A.STUDY TD DETERMIHEEflfiIHflHiLENTAL AGE SOJRES ARE BEST DESCRIBED BY SINGLE-CYCLE, MULTT-CYCLE, OR SIRAIGHT LINE GhOHIH EQUAEIUNS By Richard McCallum Clark AN ABSIRACI‘OF A THESIS Submitted to the College of Education Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHELOSOPHY Department of Foundations of Education P“ ‘I inc purwose cf Vhis study was to fine which of three methods of describing the mental growth scorer collected longitudinally for Che hundred individuals Izorld most accurately describe +hc growth pattern formed by the actual test scores cf these individuals. The three meU odsused descrilmed tal QTOWth as : (l) a straztht line; (2) a single-cycle negatively accelerated curve; and (3) a multi- cyclic curve, It was as: umed 1hnt a statis ieall significant dif— ference in ct so three methods of describin; the obtained rental a 6 scores for an individual we 16 in catc tFxH t’e gore QCCvrate method represented a more nearl" cr‘rrect theoretical (lure of the natxrc of the mental grcvth cxrve, Cases were selec+ed from t" nearborn data ass ”.leL by Doctor C, V. Willard from t“; H(1rf b 0rd FcPocl, 'carborn, “50‘1“u1 on +hc baris of a range of test scores obtained d ring tne re—adoles cent period and on the basis of rhrrjcnl VQCELh 'csi‘ :=s, cxtcrfiing into the adolescent fcr 0d, and ineluflin; n.1fixn 1r: f s*x mental e scores for tke individual, A straight line growth description was obta: med 3y lefipl"'n' the mean 1... oLta-“-1 ‘f an individual By the chronclotical age at tEC tint if cash Test adaivfstrat'on, S'ngc c cle growth curves "c ‘ ,1 .. ‘.,. J. A 4"”: 3”,“! .1 , 7 ‘-r ' ' ‘ ,. _’ ' ~ 1.: were conn.ted s1: 3hr lUFulIU cc LLO we r» l ”ClfllL, «hm multi— .J Lo , up, , . 31. l ,..- .L‘ - W .. 4.: 4. ‘ 1...; ‘ - c 013 equations were UT tten [5. L ,wa tcu“t s ire Litre, - ' ' ' ‘ Avera“c deviations wrre obtainafi for eau‘ :Lttod on each case b-tvoen ihe score amt all“ chtaincfi on t?' test a;a the derived f theoretical score. Frefi“cnc' Firtrilrtiouc w:r€ drawn rf the avera_e devintfiors, and tests of stauisu ea icance were made to compare the rnan avers e dev7a+ n “f tech 0? fh' three Ln: o‘s A team l aV(?"iC dCiiutiou of L.7 nonth was fenni for 1Cntal trst den described. by Imlti-Cj‘clc --:1‘.e.‘.jos, I.“ ilc 31:; c?_r3‘.'i;‘1%.j0f‘1s -’-f 7.1' :..Onths an- 3.2: nut is were f0 £111 fer sing 1C Cf-‘cle :1 .-:1 st 5137;;7‘1t line methods of description, The difference Fetwe,. the roan average deviaiion found in writing rmlti-cyclc eQuati01s was s-gz' icantly lower, at t1C one ncrcent lCVCl f Ck Mf: ance, t‘an the mean avera‘- dcviat tn Cf N'C 0th r two methods. \ 1 co - CiFC) or 44‘- n-v‘n fi1 -»q r- 1r 2Ll~11s r1 *2 ' 1 1%w~4vv~ ‘. AA ”:1, --.- n _. 'JA'C ANCEL. CA E... ta, _. do ‘~ ( \‘- Ugl...’.0(.n -U’J 4.1;0 ' 4 ' VD: \ r ‘ .5 “f1 -'. u - V 1' ‘ 4“ \-‘. -1- the sazC tCn- on 1. r_-_<_.d -,,i c‘ : cutie ---r.al a‘ c SUOMTC. that both LC straihht linr the sirgle c cle 11t‘o-s Cf (1e: (zribinb growt‘ showed a statistically s: nificant increase after 160 hc-gths of ado, Thile thc 7C3; a"Crs C deviations ottafzed ‘y the umlti-CJcle net od ‘1 -:,,. f ‘l. _ 3, .‘ ‘ 1. ' 1 1"“ ‘1 ‘. “.1 “'4, «prim, CuCh tcn he»+n ln-Crvul was FUHQ , val“ c.rm=2nts - case 50F . . . . . . . . . . . . . . . . . . Line of growth obtained from mean nersonal con— stant compared with actual neasirenents - case 50? . . . . . . . . . . . . . . . . . . Line of growth obtained from mean intelligence quotient compared with actial measurements - case 50F . . .. . . . . . . . . . . . . . . Line of growth obtained from multi-cycle equa- tions comnnred with actual measurements - 0:138 1.631% 0 o a o O o o o o O O o o I O o 0 P A GE 53 \n, \fl \n \o ‘r f ‘1‘». FIGURE PAGE 22. Line of growth obtained from mean nersonal con- stant compared with actual measurements — case 163M . . . . . . . . . . . . . . . . . . 53 23. Line of growth obtained from mean intelligence quotient compared with actual measurements - 0389 1631.1 0 o o o o o o o o o o o o o o o o 0 6h CHAPTER I THE PROBLflh AND DEFINITIONS 0? TERNS USED Since the develOpment of standardized instruments for measuring intelligence, psychologists and educators have at- tempted to use these instruments in order to discover the existence of a general pattern of mental growth which is con- mon to all humans. In 1919 Terman stated: The Standardization of the Binet scale on the basis of age-norms makes it a suitable instrument for the in— vestigation of mental-growth curves. By applying it repeatedly to the same children we can find out whether constancy or irregularity rules. Prediction hinges on the question whether a child who is found by the test to be a given her cent above or below the mental level normal for his age continues to be accelerated or re- tarded to the same degree. ’The answer is ound in the extent to which the I.Q. remains constant. Although efforts have been made to use intelligence test scores in an attempt to ascertain the nature of the mental growth curve, Freeman points out the factor wnich has limited most of the studies in this area, stating: rhe multitude of scores of children of various ages which have been gathered from the application of various mental tests yields a mass of material which give a basis for more valid estimates of the character of intel- lectual growth than we have previously possessed. It is true that these measures have usually been limited in one resnect. They have been made upon different children of different ages. They have not, that is, given suc— cessive measures of the capacity of the same child at 1 Lewis M. Terman, The gntelligenge of School Children (New York: Houghton Mifflin Company, 1919), p. 137. successive periods in its growth. They therefore give us only a mass picture of the general characteristics of growth, and do not enable us to determine what the fluctuations in the case of individuals are. Dearborn and Rothney3 illustrate how the use of norms derived from age groups can distort the true picture of in- dividual growth through a comparison of a growth pattern for girls in physical and mental growth described by Boas, with growth patterns based on individuals. Dearborn and Hothney find that at some time between the ages of nine to fifteen, there is one year when practically every girl makes a more intense spurt than the average described by Boas. fhus, Dearborn and Rothney explain, "Since these spurts come at different life-ages in individual cases, a curve, constructed after the manner of Boas, tends to "smooth" the adolescent period and make it appear to be a more quiescent period than it actually is.” 2 F. N. Freeman, "Individual Differences in Mental Growth," §gience Monthly, 37. 