of Perfection of Hierarchical Order among Correlation Co- efficients. Biometrika, 1919, xn. 355. Thorndike, E. L. (with Lay, W. and Dean, P. P.). Relation of Accuracy in Sensory Discrimination to General Intelligence. Am. Joum. Psychol. 1909, xx. 364. The Relation between Memory for Words and Memory for Numbers, and between Memory over Short and Memory over Long Intervals. Am. Joum. Psychol. 1910, xxT. 478. Winch, W. H. Transfer of Improvement in Memory in School Children. Brit. Joum. Psychol. 1908, n. and 1910, in. Additional Researches on Learning to Spell. The Question of Transfer and of Direct versus Indirect Methods. J. of Educ. Psychol. 1916, i. 93. Articles not Classified under the Chapter Headings BisPHAM, J. W. An Experimental Determination of the Distribution of the Partial Correlation Coefficient in Samples of Thirty. Proc. Boy. Soc. 1920, xcvn. A, 218. Brown, W. An objective study of Mathematical Intelligence. Biometrika, 1910, vn. 352. Claparede, Ed. L' Unification et la Fixation de la Terminologie psychologique. Comptes Bendus du Vlme Congrls IntematioruU de Psychol. Gren^ve, Libraitie Kundig, 1910. Elderton, Ethel M. On the Association of Drawing with other Capacities in School Children, being a biometric evaluation of the results of E. Ivanhoff, Recherches exp6rimentales sur le Dessin des 6coliers de la Suisse Remande, Archives de Psychologic, 1908, vm. Biometrika, 1909, vn. 222. BIBLIOGRAPHY 213 Garnett, J. C. Maxwell. The Single General Factor in Diasiinilar Mental Measure- ments. Brit. Jaum. Psychol. 1920, x. 242, Gordon, Kate. Results of Tests by Binet-Simon Methods in Three Californiaii Orphanages. Journal of Delinquency. Contains a table of the correlation in Intelligence Quotients of 91 pairs of siblings, which Pearson considers of great importance inasmuch as the environment was nearly uniform. The intelligenoe quotient is the ratio of the mental age to the actual age. GORINO, C. The English Convict. A Statistical Study. London, H.M. Stationery Oflioe, 1913. Abridgement, Wymans, 1915. Heron, D. The Influence of Defective Physique and unfavourable home environment on the Int-elligence of School Children, being a statistical examination of the L.C.C. pioneer school survey. Qalton Eugenics Lab. Memoirs^ Series vin. Dulau, 1910. HoLLiNGWORTH, H. L. Vocational Psychology, its Problems and Methods, New York, Appleton, 1916. A summary of correlation data in this field. HosNY, M. Statistical Notes on the Influence of Education in Egypt. Biomelrika, 1914, X. 280. KETJEiY, T. L. The Association Experiment: Individual Differences and Correlations. Psychol. Rev. 1913, xx. 479. McDougall, W. On a New Method for the Study of Concurrent Mental Operations and of Mental Fatigue. Brit. Journ. Psychol. 1905, i. 435. Miner, J. B. The Evaluation of a Method for Finely Graduated Estimates of Abilities. J. of Appl. Psychol. 1917, i. 123. Pearson, K. Francis Galton's Difference Problem. Biomelrika, 1902, i. Inheritance of Psychical Characters. Biometrika, 1919, xn. 367. Discusses Dr Kate Gordon's correlation table of Intelligence Quotients ; see above. and Jaederholm, G. A. Mendelism and the Problem of Mental Defect. Part n. 1914. On the Continuity of Mental Defect. Questions of the Day and of the Fray, No. 8. Schuster, E. and Elderton, E. M. The Inheritance of Psychical Characters, being further statistical treatment of material coUected and analysed by Messrs G. Heymans and E. Wiersma. Biometrika, 1907, v. 460. Spearman, C. Manifold Sub-Theories of "the Two Factors." Psychol. Rev. 1920, xxvn. 159. Terman, L. M., Lyman, G., Ordahl, G., Ordahl, L. E., Galbrbath, N. and Talbert, W. The Stanford Revision and Extension of the Binet-Simon Scale for Measuring Intelligence. Educ. Psychol. Monog. 1917, No. 18. Thomson, G. H. The General Factor Fallacy in Psychology. Brit. Journ. Psychol. 1920, X. 319. General versus Group Factors in Mental Activities. Psychol. Rev. 1920, xxvn. 173. Thorndike, E. L. An Empirical Study of College Entrance Examinations. Science, 1906, N.S. xxm. 839. TiLDESLBY, M. L. Preliminary Note on the Association of Steadiness and Rapidity of Hand with Artistic Capacity. Biometrika, 1918, xn. 170. Yerkes, R. M. Report of the Psychology Committee of the National Research Council (Psychology Tests applied to American Army, etc.). Psychol. Rev. XXVI. 83. INDEX Works and authors mentioned in the Bibliography are not included in this index unless they are also referred to in the text of the book Aikens, 153 Ament, 6 Analograph, 119 Analysis into two normal curves, 91 Anderson, 150 AngeU, 6, 52 Arithmetical short-cuts, 18, 87 