N[16]I.Q.HealyTotalPossibleAverageGain1·25·27·10·29·30415·051C·21·15·01·12·53462·0892·84·89·60·66·38416·0632C·45·51·29·18-·07358-·0113·49·44·49·51·40328·0663C·25·32·44·45·30287·054·59·59·38·22168·0734C·27·32·71·42195·145·53·71·10·42213·145C·89·90·77·24133·086·53·77·02·55229·1836C·37·38·04·27210·097·45·71·22·07·37478·0627C·53·71·34·59·74393·1488·45·34·70-·50303-·1258C·67·81·33·52·10241·0259·27·46·23·39·71375·1189C·35·40·73·89·72217·1210·88·86·15·35·34400·05610C·81·73·57·971·39392·21811·79·73·20·34·21379·03511C·77·79·05·23-·44379-·07312·67·53·47·49-·11161-·03612C·67·77·19·15·19208·03213·09·19·79·78·02129·00313C·06·05·24·67·06178·0114·59·84·41·84·69212·11514C·97·96·21·56·41104·06815·62·49·38·55·12106·0415C·19·20·26·79·66193·1116·05·12·86·82·15205·0316C·13·25·66·76·24313·0417·09·17·63·40·66223·22017C·59·71·27·43·21174·05318·67·67·13·15·08175·02718C·40·49·04·07·18247·0319·59·69·91·85·1667·03219C·67·67·11·18·16287·02720·82·79·25·18-·06177-·0220C·91·94·66·75·2065·06621·05·07·47·69-·16209-·03221C·34·62·99·92·46157·07722·45·73·84·81·87120·17422C·03·02·74·72·74275·12323·32·49·86·98·65168·16323C·23·59·33·501·26253·2124·94·92·88·95- ·0689-·01224C·38·46·68·93·54179·0925·17·15·37·55·49280·09825C1·00·97·63·60·53134·08826·21·15·51·36226 026C·40·37·90·94·04184·00727·88·86·10·43·05268·01327C·11·59·29·591·49320·2528·23·29·631·00·59153·09728C·53·67·96·87·2483·048
Table XI expresses the results of Table II, with the scores given in percentile values. In each test, the group was taken as composed of the two scores of every individual—the total number of scores in tests and retests, eliminating those scores where the other member of the pair was lacking, or where no retest was given. Thus case number 1 was just within the lowest 27% of the group in weight at the first weighing, but had advanced to the 44 percentile at the second. In height he gained from the 25 percentile to the 40 percentile. His total gain in all tests is 30 percentile out of a possible 415, and the average gain is ·05. The reader may see by scanning the table that the gains in the test group are practically equaled by those in the control group. There seems to be no consistent relationship between a low score in the first test and a large gain. This is true even though the method of calculation tends to minimize gains at the high end of the group, and losses at thelow end. In table XII this may be seen more clearly in respect to I.Q. and the results for all the tests taken together with the I.Q. weighted by being counted twice. A large possible gain indicates that the score at the first testing was low, and vice versa. Considering I.Q. values, the largest possible gain in the test group was 95 per cent of the group. This occurred twice, in one case the actual gain being 7% of the group and in the other 2%. In the control group, the largest possible gain was 97% of the group, but actually this case fell 1% of the group. If we correlate possible gain with actual gain for each group, using the formula r = 2sin((Π/6)ρ)) when ρ = 1 - ((6ΣD²)/(n(n²-1))) we get a coefficient of correlation ·36 in the test group, and ·19
I.Q.TotalAB1st P.R.2d P.R.possible gainactual gainpossible gainactual gainAv. Gain125277524153051C211579-6462538·928489165416386·32C4551556358- 7-1·13494451-5328406·63C25327572873054595941168227·34C2732735195421455371471821342145C89901111332486537747242295518·36C3738631210279745715526478376·27C537147183937414·88453455-11203-50-12·58C67813314241102·59274673193757111·89C3540655217721210888612-2400345·610C817319-839213921·811797321-6379213·511C7779232379-44-7·312675333- 6161- 11- 3·612C67773310208193·21391991101292·313C6594- 11786114598441252126911·514C97963- 1104416·815624938-1310612415C192081119366111651295720515316C1325871221324417917818223662217C59714112174215·31867673317582·718C4049609247183195969411067163·219C676733287162·720827918- 3177-6- 220C91949365206·62157952209- 16- 3·221C34626628157467·722457355281208717·422C3297- 12757412·323324968171686516·323C23597736253126212494926- 289-6- 1·224C384662817954925171583- 2280499·825C10097- 3134538·826211579- 622626C403760- 31844·727888612- 226851·327C1159894832014825282329776153599·728C5367471483244·8
in the control group. With the small number of cases involved the probable error is too great to allow either of these measures as indicative of relationship. We may say, then, that there is no definite tendency for those of low I.Q. to improve in six months after operation to a greater degree than those of higher I.Q.
Finally, in order to compare the results of the various tests, the measures of the gains of the test group in excess of the control were, for each test, expressed in terms of P. E. The averages and medians of these measures are collected in Table XIII. They show a very slight tendency toward gain in weight, height, and weight-height-age relationship; neither improvement nor loss in grip, tapping fatigueability and I.Q., and a rather curious tendency to loss in the Healy scores. This latter is very probably not a true measure since performance in the Healy Picture Completion test shows a rather high variability, and the cases are so few as to make the influence of single very high or low scores unduly great.