3 Walter Dearborn and John Rothney, Predicting_the Child's Development, (Cambridge: Science Art Publishers, l9 1). ‘ 4 Ibid., p. 232. Baldwin and Stecher,5 Krogman,6 Millard,7 Courtis,6 and others have agreed that patterns of growth for individuals must be derived from the study of individuals over a time, rather than from the study of group norms. As Baldwin and Stecher state: All of these problems concerning the general trend of the growth curve, the rate of improvement of children of different intellectual ability, variability in mental development, the possibility of prediction in mental growth, and the relation between nhysical and mental growth can be solved only through a study of consecutive re—examinations and observation of the same groxo of children throughout a number of years. "Every child is unique;" affirm Gesell and 11g, "but every child is also a member of one human species. Ubedient to these Species characteristics there are growth sequences which are rarely or never circumvented."lo The upesence 5 Bird f. Baldwin and Lorle l. Stecher, "Mental Growth Curve of Normal and Superior Children,“ (University of Iowa Studies in Child Welfare, Vol. 2, No. 1. lowa City, Iowa: University of Iowa). 0 Marion Wilton Krogman, "Trends in the Study of Physical Growth in Children," Child Development, Vol. 11, December, 1940. , 7 C. v. Millard, Child Growth and Develoome t in filementar1_School Years (Boston: D. C. Heath Company, 195 C? H ). 5 S. A. Courtis, "What Does the I.Q. Really Measure?" Nationis Schools, 11:21, January, 1933. 9 Baldwin and Stecher, 92. cit., no. 5-6. 10 Arnold Gesell and Frances Ilg, The Child From Five New York and London: Harper and Brothers, 1046), :l: o !£_u 57 L of these two factors, uniqueness and sequence, both must be considered in studying any aspect of human growth. Krogman states, "We have long focussed upon the groups, and the po- sition of the individual growth curve in the group, and have constructed averages——'norms of mediocrity,‘ Todd called them—~degrees of departure fron which there was a measure of aberrancy. _Ne now look more intently at the individual growth curve as an expression of its 233 norm."11 this study utilizes the longitudinal method described by Millard12 by examining growth patterns of specific indi- viduals in an effort to gain insight into the specific sequences followed by human beings in terms of mental growth. I. T E PRUBLEM Statement_g£ the problem. the purpose of this study was to investigate the nature of mental growth by determining whether scores obtained by individuals on the Kuhlmann-Anderson Intelligence Test during the pre-adolescent period and ado- lescent period are best described by (l) a single cycle growth equation; (2) a multi—cycle growth curve; or, (3) a straight line. A secondary problem was to ascertain the variability of the I.Q. of the individual as shown by repeated testings. Importance of the study. "When we study the maturation of individual organisms cf any type or kind," contends Stuart 11 Krogman, Q2. cit., on. 253-28M. ! 1.2 Millard, op. cit. , pp, 1-20. Courtis, "we find that progress toward maturity follows a single genetic pattern. This pattern has the form of a dis- torted S or skew curve, the second half of the curve taking a longer time than the first half."13 Terman states, "If we had a perfect scale for determining the mental age level, and if the I.Q. remained absolutely constant, the 'curves' of mental growth would be a straight line from birth to the point of mental maturity."14 "The comnon view is that the course of intellectual growth through this period (middle childhood to later adolescence) is reoresented by a negatively , - . u ... . - -, n h 1‘ accelerated or parabolic curve, arIirm rreeman and rlory. 4 Thus, three distinct theories have been advanced con- cerning the mentul growth sequence of individuals. Each of these theories has implications in terms of how mentel test scores should be interpreted by teachers and school psycholo- gists, how mental tests should be constructed, and what changes may be expected in an individual's I.Q. scores. this study should also help to answer some of the theoretical questions in the field of child growth and de— 4 veIOphent. The c 0110 nature of ph"sicnl growth has been a c 13 S. A. Courtis, Towards a Science 93 Education (Ann Arbor, Michigan: Edwards Brothers, 1951), p. 9. 1’4 I‘erman, 333 Cit- *2? . 57. 15 Frank Freeman and Charles Flory, "Growth in Intel- lectual Ability as Leasured by Repeated Tests," Monogrsphs of the Society for Research in thld Development, 2:2, 193?. 3 6 demonstrated by insoh,16 Courtis,17 Millard,18 and Olsen.19 Others have hypothesized the concept of growth interrelation- ships-~a definite paralleling of all patterns of growth within an individual. Since physical and academic measurements are available on the subjects of this stndy, the data collected on mental groxth may be Ased by others in studying the nroblem of growth interrelationships. II. .‘SPILJIL‘IOI-Ej U1? 03:11:53 USED Growth cycle. Used in this study was the definition given by con tis: "A cycle is defined as a well-marked period of mataretiun during vhich the organism, forees and end rro— ducts are constant,"20 Single cycle growth curve. The theoreticwl growth curve derived by Heinis.‘1 is expressed by the logarithmic: lb Reuben R. Busch, "the Relationship Between Growth in Height and Growth in Height," (unpublished Master's thesis, Michian State College, 1954). n , . v—r l7 Conrtis, on. cit. lo Millard, g2. cit. l9 Millard Ulsen, Child Develogment (Boston: Heath and Company, 131%,? ) . 20 COdl‘tlS, QB. Cit., p, 172;. ’D . . v. , . el H. heinis, "A rersonal Constant," The Journql of Educational Psychology, 17:173, 1926. Y : L(l-€U) X : 3’8 ' i ' .. , . . ._; , - J— a, 1‘, {1 ,(1 d 'r‘f"l‘f‘€-f(",t huff, L..‘_“7. COII. trillufi - -." ., . _,.