Array, 99 Average error. Method of, 46, 56, 77 Average limen, 61 Best fitting. Meaning of, 39 Binet Tests, 56 Binomial expansion, 28, 33; Standard de- viation of, 32 Bisection of lines, Experiment on, 15; Calculations on data from, 21, 42, 78 Blakeman, J., 113, 126 Blakeman, T., 114 Bravais, 101, 109, 119, 120, 169 Brown, 114, 146, 160, 167, 170 Bruns, 61 Burt, 167 Carey, 172 "Catch" errors, 54, 93 Cave (F. E. and also B. M.), 150 Centre of gravity same as mean, 17 Charlier, 86 "Cocked hat" diagram, 14 Complete descents and ascents, Method of, 48 Constant Method and Process, 46, 62, 57-75, 77, 90 Contingency, 125 "Contraste sensible," 2 Correlation, 11, 97 (Ch. v. Introductory), 107 (Ch. VI, methods, see chapter heading), 134 (Ch. vn, partial correla- tion, see chapter heading), 153 (Ch. vni, correction of raw correlation) | CreUe's Calculating Tables, 44, 70, 89 Criterion for hierarchical order. The Hart and Spearman, 169, 179 Criterion Kj, Pearson's, to determine Type of curve, 86 Darwin, F., 8 Dean, 167 Delboeuf, 2 Dice throws, 13, 25, 138 (three variables), 174-9 (hierarchies) Difference hypothesis, 6 Difference thresholds, 76 Distribution curve, 37 Doodson, 86 Ebbmghaus, 2, 5, 6, 7, 10 Edgeworth, 120 Elderton, E. M., 125 Elderton, W. P., 79, 82, 87, 89 Equal appearing intervals, 1, 46 Everitt, 125 Expectation, 17 Fechner, 1, 3, 4, 6, 7, 9, 49, 61, 64, 67, 69, 70 Filon, 179, 184 Fitting a normal curve to data, 39 Fittmg, H., 8 "Foot-rule," Spearman's, 130 Fourfold Table, 123 Frobes, 6 Galton, 69, 66, 119, 149 Gamett, 121, 172-3 General Factor in Ability, 106, 138 et seq., 142 (condition for g in three variables), Ch. IX, Ch. X Geotropism, 8 Gibson, 113, 114 Goodness of Fit, Pearson's test for, 77, 79 Grading magnitudes and their differences, 11 Group Factors in Ability, 140 et seq., 171-3, Ch. X Groups, Method of Serial, 47, 55; Method of Non-consecutive, 47, 56, 95 Hart, 165, 168, 170 (Hart and Spearman criterion, and correctional standard), 179 (erroneous nature of criterion) Heron, 114 Heterogeneity in data, 77 et seq., 148 Hicks, G. Psychophysical Methods, 46-76 (Ch. lU) Quartiles, 16 et seq. Quotient hypothesis, 6 Ranks, Method of, 10, 102, 104 (worked example of r by ranks), 106 (table of p and r), 130 (Spearman's Foot-mle) Ratio 17, Correlation, 98, 110, 115 (worked example) Regression, 100, 108 (Yule), 113 (oriterion for linearity), 117, 118 Reliability coefficients, 155 Rich, 70, 197 Riecker, 58, 71-3, 93 Right and Wrong Cases, Method of, Mune as Constant Method, q.v. RusseU, 11 Sampling Theory of Ability, Ch. x Sanford, 10 Scatter, Measures of, 19-24, 99 Schuster, 125 Selection, The Influence of, Ch. vii, 134 (mild), 137 (rigorous) Semi-interquartile range, 16 et seq., 19 Serial Groups, Method of, 47, 55 Sheppard, 43^, 62-3, 77-8, 84 (Sheppaid's corrections), 88, 116, 124, 129 Skew Curve, Calculation of, 89 Skewness of psychophysical data, 64, 77 SmaU, 8 Soper, 114 Space error, 48 Spearman, 62-65 (mean limen). 130 ei aeq. (Foot-rule), 132 (r of sums or differences), Ch. vm (correction of raw correlation), Ch. IX (general factor), Ch. x (case against general factor) Specific Factors in AbiUty, 140, Ch.ix, Ch. x Spurious correlation, 148 Standard deviation, 20 ei seq., 22 (about true value), 23 (of arithmetical mean), 24 (of sum or difference), 37 (physical meaning of), 38 (and mean variation), 38 (and probable error) Steinach, 7 Stephen, Leslie, 164 Stratton, 47, 55 "Student," 150 Summation method, 19, 87 Sums or differences, 132 (correlation of), 24 (standard deviation of) "Tail" of distribution. Difficulties due to, 52, 62, 64, 75, 90 Tannery, 5 216 INDEX Thompson, J. R., 141-2 144 Thomson, G. H., 9, 15, 53, 54, 55, 56, 60, 64, 74, 79, 94-5, 121, 138, 174, 175, 176, 178 188 Thomdike, 153, 167-8, 170, 171 Time error, 48, 70 Titchener, 5, 10, 57, 58, 73 Transfer of training, 190 Two Factors, Theory of, 164 e/ seq. Two-row Table, 127 Undecided answers, 76 Urban, 13, 27, 50 et seq. (formula for Limiting Process), 59, 62, 64, 68-70 (Urban Weights), 75, 76, 87, 89 et seq., Appendix I (Tables) Variate Difference CJorrelation, 150 (worked example) Variation, Coefficient of, 1 14 Waller, 7 Webb, 172 Weber, 3, 4, 7, 8 Weights, Experiments on lifted, 13 Weights of equations, 45, 66 et seq, Weldon, 25 Wilton, 160 Wirth, 54, 69, 87, 131 Wissler, 153 Wrinch, 25 Wundt, 5, 7 Wyatt, 172, 180 et seq. Yule, 108, 119, 120, 121 (these on re- gression), 137 (partial correlation), 146, 157, 165 CAMBRIDGE : PBINTXD BT J. B. PEACE, M.A., AT THE UNIVEBSITT PBRS8 THE CAMBRIDGE PSYCHOLOGICAL LIBRARY GENERAL EDITOR G. DAWES HICKS, M.A., Ph.D., Litt.D. 