WeightHeightHeight-WeightGripTappingTapping fatigueI.Q.HealyP. E.P. E.P. E.P. E.P. E.P. E.P. E.P. E.Average2·851·002·02-·50·03-·50-·94-1·92Median2·801·25·55-·83·32-·500.00-2·54
In view of the fact that one of the experimenters[15]found improvement in school work when her study was extended to cover a second time interval after operation, it was deemed advisable to similarly extend the present investigation in order to determine whether our operated cases showed any improvement after twelve months. To this end, the fifty-six children composing the final groups of the first study, were sought after a second interval of about six months. Conditions made it impossible to give all the retests exactly twelve months from the time of the operation. As a matter of fact, the period ranges from ten to seventeen months. An effort was made to keep the interval between tests equal for the two members of a given pair.
The same tests were given as in the first study. About half of the testing was done by one of the former examiners, but she was obliged to turn the work over to another before it had been completed. The second examiner was highly recommended, and had had training and practical experience in the giving of tests. She was instructed in the methods which had been employed previously, so that conditions were as far as possible kept constant.
The results of the tests are collected in Table XIV. In the first column is given the length of the time interval for each case. It may be seen that the final group was composed of forty-two children, forming twenty-one pairs. There were fifteen pairs which received a second rating in weight; thirteen in height; thirteen in grip; fifteen in tapping, eleven in fatigue as shown by tapping, twenty-one in I.Q., and eighteen in the Healy Test. These numbers while they are smaller than we could wish, would seem to be great enough to indicate
N[16]Mos.WeightHeightGripTest 1Test 3Test 1Test 3Test 1Test 311550·463·546·049·713·018·01C1553·562·846·449·711·015·021540·947·942·645·99·010·02C1752·365·545·249·810·015·031655·067·547·050·212·813·03C1461·557·851·754·014·014·541351·160·247·550·59·04C1349·454·248·950·89·571439·945·842·945·67·06·07C1238·442·141·943·79·014·081160·869·250·852·310·08C1145·457·936·848·715·0101148·956·746·148·612·512·010C1147·151·845·648·110·012·0111247·855·045·849·511·011·011C1241·647·043·646·811·57·5121248·066·544·814·012C1141·069·641·56·0131290·0112·061·361·826·528·513C1274·788·056·860·022·027·0141256·066·051·053·316·017·014C1281·998·057·959·522·022·5151257·551·115·515C1067·250·115·0161256·060·351·653·519·018·516C1151·255·048·750·110·010·0181258·247·318·018C1145·346·78·0191290·0108·057·760·522·020·019C1152·459·046·748·015·018·0201244·247·211·020C1161·349·615·0211270·785·554·116·515.021C1062·469·249·619·017·0231251·747·811·515·023C1164·151·414·516·0271243·745·49·06·027C1141·044·609·0281271·378·554·956·323·528C1174·285·853·455·921·0
N[16]TappingI.Q.HealyTest 1Test 3(1)(3)(1)(3)11351428293·0-25·011·01C1061348085·0-50·011·02105135107113·028·524·52C1521399186·03·019·531361449491·021·515·53C1351358296·017·025·54103961118·54C1098310233·071259193- 6·016·07C105951124·511·081131289192·032·58C13112198111·04·01068+ 74145+106110116·0-12·011·010C70+ 74148+124104107·027·048·511125+ 90120+125103102·0- 8·015·511C155+125102+11210195·0-29·0-20·01298+ 698620·01·012C1029890-10·041·513160+165176+1877061·043·062·513C150+109188+1746660·0-1·521·514190+172228+21596102·012·577·014C175+152165+186140138·0- 5·048·515172+167192+1869797·07·019·015C140+115145+1337898·01·054·516145+131657449·079·016C145+ 99748130·045·518133+115126+14598101·0-13·513·518C100+ 99108+ 929092·0-32·0-35·019168+136969757·560·519C100+1159890-22·0-15·020105+115122+118106116·055·020C150+120154+154118140·030·048·521152+111154+1556466·020·038·021C140+136174+1508693·070·588·023150+119157+1578580·049·562·523C122+115141+1418188·04·064·027108+ 92114+ 95110112·0-25·025·527C115+105101+1187298·02·039·528150+148176+1688183·029·577·528C178+148172+1579594·064·583·5
any very consistent tendency toward improvement. The question, whether or not the results are affected by the differences in time interval, will be considered later.
In weight, the test group showed an average gain of 11·013 pounds, with a median of 9·1 (Table XV). The average gain of the control group was 9·113 pounds and the median 6·8. The gains in the test group are less variable than those of the control. The average of the gains of the test group in excess of those of the control is 1·9 pounds, and the median is 2·2 pounds; while the unreliability of the difference is ± 1·46 The average, then, is only 1·30 P. E. and the median 1·51 P. E.
If we turn to Table III and compare the results there set forth with the results at the end of the second period, we find the gains of the test group exceed those of the control in the following manner.