“ .. s .1 . C = base f net-tr- lobar tn ‘ , Personal constant. According to Heinis, "the personal coefficient of any g ven individual is eqnnl to the resnlt of the intelligence examination divided by the normal degree of intelliéence corresponding to his age, both measures ing C7 (0 given in ansolute grndnntion."25 Mental growth. For the nurhose of this study, mentdl growth is defined as the pattern of increments shown by an 5 . o D 0 Y t -‘ :3,2 individinl on renewaeo testings ritn the Knnlmwnn-inderson J (/3 Intelligence fest Enlti-cyclic growth. Growth data which when graphed ’1 showing a pattern or acceleration and d,celerqtion ntich show U) more than one grout“ cycle. Isochrcn. One per cent of the total time required for a growth cnrve to change from n develtpment of 0.000000159 per cent to a develoyment of 59.90317 per cent. 22 Heinis, loo. cit. 23 F. Knhlmnnn and Rose Anderson, Kuhlmqnn—Anderson I1r1te11_ij;enc<=e~ feasts, (Princeton, New Jersey: Personnel Press, 1952). CHAPTEM II REVIEW OF THE LI FERAL'HE In order for any study concerning human growth to have scientific merit, it is ess sential that some Kind of patterning of human growth be present within individuals, for unless some pattern exists, no description of human growth significant for individuals can be made. Although the literature shows many disagreements about just what patterns are present, there re are patterns-- it) is much support for the concept that th. 1:4 that an individual's growth is not osn e e13 erratic. Gesell examined thirty oases fifteen years after they had been tested in the Yale Clinic, and although findin n; variations, he stated, "In no instince did the course of growth prove whimsical or erratic."1 Wellman and others at Iowa caused considerable czintrW)v rsy with various studies showing the effects cf environmental change on I.&., which :uight seem to refute tie idea of a growth pattern, but Wellmvn stzntes, "Our results show that even when children are Adding treemendots Chin: s in l.n., the changes are ldwful and pre— Notable.“ One factor which has been examined as an Operating 1 Arnold Gesell, "The A» raisal of tentnl Growth Careers, W _o__f_ Consulti Psy_cholo.-:-;y, Vol. 3, No. 3, p. 73. 2 Beth Wellmol "Mental Growth from Pre— School to COlle(e ," Journal 2: .A.4V1m ntil Education, 0:13T-138, 1937. 9 force in the patterning of growth is the advent of pubescense. The factor of puberty has been rather well accepted as having an effect in the area of physical growth. Chiesson and MacArthur in Studying the growth rates of different reces of rats find: "(1) The large and smull runes and hoth sexes follow the same puttern and course in sllometric develorment; (2) The breaks in the tuil and ear curves do coincide roughly with the {itt'ainL-xent of rneturity."3 Davenport renorts, "She human growth curve shows two (and only two) outstqrfligngrrmriods of acceleruted growth—— the circumnatal and the adolescent."” nichorn in studying physical yrowth stat s, "Phe growth expression develo»ed by strict mittemoticel methods frcn toe cycle Maths is a complete sigmoid and txe point of inflection is located yrecisely it puoerty."5 Huger and otoessiser also found the advent of ‘ puberty affection patterns 0: yhysical growth, stating: r "Stature, Sitting Height, Shun show the some peculiur growth curves: the rapid grow-:tn in early Childhood, one slr.icl;enim; (off wt about 12 and the quickenins up et 16, giving rise to Vihst has been ter ed the 'pubescent dio' centering ot about 3 Leo Chiosson and John MacArthur, "Relative Gruxth in ‘iuces of Mice Produced by Selection," -}r-:)‘~Jth, C308), (1914-5). 4 Charles Davenport, "Human Grouth Curve," Journal of _G§nerz-e..' l-hysloloij, 10:2 5, (1926—1927). 5 H. L. Eichhorn, "Phe Growth-lenroduction Cycle," 0‘ 9 - I r, ’- .’ fl‘EEL, 20:2»2, (lg-5o). )0 15 years of one. Then the post-puberty rapid r‘s I 0 (D t. maximum." There has been less success in relating the pattern of mental growth to puberty, perhaps in part due to lack of re- search in this area. Breckenridge and Vincent show effects of adolescence on physicsl growth, but stdte, "We have no compirohle charts to show tempo of growth in iitellect."7 Abernathy drew browth curves on edrly, mid, and late meturing children dud concluded, "There is no evidence from the cresent ‘ ‘ study of Changes in rite «f Wéntdl nrowth whicn may be ex— olained as concotitunts o” pkysicsl events."8 Garrison sretes, "Ad inspection of the oirves of dif- f erent children sh!) t“wt some unintdin fdirly constant rates 3‘ —L! ., ‘2‘ ‘.‘r, ‘ '~ p 1."‘ ‘ s.‘ D I ’ r d’ 5:116 UDMPIS Shbudd ni-e shi-ts. LhfiFfi shiits may occur at C‘. cny WJE level and over a wide runge of mental functions."' . 1 12 .. L Cru nptjn 10 Roster, l and King stioied .ne scholastic Q J Henry Huger and Brendu otoe ssig er, "On the Growth of Certdin Churuc ers in M31," Annual Eugenics, 2 $2, Hlflfifl 3190”)“ idye and E. Lee Vincent, Child Develop— uuent, (Philnlelohia: W. B. Saunders, lyhf), p. 9. J Ethel fiery Aberwnatl v, "Relationshits Between Meitdl and Physical Growth," Child Dev Velooment, Vol. I, NO. 7, (l€C7), p. 60-31. C v H , - ., 1 . ' ” h'rl garrison, GFO'tn and Develoomeui LU flieJ'Ija I]? , by {3,81} 7'] {16"} CO . , 10:0 1', , 3—, . 151’ . ,I 10 wird C. Cromot oi, "the Iiflueice of PhySlOlOngC A:e KLV3W Scholsrs:i ," Lsycholgaicnl Clinic, 1:115— —120, (l 07). 11 Wilfred ‘vos ter, "l‘h‘JsiolozT‘Jicril .\;-:;-=. as o. Tl'asis for the n ”1 'n "v U11-~~i"ic1uion o: Pupils entering digl och>ol-—iel3:io of ru- ESC%;HU? to Xélt't," Psycholonicsl CliniC, “:33— '::3, (1’10) r... 12 Irvine Kine. "P ysialo i071 ife q.a School Stendi03:" §$fl£Lh§lOfigcel Clinic, 7:222—2zs, (1—11) ll stnnding of postpio>scents in relwtiod t3 ire-pinescents, fill finding 3 sli ht advantnge for the nost-puoescent group. Geselll3 3nd Stone 3nd Doe—KollznvznnliJr studied the mec- tal growth pattern of c ildren experiencing DPeCOClOIS vxoerty an} f31 d no rapid rise of mentil develo meat corresponiin to tiv 3denced wnysical leve13nment. S uttlenorth, in his stidy of the rtysicel and mentcl prowth 3f cdiliren iron ages sit to iineteen, conclides, "The .. nutn establish the etistence 3: s3ne relit ions‘nip between in- --v (Dr tlliueice 3nd uU-flge, cit tye relationship is very tendons . c: unierlyiqg fflCtkuWT is JnIan.n. "IV C’ I ” L (I) and the natnre of .s ' \ Murdock 3nd Sillivm3,1’ Nectsler,17 and Johnson, find more definite evidence 3? the ef fect of adolescence O .43 ~-‘ \‘° ,\ v‘w- . ‘. ‘ 1’ ' 5' " ' ‘A . a f‘ , . . p n '\ ”entil giwndni. In tes.dxr, 33 Cnildrex..rxii six fm3.-i:teen , D e ,lspIVilGfi]_f3? ikentfll fircnvth 3nefilting Page elegy, Vol. 3, No. ° ./ 3 Careers," J3irnql 3. rev. 77-70. J.’ b .. ,_ ‘ 1' Calvin 5.33“ -. » e 1:r3nn, "Notes on t.m {rental Dev:e loinent of Children E hibitinfi the Somatic Signs 1)339rt- irnecox, itflxuw: 4 t3;:, (N ti3n 11 Society f3r ». 1.. ,0 '_‘.i.. , L: . «q, ‘ e S. .J ..' " )_' nJ". tl‘l‘C } [1 Oil, 1 f y! ) , jl 27W 0 t 15 Phfiink iiiuttlxagorifla, "Bne E’stfl(3wl.“in? PKn1tnl_ Gr r'th CI“ fiirls n1? Bogs ige Six to Hin=teen in Yelqtion to Are 3 Pii"1... uninhdth," Ifiory3gg'qrfi‘rr gg_ tie: gidcifi=t;' f>nt 1-1;..>;3r3;.'r'3.:‘s”:, Vol. 21, No. l, “ I. . : n. . la Williln Jonnsun, "2L9 Lentwl Growth Czrve of Secondary Scihjgl suddents," (unplblisned Doctor's tnesis, UniVBPSitY 0? 311.1ch, 1323) 3.. 111-1115. 12 ngngS of 95s, Harinck val Sullivan * find pre—fliolsscsqt suarrtwl.growth spurts as Hsli as nhysical growth spurts, al— 4— L; 'Q- .J \J t pd *‘5 (D h < 5' C; "3 C H D p- F" (I) m (a =entul thin physical acceleration. Wechslsr states, "General Charwcteristios of the curves <3f‘ {growth for most iqts_lectusi whiiities res=mbls t*9 grawth carve f’nr v.:cr1‘o.xl’:r;/. CLis is can rater 39(11): “ radii rise “a? ;e 1: is wgvruichsfl sxcspt fsr : iris” WC“?19PWC1JJ, sonisi.here set s-x v‘es 10 133 12, a rise sunstinss refsrrsd t7: {8 tan gsuyn:csnfi lxrg ."20 Johnson 1 alfutfifijdmi sviisnss hn‘":1r113Lsscnit splrt ~~ . ,‘ l-‘ . —.. P .“ ,‘-, °_, _- L'V -. -i 44;- .. ‘4‘ ' J--_ ' ,. *(1 :zfl.,.’l‘ll {,4}. U\\h'.1 1011. )-!1115\ but" t-~‘-:l-..1'} '/r .Jl.lr' ‘ilrljffix :rfllir fsa* ;;irls {pi ?V4rt entL JP fiftesi yew? for boys. While (KIM? i:ver“igf~tors ‘ rvs c.«vviisrsfi ?*tyarty a ti:u:2 of ¢um3elez*1ts7 - axial uzux fit, ;;tUEPFVS?J£flé$H3 tnqt {iris is a? fsriof if fiscelsrntifig wewtzl gruwtn. Dull stv*ss: It sesms thwt infwncy is J rsriwd of ifitsllectuul germiuxtion rwthnr tLea gruntn. Gra:tfi iaself 'Mons nct go runillg :01n111WIILil swrl; cuilfipocl, SA: roaut N LWBWFE: if ’3rff. 'Hgfllffr;l1ti}l'IiY‘aPa‘E‘PJY‘idlaf ":31] i nearly a .trai:ht line caxrss Jfltil Wivlsssaqrs ait'r {quick ts 1‘1 3 is ravitlu'rneb‘riad h. i1 tls sufa 9f final arrest it a Saint uhich is 1? ”2t indeiiriitely determi ‘ ‘0 / 1'5 Kathe rine 1411' wC' r-mfl. 1.10.115; £‘4lliv m, "A Cmutri‘r;~.¢;biz)n 1. aiStdiy LH imeatul 1 ./sica1 imzisira.wn1ts in bknrmal fl ) o L. (I bsgficr \ID‘C If } Clrsu, lmeriCLQ Igisig_; decwtiga Reviow, 26:20V—2 f, I. 'D' . ‘ ' ’2’? ' é? '- ) ~30, 3K... Jfi/Jq, (.19 )0 q \ . ~ .\ ‘14 1 A80 .18 lFJI‘ , ‘rv/l ) o {3 it o , _ \ O [1/3 0 A] T I w ‘ n 3 1“. CJJ 115‘)‘4 Ut). \J t. 1‘. 111—11. 0 but is 'erD'xlilj/ r131: sligiwr mm) 13: years 31‘ "the. ' . ,x.,, fl TL.Jl'bthl': tees;t-intsl igeace ”rows nesrly as rm 1113 wt sue a, £25: at tie sgya of nine." Eke concludes, finiquatw derivsfi 5 has '14 I C 211" ‘J ' t A.» * a- n :_ ,. x L L', lCleiL t\,SL:T-, Iv “11", 1"? th.1U “.5 ’ f“ PEOdtlflddl, wcall arc; its accslsrwtioi ts icwcfl a limit , j . ". . - A . ,_ . ‘. . ._i , ,V ,, '_. L. .. . A , , . .. .L“ I ' . i.u the. sari, 402 or yearnins chm the E19 1.! 20, cit it cm 02 r , . ,J- ,. ' , ‘ ' ,1 . ,.., A - . A.‘ - 'l“./ r11r*l]a, he eutansl t: recon ' _inlt mic} sconxr this tast. - .. ‘ ' , ,3- - o" -' p ~ «I» .- 'q-‘ ‘- 1- 514).; lrc: tu~ii stzig L.» 1,turu >. HPflulL ,ron'., Cult a " ‘ ‘ \v- w \ “ 3 . ‘\ +‘ ‘ J- 1 ‘ a .. .t,r- AW"lU‘L’Ju 1 Clrva .5 lin9,r to :Jult Ci'L3cq n0 1 '3 : ~ : s. 0 ~ .. s- "2'“ I): “f L“; 73")"; L”: 1()3.: ’.' "L A '(-l’1 fill" an J!)v,"0n"“. -1 , . o ‘ _. 4' 3 l‘ r’ "g; g l 1 I”, o . n Q {\ :rca [Lb :t; J 01 1),,{w schvsi—Uaii. unildie1 ); . .. - . 'Y, ,. n ‘ . , , '. .‘I 1, .. sscerxt i'1 the 2M11JH O; .nmztn :dfifiC1, ;4i.coczm¥ ' . .2 an. “ A. . = .“ - “. .,. :‘.,. '1. "W .. icn1.tl uuqb tue _1owtu vi ianiliwaxcs iron 1;) to ly/ 194'L* "~ w ‘ . ,\ ‘ _ - ',‘ , . 7“! V ’ I ' ' (leLlul 09 s ;n% “sea 14; tsrms an? 1 i'usngJlic ckprztion. Odom stiiisd the mental growth curve h~ouxh tuc 7p— 1‘ . ,1 o o . - _ 3‘ ‘ ,. , . ' . 91113fstiua 01 grasp thBllld€dU€ iests imfl conclaled, "Baa r") __‘ w _ _“ ‘ ._, .,..V ,_ .- ’ . l “l" 1511;"! L' D" 1.1 , 11 4.1.13 UI‘LJ‘.'I s L: 3f I :1 ud 1.1. 4Luz-3 (152-? , n 13:1‘/<‘3...Q~ _££;;£§4;; flaggdrqnis, ‘31. 22, Rs. 2, (1,20), gp. “—la. '3 ‘ ~1 . n. '- -‘ ~ n .. - ‘. 1.. =.- - .2 1 2/ l“ A“. Laurotvn , zlxwithmi UL bcu lxryiwxflJHchglCQI ‘11 ‘1‘ f I ' u 1‘ ‘u":“ ' / : 1 0" 7" ‘~ ‘ :v - - ‘ ‘ ' ‘ .-" (a “ dilddtiuu i]. Let u: ,' JOLII‘QIL C3; lax-3,101 ' ‘, i .3: ’1}. LC;H_}';.{.)1_Q‘JW , L: ”r (.- :3 .. I. ’y 5‘ I” ‘ .. - , 11'2“ ), .L . fi"'~J . 31‘5"? . , L ,a I - ll t1* ccsrsuces in heat"l grout“ qqz Oscline, JOJPJ” l I’ ‘ . 9-. ' l“ / I, ‘- O _ _ fl 1', , o 'w,‘ n . .. 2.. was, ouPQfil c. Ufiflcrll Psych u.— t: ‘ f V ‘ o v " l 'I # 3 J. Jilcocas, "On the Mistriaitiun 41‘ Grhl‘n 0: .3 1 4 [Kifltfil gr: tn curve is shown generwlly to de negatim 1: en- csfiLersted when lott d from the results of group intelligence 0 / _ . be ts.“0 However, Octozn fauna occasional exceptions to this W m {K3 tuern, with some CdPVSS slightly uccelerwted qafi othert agagxrwxximntiJr,'1 strei-ifi: line. A serioas limitation 4f many of the stuiiss cited above has. been 3‘foi'.'1te:l int by 'r 1:1-.{,27 De::.1rbor'1 sari lothnjyé, 28 Esn;1trtlewarth,29 Millwrfl,30 DsLoq5,31 and others who ihfiicqte 0116! oi“ths fuctfuwi*'hioh i'u: limitefl.tr x/ of the sfixtiiw‘ ClitSEHi nbove-—the was of grcur WQlHP to asters (If (grum1th. As early o? 1921, Pictn r wtfirwefl: I feel ta 9 JON come for systematic L 4 La measurement of the , 3 c chilfiren over severol years, by means o? hath 9fl131t10flil qnfl mental ests, .1 71ll COMbifljtionS flf tt959.3 26 Charles Odom, "A Study of the Pieatwl Gro t) Curve Jlti: Special Reference to tne Results 3f Groxn Iitelli ence Tesytfq." Jolrawl w? Cducationul P3;Cdolh'¥, 20:h15, (1020). 27 LIWPGWiC Frank, "rte Problem of Chili DevelOVHEGE, —Jll;LSL Dav: lovn,ut, 6:10 (1935). 25 welter Deirhqrn we? John lotinhv Predictin: the u 3 if—LLLSlig DeV€10328Q£:(C"”0F11H-, L1ss. Sci-Art Jillisners 1411.), 15:. 232-2343 29 Shuttleworth, 0H. 31 . to. 200-201. “- «a- ’ “l 30 C. V. hillnrd, Chilfi 3r; 3; 1nd Developr‘nt Lg -h3 tei2£;§:nt1rl School Yeors (Boston: D. C. Leath Com soy, 19:1), - "C 6 . -. \ a. (‘1- f‘h __fi ' 9' n 0~ ‘1 Arthur R. DaLong, "A Loagit filial eta», w: Iniili- '4“]‘ 0111. ~m1,Iici;;1n EH urwtion J01r~wl, kafiwnbef, 1(51. r3 _ .vv . f 3/- Rudolf Pintner, "Intelligence and Its 1'19'153.1.“’:‘-:11"?.7lt. IQ C33Wn,osilm," PLs Jourq;1 of Tfiacstianql Psycholqgg, Vol. 12, (3- 3, (1g21), p. 1&2. . Shattlevvn tn st1t39, €3ano¢t 335—31tiwl >331~3 1isit3 for' any Stuflf 0? CPO 3“ is th” r3333 34 4pmlicntion of , . ‘ ? .ueflszlrpw34t3 wnicn 4r3 03443r43le frc1 Ye; to Je4r."/3 Ekwatfl< argues in A; ., i :1 l'lI‘ tren‘. ”auctions tstudied bot1 own, 4nd 43 the r4t3s O 3 wt t S3me vein, "30393“71"“4 H41 414t3 ffiw3 line 0? L' ~ dv Ca‘j‘l- or each of thsse ”llct13ti4: structure. 3nd 3 that ilnavnovenentst9 .JJ ‘ J *5 63? fégble-mindefi ch11- Kuu showafi a ténfleflcy towqrd a regdlwr 380F918? in I.“ -‘ I“:3.9. 1Js1lu§ ttm> Kai.119 'TQ.LN)fl, ‘the Ihersm)qql.ihaastrant (38» V ‘ - . ' "- I. . . ' . ‘ri’thl was muuu Hebe confiigtent ttwn 21d mean tue 1nfiLV1fiu1l's ‘5‘ H1llwtfi, OH. 01t., t. 53. Pr EC G1stflv Frc=2l10(‘:, "Méntal Development thinfi the Q fl o 7‘!‘ ' n5“f353011?90“1t qafl \do lesc w1t Ierio c :?V3°V a? Allofitlonnl .\.S‘;': ’v 1 1...--.- -¢~41;;ch}, 'Jol. lw, No. 5, (3.1rw), . ’«01. ’3 1 . , _. - pg. 29 H. Heinlfi, "A Pe1190n71 Cun.‘11t Th3 tournfil,of J ; . ‘1- . 1 o _ __~ . -ét;_;,1onwl figlcuulQLJ, 17.153-1?X , (1’92;). vi 9. thlmnnn, Tistn a? 1>nt 1 7“Vrl““m°‘t (M319WV0119: 1.; t . - -—‘- ‘ ‘ACLV1t10nwl;lhlolls EHN%, Inc., 13wV7). l? Kunlmaqn,ul who saw in Personal Cunstwnt WA innrova- ment over the 1.7.3,. concept, T‘I‘EDHI‘ed gran-7th cuvve values For verar 6.21% month using; the Helms formula. is ma‘3.:.r 1'21, raftrez? being checked age slightly mniified by Hilien, is fire- 3'") 4' — 1‘ ~,:—.: 113551 in tarmlfi)‘ er'u in K‘U‘lsnrmn'3"”‘ bunk, Terr‘cr: ; POM" 11 C L!) ,, Develor-méifl. lfilflenb "11530 AW—ti 13' 7° H.571; 9 1359/10" (hm n=.1“:1':*mn' Fab—aqmml {Jr-cup} my? Cnncluded til-It the? 1’ °; 31m°1 COilistfilflt is _ .,. . . 3 . ° - . “' 1... \ , - :1 H, .g.,. ‘. i‘ \.. _' ‘ _ :1 31w:- r59: :mcwutfi e ex‘wefigl J°l 3) A; f: F We U Nam, IL New? 109331.“... 3 . 1'}; ”3' f“ ' ‘- ' ‘ ' - »‘ u ‘, ‘0 h" - \cv 1- J- ” ‘ b‘iCLell i918 LHQLI ULL' 0; {3:19 ft: '40 f‘ua’ '1' tLI‘E (11 T1: "* '1. ‘gr J. ,. JV. ,5 .H", '¢_ .: L‘. Lu . K1, tn,- ‘ Ff; JU‘L‘ ‘JUHf‘u-ILI‘J 3.1" 1V \3\)_L.'.:1€ l ‘niL-J uhe Iov-J‘o ‘nll'; be, ] I ' 'I I ‘. “3‘ -\ .‘ 31.“: .- ‘5 4~' —\ 1‘ 51" -‘ ° N ‘l\" I, l j- I TL ’3 ~vgfi "I “t ‘ . Lvil ukIlt‘uJ. “1412 “'3‘ Mul‘. 130115“ M". AC“.-- .' ‘11”; " 1111*.1 1'14.J."'"21 if} ‘. x'x-‘ -, , . 4. ..‘3- L: 313..., .. "| - ‘— ,,\_,. .—. “a, A. . 3, L'VLJCJlUAllui) Lulu 513:: .L u'fum31 uOUSL/V'Jt is !.;u. ‘3: C‘Jlifib-iflu tul'l .1) .4 \- - .. L'. 1. Pin 1134‘) Z'. . ‘ Allen" in 9tu3fllnfi tn” rplqtianruifi “3 A. }T. Rilr’eu, "A Co:"z;)a1‘zxfli’\"f Stufiy 0i tie I"t9111?"" “35’ "“0613“: an“; fie s' Pprsmnal Co] tent," J..:u1"r(11 0-" 3123111131 ‘ \1'fi0 “(){P1' 1., . ’v° 3 . .L', ‘u‘ (2., ".- " - A C: . gf‘)‘ t‘itxte for ti .121_2::*’ (1‘33). kc»:- ’ I! ~._‘ ‘1 0’ ‘ ,‘ N 4‘. ‘ _ will, Mme .‘ztt‘LJIS 3-:1'r133'r11l C cast .1“; S a V) L- L: 13 I. %.," «JQAJVrfil in? Cfiguéatixannl 1’ «(:1 01!);{, '5, . . .- , r . V q ’ Lr-r i‘LdLJlgl’liln , “$1. 1. o ’ p Q («15. A 1“) hildfifll, Op. (3 t., :IJ. 35 5— 5 ;3. If? ‘ “1,- t .' _‘ "T‘ 3:11,]. ." ‘1‘ .. f), L .~ ‘ ~r -_ Luilfiie] 11. ALl: U 1‘ - l’.HF‘W,‘:v‘uL43r31mlu1L-Jq~ °rlera Jeysts :aql 19nd Pfln 1L1.A31115\N923!ib 1;] GT via 1 BS-ZQi (1937). ‘l‘SJH Izltelli ° '.'.Cf‘?1tlunf- L Psic'zfllogiz, 3f:2 JO..II‘:1;l g; /3, 4 ~) 1 t A -\‘f\ ,s “.4 .A 73... 2'. .‘3-3‘3313 \) O 3": $.5- A c‘ — Arm 5-? fl 3 I Kahli'l:at ,0 01 i Ix" L1 ,‘1 .1- , W '1 COPY.” J“ r)11k1 AC 3 v 3i . J“ ,0; at 116’ ieve: l A 7101' mad 5.18 1 Fill/.3 ccuptwnt aarsonwl ; 01 meat ‘— UK ucvn 1112’ 0 fl: . I . “O“. r! .v.v J. O N "71’1')'\ ( Hamtil “nigh 1 0' I alt nt, *3 1 I .,— £3111 62 I; 18.1.1 v l :5 \‘ vb. h1\ .L. U SLOW § t1} 0.- (p 11 ‘ . L) J“ l: ‘1 f“. .l C 3 ." _§ 5‘ 1 h it L11]- , f\ \_l 4 OT 3 .- .mL C+u 71A \I . 4‘ .\ 4.. A... s... x A .'p. 9 L ‘I\ lit . . . r.l a: __ 3 J C .13. D. » 1L. 3.: . ‘1‘ \AK \‘1. I N. 11. \b )4 .. r.\ .1 3: ’LI. '3 l v. r. \, ’3. NW -3 ) /. CJll an? "r’ QC;- u~ 5r 0 0.1:, Jar :1 ' 1 :1 , .3 'L I on 160 ’llQCtefl ’\ ‘1 not LIV k. (1 3!"! \ Fr ct 1 u L ‘41 a.-. a flu g. 0.x .1. 1 1L 1‘. ‘r A... l 7-.. ’ a. . L.“ xi; 1 (A I a I! h. 5‘ a» it 73. v.-. .\ 1!. a: u" :3; .2 ‘95 :0 )‘ \l, ,v 51 r\ 2% no 11- 1 11.. fl 1 .m. I: r” a mu .1.” NM .5; 0 at I. Cu ) ”A 9_m‘»m 2. sown Z n.7, :J 9/ “3. 1 l .11. 1 N ( 2.. D o 3.1.. a .1 u. mi. 5 I a ' .r I‘- 391'1:I "’t 1; .. cal“? .hl C ’ m. n. A, 0 tan. 5‘:- 10:):“I: . Ac - o I .l 3.. 1 v...” h.: . .U *1 ' ' , , t r d an; .l5 3 . l3 ulu ieve; 1 1 Q I (IOWA Citi ’I . e H o «i h). D 0 .1 Huh 0 1* .OIV fi- L P‘ \ll~ , Luca) 2 U. ‘4. l ) I. . 3M 7 wl‘ J .‘Hl. We 0 A.- J II" ‘1!" (v/ 1! O 1 gr x.” ”I H -vv WA. 1 wt. ) 4L 0.. .9. S T. 0Q C 3., H h. Ins ver .71: .LA‘ V .I A +.fi hr. no H. a; O _..l s1 .rL V .> r.» . p 1.1 HL 0 4i a.” I O \l H ._ . o .1. H; 5.). -..U .1 1,3 t: 1 F: 1 V T J; 3 Hal ” i T- 120‘ C. n H 2 f. i C o... ['1' .L ‘r .1. H-” ——'..-:-—' -.u~?‘. nigh tzst-retest correlation 31' the? Drum, Kit." if‘vL-zmi that Lewgu?ox1mwtely 93 yercemL 3i LLE children showe3 flxctantions ' c .1 .‘.. ,'. . ' ° / >1. _. Cutcellal iq another stuuv of Sn nFnrd quwt 1.1. vallu- t1<1515 of more than #09 Cuilfiren foun7 thxt foqr cwyes or abuut A '. . , Vilfir Over»le I.-¢. pcflths. One O;k~ —ten1th of on? wer031t Ivernceant gained over 33} oints, Five percent over 19 points, beta. ‘wlL/MV” over JJLj:oints, 'u17 LHDHLI—f l'M-‘“er09rflzcjv¢r 7 {J Lincolqu rtuiied test-latest CHIN ‘ in t3& I.Q.'s 1:15,; :3 rq/Lf: f‘l‘om :a 1.35:?- Qf‘ '75 1.2;. 33Oir1t51LJ 1 ”mtdax‘Bf poLLAu -urb*‘er0=ut.r ffie 0&999 VT‘XI’14‘r3 3.5) pointn 0)“ "-mr'? U'I'Qill'fl 53 8141:] of 7:719 var} ntiuns 1:) ”HP. 102971133108 ‘flévtlifieat of 195 Cuil Gran Showed simila? ”V79 f‘rnn a ¢win of 37 points to n lobr o? 33 voints. Six- te‘Bfil ;»ermwnu;43f the cases fTLu:t.1wted 20 or {NEW"H)1ULF r‘ . Clarke 131 C arkeég stgflipd 103 wfiOIerceat mql fiddlh / E ~ 1 J1 PsyCue CuLL ll . / S~‘ Le , "St J11fnrd-Binet I.g. Variations, ~=LLQ_SL1 and Soci~tj, #5 17—{1;,(1‘37). I") wfia 1 . . L 1. ,,~ mug-arm A. Linc-01:1,"A3 \1'7; I of‘ Cay-1:333:33 Tm til“? Ix;- Le -, 7 ..- - , ,. "n [‘1 ‘ - '1 n 1—iggau33 QKWLHHCS 03.yg_ £:1°’Wllur w, " J51r31131>P?¢ t Grouti in RPAQiWy XQH15V9fl9nt," Chil1 Develnvma“, l ”1:, V\-)} 0 ll, :‘ ’0 2, ‘ I:o 71‘1].‘-:1, 1 ‘ ()0 ’3 ~ _- o ' 9 (“J C. 7. lell-qv1, "k? 1147;3‘19 f)” -9NTtWTT? Cévraitn 7min" 1):?rf‘0fi- (fie-'52: in 839111113," Ur"; fiflif‘fic‘d 7).“,u".‘;f*z"r'. "Elf-.318 (SUM ‘5 ~ . . ,'a I 1LI‘H.H", Ilc‘J 'wn: '11/9Vvi U (M‘ Llfizdufiwl, 7‘370. 5‘7 141...“ v r A nu M- ,. :3 n q...“ ,-- u ,1; .. J 4' J"- L. A 1.. (.133 ) UT x).!'l..l.‘ ‘1")- 1r9‘1.-’.1'.1-.3' 19 I“? “6 1.7!; " ‘ . ' r. o 1¢tti€v7 i‘t," d) 1011GWC3 r c,1r'c Qd9¢ s (first Lqflpqu, .2 _ . . .,. . _. ’ . ,. \ ’, ‘L‘3Hl ‘ d ldC‘diyxli3tat3 C)119,0, 195)), ‘ Phomvc N-lly, "T*~ IélfiticfiVhifl B~t4391 Achieva” ’7‘F3?7t . in *%?ight run? tlfi? Begixnlingtzhénwtlx i» ikvddiJhg", IJn— *1?;119h d Dactor'w flhesic (W~s“ L nriz‘: Ii bt':q Stxtd, tn?c)‘ 1L :5 ii. E.~IAHL. an? 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I‘QJJ m9... ”I in." 1.. h R. 4‘ ‘z.’ " I“ ‘ I‘ ‘ . .1 1‘ ’ " " ' ',‘\ ‘ ‘|.' y\ L, ' '1'. ~.‘r W‘. -ul:-.:..:r;'.y3twg A“.1.11241, ughzolixhnfi Il,:unr s unééis .wtgu . .' ‘, ' .-.... . :7 '- n- 04-.~.‘- \ 7." ' 'r -.~ *° (,‘j’v IJznsin , Liohlm u. LiCLibWU g. .4 Jul.e a by, 1,,» . /r) ' 7‘3 .- - l ' 1- , ”I ‘ un H1 39 “ 9= rr,’.n ".. v . ‘Jl'k—)‘I. {/11 b 1 A 4 \ 'L‘ 1 , . ‘, . , ‘ . - . . O h ’ ‘ ‘ ' - C‘ a . k h. 1 ', __“ 1 '. z' ' ' I- ; ilflbu L4u..-c, ulCLl 4;. L.Lnlb1u 04.4: JnlJ.rbi.J, l ,4). 5“ I—u P 5..) 2... }..u ; v 2 I 5-: \ L l- . . I‘ k; H' In If] {h 1‘ p. D I.) .l‘ fd ‘ O - (5 4-— . L ‘V (‘ ‘-. 1' .‘ .. . n l a Dem, I. 9. DC 01"th , :).--( ~ 3 , .. U .4 ' ‘. ‘ . ’ - . . fl . - .- I. 7- t- 0,. '.‘ .0 CE¥JCX ' .~ 1 0.. I (Trve14)\m= I-zl .J.: 5, 'JJ .U)1.rn.73 .x r 9%1‘ - u9~~LS (1' ( ‘ ‘. ' ‘ . I ' I . 'l. g : w l" V ' l‘ H J 7 . \ [J .‘r‘ltl , l'.l(:',lr Ll . 1.,L’.XJL.,(:' IJt-J 0‘. \j liV'AI‘C 1. VJ , .1 11.;5 ) O I (q I" - u '1! _ ‘ ‘ w v ‘ 4_ 'Lo “ ‘/ 4 . 2) D. I. ”an, _ ’ X‘AVT‘HL J‘- l. .1'."JI‘L1.1.J-JLI 111 :er-ltJJ.\J'l - 'V . fl \- 4 " t T v —' .'-l , “ "' i ‘ ‘ . L n .' i“! “. , ’Y Q “*‘R' .49 V ..v-c—14 )pee-unw~nu i4 ~1. u, :n,wn.is:n~ u s.~ ' .‘v.“ A z : H1 . ‘Y . 'I- 1‘ ‘” '~ . "J *U v‘alS AJJ Ara- , 1.4nh- LII UHiV?‘&lp; a. bio...,u., lg] ) 71-.3 FkéreuiitJh, "LLRV"CLJU r‘f (} .rcti: " EStLLTiséc 151 Clagj/i \J--. 11’ ISU- 3, UlliV‘? 13:1 ‘ '7" .3 R. , ' ' ‘ - ‘ 5' I“ 4 . P. 111111;. arm A. ‘2. D- Long. , " rm .Xptsr 1.9: .1 n. : ('1 II}- . ‘ "_ ‘ ‘_ . . . . ' \L . . {it “Hi 0: Eyed—1051415 "fix? up," v.'.'.1'.. L 3‘!-'—31.';':;!i1 ”£173 I"t!);.1‘:'!:41119.5", '~-r::‘ ~ . ., _ . ; . ' r 1. I‘D-HI .5L':J‘ 13011.” 51‘, SGI‘L-‘Q II, 1:). 1, li“...’. CHAYTBd III Tlilfi GROUT STUDI'ZD LID 1'51.) ."IODS U877) I . ‘4‘}?3 CIR-QUE" Soxrce of dnt-. The population used ms 1 bqsis oi "I this stafiy wxs Vlvctri ¢rou tne Deur3ura Data, fivwilable It the Child Developmnqt Ltdurwtories wt fiivti_éa State Univer- .1., .- "_ 3-, H... 1 L,‘ .. I. _..,. , .-.‘. .1 , ‘_ -. Pity. ;qQ¢P Mint ‘~h: (allmcpvi a! tne t:»cnaxn of tug lenrJ "" :7 (Ira, -..'_.., ‘.': ' .,‘.n. . . ”L' .9 r‘ Y surz. 0.)..001, Deanna 1, ”-0110 “.11, 1.1.x; tne \lir‘tculfin a. v. f. :: ,‘ , . .‘ ,, mm ,I , , , h w , . - ,_ ,. , _ a _ were mane um nJre thwd Eva ChlldPeu %; ”HGJ arugrcsrel .rom I” v-r-I (I: :5 *3 r— 0 r r 'L r' ¢ 9- 3 4 v ' - r‘ub -- b'a' LTJfl ”“4 buud/ when the“ 1'.L LL» - ‘~' , ' '~ ~ ' I’ I . ‘- 3'. . -. "' 1 ' " ‘ofIr 3 “ .N.” ’\. - *1 ' \.\ r91] 81;. dilrtxi tLP-v l Llwlu um? I‘ u wlb aux/.19 LUHJ]. $139.10.] 9&1‘3 zlto "591'”? lilESLfi. “he 1 0115 ”mi IE HT?" 1.138". I] , .,_ , I.‘ ..- r‘ l 1, ,.I L- , .3 ..1 In r :1 flL, 810;.(3111u 5: neiu,n. lflm “.1: ‘3 L. rI ‘~ ' ‘ . , ' ‘\ .‘ I" , O y r‘ , .' . ‘ ‘ q ‘II ' ;r n . '. \ . -‘ "~ .~. ' \ - .h??? .aqu three blues 1 yr1r, Hcdbll tefiuh 91e ~Jmimlsu~nufi ‘ 9" . a f |--‘ (‘ -I' ' ‘7‘ q . ’. I“ ‘ I“ \ "V ‘0. ‘ f a (1..n4Illy; %Hd 0L:&.OPQ Acrievedegt tests were :1ven yearly f‘r'Q-I ‘r-s} g~;J(u' All 11“.? .) 0 qrjyvg ' -fln.3Q10n¢I ‘13 L. 7 r 1 1 --o |..'|" t“. J‘JLAI ('4. «‘1 - x no :1 l ‘ L-I . \)Vu 1 ant}: {’.7-nU 34. L1()(- Wha— .exric mSHSJP€S were “are FPRQJEQt. In Hillnri's Opinion, In ,_ - . _ . r. - Iflse chllfiren in this sonool are, 13 general, typical 3: tap V ‘7lésher levpl of -ociql watxs F3143 in 13 industrial communitv .1- Very few of the COS? q Se l6 C t i\)(1 tion of data following criteria: covering were u chrono ‘ v .Joiql 1* " L a ' fl (3,3; 14,? ‘3’}??8 . 3! 039’s. Seleotcfl ”r0" ”Le entire calico— one hunflred cases, “ivkel accorning to the (l) at 19918t six mentwl age scores loginql iol Li 1t least 11 mom is ; (2) qt least six 1eirut me e M41 neat covering o period or MO m01ths; full (3) 51Hr1 Fittinp;tfiv= first tux) criterixx ere ex unined 1J1 ier1x* or rraleeo_.o: too.(x19es vdjfi: the 1'Liest range 1x: chriwxvlogicafiira3e. 'flahle I sfiux s t14311x3o°r :‘ HEJSJFEmrfltS in} the run,o of meisarewents of the onses used. II. IILJEIUILo “1-3) 1U.J)u"'2f3 The neitwl groith anti .vail ble on w1ca a? ,he 03e— 14ndred 0159c q; flesfirioefi by: (1) using w..n I.Q. us cue I 1te 13f ;1ezfirwl igrozdzu; (2) <3e* lel' ~1zue H1 "1 :rsx)nvl. Oculst nit" from tge tm“l* values Cl mental growth ‘erived f on the Weiiis f 1111-41-3, m1] rr'euen tecl ‘0'; Kuhlmath; 51131“. (3) deriving; two- <3yole Courtis eqxntiins. Using the Vixn 1.1, In uSing t1: ueaq I.~. as the “fiie C)? wantwl 'rowtu, Iqtallicence uJotieatF ‘vre derivel ’r w e'u3L test given wu inflividlql. “Jen tte $11 of tie I.;.'n H- n div ile1 ‘” fine nxooer of tiete laiaieter“l, .ad the Pc9111: run; used 'u> tue r~1te 1)? WLIHTII rwriuh. -nis I”1“3 ITIS tibia H lti 11:1 on to“ %49 in mo1tbc of the whilfi when ewnn t95§u was giveu, ”n4 the NrOdzot “is Con”: 83 with tie weutfil 1 V. H Growt 1 H u. it No. ad, 0 1.31.0; V0 ' l. 2, 2 1 illird, Not1re m‘l Coarncter of Tre- L A in ~8H‘1na Aciievs ext," Child DevelmeelE: €JH9. ”F. 71—73. TABLE I NUMBER OF MEASURES AND AGE RANGE OF CASES USED Number Number Range of measures of cases in youths .1... Cases 6 7 40 to HQ.5 3 7 11 “5 to 49.5 8 8 23 ’ § 50 to 5u.5 39 9 25 g 55 to 50-5 5 10 25 § 60 to 64.5 6 ll 8 é 65 to 60.5 o 12 1 2 70 to 7M.5 2 E 75 to 70.5 3 i 80 to 84.5 0 ; 8‘ to 39 5 10 i F0 to 9#.5 5 3 05 to 99 5 3 E 100 to 10% 5 8 E 105 to 10‘35 1; 3 110 to 114.5 1 115 to 119.5 1 b"... a3; obtained fro fine test. “b" Detwn=n the theoretical strniy actual ment11 re 3ure:nents 0:)tqined .5) srnwle 002;”t1tional prucu (v D 4‘J’ ,o 3.: 01 b r I w- ison ti oreti \. A .m r 1JL1twl 91“'1tn ”11. on the tests. wale c311 F112 Droutg of (311.3. 3511‘ 00111312.. with the «1ctural 11:1F>."s.11‘-€1:= «19111111913 I from tug tcgts. Deriviz’gg "P-~rs:ox1'11 Co.1.:">.:1‘:s". 11:91.11 $1911.19 P431°vorx<1 Cons t1nts we! 19rIV9d by finding Lu? r1310 bctween the ab— Solute grovt. V11 '1r1ve ITOJ Lu) ““ntwl 3-9 fie ”ruined fly tue Kunlmwnn-A1ierron test to En“ 10831132 Wentnl age 11:11.13 0.?“ tiw CE:1‘OF1011J_§10"31 4.39 or he 1111113: 1.": 4:211 the 131,131: H38 t1h;e u ’fl1is *rucu7-n%1;‘179 3 1113vww l Cujfit.n1$ for 930?} tsot t1 PG )3 1n indivifllal. TLM Raw »3 thése Férsanzl COHStfiffiHJ‘ 1r u1'=-.IiV1ie_ ‘gr1.1° nun;z cu” tests t”d;;1, ' vir1 :1 ”2-11 P81“ .141. Corn tvnt 3.0r e'azh 11111vifl 111. {This "153'1-51 ““u’.1".1 “Hunt/15f, ‘15:: ti. :1 1.1111111??? 7)" ‘61-? 13.11%]. E (.lu.‘ J;l‘/J-r){;i: "\ 145W3‘31V311. Che rug“ilt BZUS tLG -. 9011> 1331.'~13 ml {IKJJth Jv1divalxn1t, 1L101. :1: Lr"’flxfix11 Prov trmé tab xu“; igtfi 1 agentwl We sau~c 1AA aqu31r91 Witt tL“ nautql 05: rcvrd fii:t4nllg Jul-i~ei “run but est. TuDIS III 11119trntss tp% 31‘00611193 falloncl 910 ?191re II $.3ms grax.iC®11y tna Ct;E%JP€tl£V11 u-u” 1 urg.1V‘3 F312: txe u53:g Pfig‘flflil Ckxn3t1at ‘0" Curse-t 37:73 Cu :; as”? with um? "("11‘11 1-=~3.1't':1- 1:1: -I‘F?'<;<={.‘t.€-‘ 3.1Vtvgijigf'?. TABLE SAMPLE COMPUTATIONAL PROCESS USING MEAN I.Q. AS RA?E .”\“" at CASE 3511 Age Mental age . . TheoretICal Differégte in months in months I.Q. mental age between (1) (2) (3) (4) (2) and (b) 101 115 110 120.2 5.2 113 132 117 130.h 2.4 125 1&0 115 108.8 4.8 128 155 121 152.3 2.7 131 155 118 155.9 .9 137 164 120 163.0 1.0 141 176 125 167.8 8.2 100 150 125 171.0 8.6 . oun. GROWTH OF CASE 35F co HEARD MEASURES DERIVED ERUH HIT} THE ’L‘ TABLE III SAMPLE COMPUTATIONAL PROCESS FUR DERIVING HEINIS CURVE CASE 35F . C.A. Mental 1.A. Mental Predicted Differ— C.A. L.A. Growth Value Growth Value Ratio Value ence 101 115 307 327 1.0651 116 1 113 132_ 324 346 1.0679 132 0 25 144 33< 362 1.0560 149 5 128 155 342 367 1.0730 152.5 2.5 131 155 345 367 1.0637 156 1 137 164 351 374 1.0655 172 4 141 176 355 381 1.0732 172 4 144 180 353 384 1.0726 177 3 m... .3 s .... ..... -. :3‘TS ’w '04 I J+‘ 33‘- ‘ L 3‘ SW‘ 3.. .H. ..Ht .H. . H H “o: c. o -. . H ... ... H . .... I u . YO.3|.|3.|$...3333331 a H. l.-. . . . . . 4 .H. H. . . .Wev Lw WW“ 3P.Hll.3 t . .. 3.3 .H H .... .H. CH. H....HP...... H . ”...-31?;-H 1.7.x .4 1H.. .H .. H. . H H. H. .H .. .. .HH .. . H 9.1;..H . .. . . . 4 . . . .. . ...1. . . 1 I. . H . .. .. . . :HH .. H. H H .HM ...HHH H H S“ H . . H . H . H H . . H .+. . H . 33.l “-3 31 . . a; 3L3 3 . H $.3353 3 .- Al .---333.73.43- H 3..33-- 3 .H...-33.3-...-.- 3. 33-3 - 3H- . H - - H ...-mqfiml . .. - -..-3.-.H m; .. . 4 H H -. . . H. H H H H H H H ni3 H mi m mun. . . 4 $.- H . . 0 >1 - 1314.1 8.0\ L H H H H _. H _ H . ...H 1H0. 3“ ACLU .. .. ,. _ .. _ H . H . . 1 3.... A. H 33333313- . v3 3 I3¢.|cll ...3 333+. ....... H33 w! 3. 533,-: 3- 1.3 IT. I 9.33333 33 3 . 333Ib33.m..l 3HW333. ‘3 3 H H H H , _. H . luau. H L... n1 H . .H .. . H H H H H 3.1-1. 3...... .0... Hm... . . . . H33333IJ339-33. . 3. 3. 3 4H 33 _ bv.J3Jh VHF-3313333 . .4 . . . H _ 4 H H _ .4 M1 .v 4M. 3.. H H _ H H H H H H H H tH . . 3H .. AH H .. ... .3..333 .3-.- 3-. 313-93.33- ». 3 3 _. ,. . ...-3. 3H: - ..3 -43-3. -.-.-3.-.H 6.15.33. 3. 3R1D4 - .4. - __ . -... i . .. ...:- oa. .H... . . . H . . . : . . .. 3 _ _ 3 ...-3 .. H H H H H w 3.3-. . U 3. . . a H .7. H H H .3 . H fit it H ”.....TH . . 33. 3-3%..- 3 -.Hi-I .- , . 3-flV-I4..3 . -- h - 3 .7 .--H3331. . . . +3 .3 3. ..hv 3:39.733 3V3W333H. - 3 .. ,. H . . . HH . . H . . H Hm. 1f“- H -... .. . . H _ _ H H 11W . . . . H pr H H. I. H : H. . ... . .3 3 . .3 .3 ,3- H3 . V .D 333...-..3n33 r1333. 33 333.333. . __ w H .4 w Hf 3H3 I H H . . H L “H1 .c .. .lwlflwt. .H - T . H .I H H H . u .. — . H H H I... I.-. . H H H _ /. H . H _ . . H . , ..r 2. u. ml . , .---i. 1.33 H 33..- 3 3- 1 3.... 1_-- - - 3H [ml--..- H... 3H3 ----H-- -.3 3 H3 3- 3. .3 .--3 “- 3.-_-- 1333433343.--.33m‘ .3 -. 3- 3....-- . H .. H H H . W: H H H . L 05.5 H at H. . 4-3 .. 3 . L. . . ,3 3 ... . 3 . _ 4. N3 H 43. T3 H _. _ . H 4..., H . _ H H H: 3. Hum m5... 333..- 3.I.H- 1.3 - .3 3. . -. -. ...-“....H.) ...3 - 3+ ..3 3. - ... fir-3. 3...- 13v! H1-3.3-w.bh-. .1. ..--.33 .-3 . . .3 / _ . . 3.. . H... 14.43.. . H . H H . H . 1‘. . . . _. . a! .. “I D H H H. H H . H H H H H La... . 13.... Ln»... . 1 . 3:333 .3 a 3 3r 1 . H .. . _ . 1 . . H . . q . .. H. . . H . H . 1 . . H t H .Uu WMH H 1+3- 3” 33 T3331 Imlo 33 3 l 333 r I33 .a 33 3 . - H .3 .H V . H33 | W I o! Hid”. '3M3 933 3| 3“ 33W .3 V 33 ~13 I 3333.33.13 I”. 3.3-1.334” In: 303.334 431 . “3133 ,HY. 3 .3633 .. m. H H H .. H .. H H (J, H H . H H .n g 1 u” H _ . H H. . a . _. O. . VP. . H H w . H . . 3 .-l . - - 3 45.63 H ...D. . H H . 3 4 . 3. . . .H x! . . H .Tl/w H x m? .. H . H H . H H H . H . H ..-. H a ; u . I .3733.- o3qlli . 33 33H .3 ...-.33 3. 3} 4333 w I3 334.- 3433. o 33 . n 30.3 3 733'”..’.H13,31Y3 1336.33 - . .- 3 I3wlo 33.33-l....+3333|. . . 333 r333 Yb .3 1T3.- -HYWII‘ H _. . H H . _ H . ~I . . .H H . m). .. . . 4 . . H . , . H . .. , . .r . .. 3. % p 433+ hm .- . . 3 . .31 3. + . I . B H l\ . . . . 4 . . H H H H a l .. H . H H //¢ H H ,0. 331.T33 1:33-33 H 333 T I3 “-3 3 1T 3 3A33 3 - .3 h-U .u3- - .333 3+ .3 L3- 33 .73 3.3 W H 3.313%33314333W333J: . j H H- H H WV H . H . . . . . . . g : H .. . . ..JH . H . W . . . _ H . 3_ H 53.1“; _- .3 3 3H 3 . . . , H H n. . . , q . . H .. . H H H, HEAV 0 H nw .1. ,n H mRH . . _ 03‘ w H H H on . .LIVH 4 pfi I‘Lv'l. 4m 1} QJ o J H .3 4 C1 3H H . .. H . H . .. H . .41. H. H H . H. H ..... taFH. A .. .31 H . . . . 3 . H nu 4 3 a i H .. . . H H . ...... . H . ... . H 3.-H_._. ...—.4 >.. -HH»H~-4 9 4...- 43-17....- 4 4 4 4 p—o—o ..- -... .43.... -_.. -..- H3... eqll'7.t10(ls ‘93; r} gerivz} “P’Ceigre Ult11493 by .U 3' n‘ “‘3 (4 [x H J C, All JLree zrnqu were carve 0f gruwgu n.0w1 3‘ ‘,\..'. fi-L . .., .. O- Act-2.. .‘lk, Iris (Mama - t: l‘ - -. 3' , . J- ‘\ ~ ". ~‘ ’ tilefl z'I‘;~.u~.; UL) :thJL‘ EJCLC Bqdflticn uri two-chfiha curve .;M‘ t r) I‘I " _ g I» :3 O x 0 \JL) ' 11' b 1 (Ann lrUur, Rinilhwn: ;. (I '\ L‘. b‘ L) 17 ‘C‘ 8 ‘ol " 'IL R”?3 1}" +.‘ t5f‘ Ufil ; VF}- &_L J 1’) ~:( C. ‘- 11b“ ‘ I .D A . W. ‘93 .... 4 .J I -./ ’ fl ._ \ . t,‘ ( k go .‘ \v vc-C \\ I, ‘ l o}: P-" ,i‘.’ ".\ m 'fl I .- t ‘ I }.Jo ‘\ ad L 4 ‘i \‘1 "18 ‘1u 'krbzrfiat‘rwl _:11t5; 21-1 Mfr: 35; O“. Pigle—cycle 1:);g'r‘1tmzzic pza'vasz". s nbolt tne t m. o? CJulfi Jreaks M»T€ me— ur’ . r a “ p ‘1: 'fi‘. . .'LXL ‘n. 31 bus . 1;: .~ByC]j3 L. 3r cvc‘e “" »9»~ 79L=rmi;=7 frag t‘d -4. ‘, , I" ¢-1 . ‘ , <. , I. ‘ a -J- 9.. U” 0 u‘a v .111' u: g.c uirzu u-"l 18")L3'tfl"x)'110 }'; .:->,;" my): til-’3. line . ,. J- -- -, .L:. h ,s-',-», ..-.. neweeulu . CUJIUAn rqunl‘ne vaA V‘. 4 , \ —‘ - “"' +. vv Lhei on :1.b;e—cgole lumpibn¢1c ". v ‘ 1 . -’ I r \"\ ' 5 ‘ l‘r‘ "\“\ 01,011 Cd": H”? '1 la. .1. "... PL”: 5'31 Cr‘tfiu- g: L‘ A A - 3‘ . ’ . . f" .. - ~ Punituvn lixlflafl 1”F7 1941.1, 11d . , '.-. a , ' , ..,,-.‘-., _-. ,1 L",‘ , .. O! ianLHJJJ'Il ' 5.21“} UL. UIH‘.‘ TQCJLL-l iDcviwtiOJF 33 tLé fie>fl\wzl‘tb?0ret1031 n- . . f‘ 4. J- - ' .-- (- v 3 ‘ II V \ . ‘ 7.0 ~mq. .M, $3le 91.18.45. J rw" b, 7% tar) r .513 ‘\ “2‘ L. "’ '" . .1 ‘ - '1. t‘,.:) COrR';;|JU.-' Ui‘_)'f‘. ll I‘r\)0e\:1ff?f: 1‘1- :. ...“, "1:._.. ,. .|. . L‘- T7;~'1€, 11 L «‘Lt)»lrl'~') III 5.410“ FF Mir? ..- "-w , . -‘ ,rf‘ J... Law- -_, - ,‘- 4-. m.:3\>l“°t-0’11 carve MIN pnt‘ *Cu (1‘7-‘;{.11'e.n*"1l,*1 u ’ 1.1-3] 3‘11"} t iJrl LII-lit}: "4:1,“ E;()‘V t“) 1ISJ) ‘j‘EJ'Z‘H‘I *Hrls RrotterP, lain). 1'": g ‘V 'J\AU|‘ TABLE IV LO {Q SMVIPLE COI'LPU ‘.‘.-’1'L‘IUI\J.U4 BRUC 3:38 FUR DERIVING CUURTIS EQUATIONS CASE 35F First cycle y . 153(.70750t - 2¢.87) Percent Predicted Age Score of Max. Isochrons Ecrcent Value Difference 101 115 75.2 M1.68 73.3 112.1 - 2.9 113 132 $6 3 50.17 87.5 133.9 + 1.” 125 1a; 04.1 55.06 04.5 1MH.5 + .6 128 155 60.78 “5 5 146.1 - 8.9 131 155 62.60 06 3 107.3 - 7.7 137 161'. <7 15 (7 3 11:40.3 —1’II.7 141 176 63 ”3 93.2 150.2 -25.3 104 130 72.10 98.5 150.7 -2€.3 ggcond cycle y - 3611.06338t - 115.53) First Cycle Resi- % of Iso- Fred. Age Score Value duwl Max. chrons % Value Error 101 115 112.1 {) —2.‘ 113 132 133 C O +1.9 124 14a 14m.6 17.46 3.0 1.4 +2.0 12g 155 113 1 - 3.9 19.4 20.65 7.8 3.6 -5.3 131 155 107 7 — 7.7 16.0 23.65 15.7 7.2 - .5 137 Jfih NMLB -1ufl7 32.0 jM)23 37x3 17.3 +2.6 141 176 150.2 -25.8 53 1 34.48 52.8 20.3 -1.5 141 150 150.7 —29.3 63.7 37.63 62.“ 20.9 — .0 33 . 4111, . , < 4 4 . 4 4 fl . . J1 1 ..l...Yo.r11oo.. .... .... .1.. A... .... ....1.... ......1... cf‘t .¢;vé.6. 31.. ....11“. ....1?Y¢v.. -o.oo....o .. -... ... .. ..- ... ... .11. . v 1... .?.V. r:-.< v.of .... .... I... ...«Lva... .... .... ..v1u >... a-.- ...1.v o>.v coco 1...v.....Youa. .1.. .t.. ... .. . . .. ... .1“ . 1.1. ...v .... 9|... 1‘ 0 .9111. ‘ . u c c . r s . o . o . . ¢ . o o > < o . 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A . ...: . .. .1 n o. 1.. ..-.v .... .-.. -... .... ... ... .... .... .... w.. 1... .... .... .. .-a. . .... . .... 1.... .1..r.... ... .. ... .. .--.14...1 1 A .... .... ... .... . .. .... .... ..- .... .o.. y. . .... .... .... .... .lO. .... .... 91.. ..l. .. . . .1 ... .... .... .oo .ouV. -1.. .... o... .... ... .1.. .... .... . .... .-.. .... .... .. ... .... .>.. ...L ...1 .117. T1-.. 1... c. ..1 . . ... ... . .. v... ..-. .... .. f... .... . .. .. ... .v.. .... .... .... ...9 .... .. . .. . .... ..s. .... .... 1-.. ...- .-.. . . .. . . .. . -... .... .... ...1 ..Vv... co...A... .. .... . . ..u. .... ...11¢o.. .... 4v.- .. ...... 7... ...o ovr. A..- ...... .9.|1 . 1. 1:7. . .. 07.. ...11 1.. ...- .... 4 1 4 4 J ...v . .71..v. .... .... .... .... .... .... .... .... 9... ....1... ... ... I... .... ... .... ... . . ... ..-.11v . 1.. . .. va..T.... .... . .. .... .... . . ... t ..V.... ...111... ... .... ...d 1.., ... .... .... -... ». .... .... .. . . .. Y... .... ...- .... .11.. .... v... .... . .. v. . . . .... .... .... ... . .. .... ... .... .. . . .... .1.. .... . . .. . 1 .1 . 1 .. . . . .. ..o. ..- .. . .... ... . 1 . . .. . ... . .. . e _. . .. .. . .1. ... . .. . . . ...1 . .. .1 ...L.... . .. . . .. .... .. .. . . .. ... . . . .. .. . l . . . . . . .. . . .. ...11... .. . . . .. . n... .. I ... ,... .. .. . .1 .. ...1 ... , . .... . . .. .n..r.... 1.. a... ...An .. . w 1... r.q..ro... .. .... .1.. ... 1... -.. .... . 71.... . .. . ... 1. 1 ..... .. ..1.«-. . .1... .1.v. ... -... .. .. . .1.. .. .... ... . .. . . . . . .. .1 . . ... .. . , ..-H .. ....fl.... .1. .... ...c ..o. .... . . .. .1.. .11... .. .. . .. . .. .0 . . .. . .. .~..1. .. .... vo... .1.011...1.. . .. .... . . .. . . .. . . . . . . 1.. . ... .. ._ . .o..«?...11.... ...-4 q 1 . . .. . .. 11 . 1. . . . .. . . .. 1 . .r . .. .. . ...1 ..1 . . .... . .... . ...n .. . .... .. .. . . . ... ... . . . .. . ... . . . ..1.. .vv...A.. V1... .. .... .. . w .. .. . . .. .. . .. . . . . . . ...... .. .. V1. 1......... . . .. 1| 0 . . ... ... p. . . . . . .. .. v. . . .. ..Y1 .91. .1 ..11.. .. o.. I... .... . . . . . . . .. . .. . . . .. . ... ... . . . .... . .. 1. .... .. . 11.1 . . .... .... .c. ... . . .. .. .. . 1 . . . . n ... ... .1 ho: .1.; ..M .7... Aw.. ... ..c. 1.. .1. ... . . . .. .... . . ... ... . . .. 1 ... ... 1. 1 . ...- ..n .... .v. ..IooA.11. .. . .. ,. .. .. .. . . .. . 1.. .. . . . . . .. ,.. . .. . 1.. - - ...- . . ..1. .11 .U 1..“ VII ...o .. .. . .... .. .. . . .. . . .... . .. .. . .. . . . .1.. .! ...- . . ..- ...91J .... . 1... 1. .. .. . . .. . .. . .. . .0. . c. .. (w 1 . 4.. . .1. . .... ...1 ...1 1... .. .. .... ... .. . . . .1 y. . . ... .. .. . O .... .. .. +¢A11..-1. ...- ..-. ... .. A. .. . v1 . . ..v . . . . . .. Q” . . . . 3.1.v‘ .715‘1 .1... ... ..-. ‘.‘ 4 ....IA» u. . 1. . .. 1.. ...4... . .. u . .. . . . . .. ... . . . I . .. L., ..V.L....+'..1 ... II. V.. . a... . . y ...I o . .1 c | n .o .. o v .0.» D . 1 V5 . u'l1 I l I U . 0 1 n1... T... 11........ . .. v- .... r .. .1.. .. . ... y... . . .. .... .1... - . .. - ..1v.‘. I1. 1... .... ..-. .. D 4 T51.-. 11!... . . .. . .... ... . . .. . . ... .. .. . .. . .., .. . .... ... . .. 1.. I ....10........«‘. .... . . .. . . . ... . ... .. ... ..., .. .1 ... . .\2U .. ...o.. .. . ....”1... 1 V 11 I T ”1h 1 111 4 . 7.111111: 0 . 4 . . 1 . . . . . . . I . . . 7 . . . . . . . . . . . . . . . . . . . .. V .1 A1. . . . . - .. . 1 ..Y. . . . 11.1-...nv .... ...- .... . . . . /./. . . . . . . ., . ..IA K ......... ....4.... v . pt.‘ .... .v . . . . .. .. . .. . .... . . .... ...Q. .I. ..Avl... . .. .. ' ... .I? r {104 q T1... :Yvfi1.-1. . .. .... .. . .. ..~ 1 .. . . . . ,. .... .fl-.J .... .... .mul .... .1....L. .1.. ..11 v.... .v. ... .... . . 1 .... . . .. .L . 1.. . . .. . ..., v . ...- . I... .... ..'.A.. . . ...I .- ... ... .. , . . ... . .. ... . .... .. .1. . . . .. . .. w... ... ..-. .... . .. .... v.0... ..VOAT.... .. .11....11... . . 1. n . . u . 1. .... .. . ... ... ... .1 ...1 . ..‘H’ .. 4...11.... .... v .u ‘1 41 .....1...,. .. .. . . . . . . . .... .. .. . ,T‘ .... . .... . 1. . ....11.. . .. . .. .. . .. . . . . -- ., . . ’.. .. . . . . . ...»-.... 1...1..1..-......1..,. . . . . . . .. .1.. , . y . . . .... .. . . . 01p ..1 ..1.T.Jr‘ .11. .... .... ... . . . . . . .. . .. . , .. . . . .. ., 1 .. . .11 .. . . .a ....... . 1-.. ... . ,. . . . . . . . ... . . .. ”.93 . . . .. . ......1Y.... .....-.. ... . . .. ,. . . . .. . . . .. , . .. . . . . . . ...» .11... .... V b 0 ‘ N A .. o -... .. . . .. . . .. .. .. . . .. . . ... . 1 . . . .. 1 . ... .... . .... u. . . .1 .. . . . . . . . , . .. .. .1. . ... ‘.... .... ... .. . P . . . . .. .1.. .. . . . . . . . ...v .«u a... .. . .a . 1 Yea. . Qt...c9_v..4-...010 .o. . . .. .. .... . . . .... .. .... ..1 ...A ,.... ... . . . -... ..-. ... .... . 1 1 A a u i . o o v A o 9 . n n u 1 a . ~ . r 1 n o . L c t 9 . o . . . . ¢ . v o 1 ~ | w a 1 u v .1 '1 1' .. ‘1 ,. .. . v 1 a . ~ . v 1 t . a 9 . . . - - . o . v 1 a ¢ . 1 o . . ‘ 1 1 7 . v . . . . n . . . 1. r 1 1 . r . 1 1 . o . . . 1 I . . 9 c . . . 1 . . 11m- I1 4 4 .. ... i . , ‘. fi —. . . .. w- w. .. . .. — . 1... 1 .- ....t .... r111: .... .1.. v. . I..| .. 41.- 1.. .. ... ...H .. ...- ..h. . -. ... .. .. . - . .. . .... . .. .-. .1 o .... v...1.1... .... . ... ... . . . ..1 ... w 1 A. .V ..v .. 1 . 11.. b. .. . .1 up |.OG .... .. 9.1IT‘... ‘. ‘ 9' '0‘. '16 1.6 . .. ..111 . . ... .... . -. ... .. . .l. ..... . .. n. . ....11.. . . .1 1 ¢...1V¢.. oat .... .v....1...‘..- u»...v4¢. ... f.1. ... Y‘ 2 *c’ ‘l‘ . . p. I ' ‘1’ v - " ‘ \ ' ,. ‘ " r‘ ' ror each case tn— 1Ver1Qe webiltlui in mout.c 0, pr? theoretical description of rental grouta from the wctiil ‘ 1 1 1 ‘v‘ . ‘ u ' " l“ A ~' .‘ ‘1 a a - ‘r- I - ‘ .‘ teasqrements oi .inx.th .eriveu Irom tzr .rn1vii tes ?ou11. This Rifference was called the averwue error. Sten- fixrd fievictiwns were comrwtefi for each error 319tribxti:n 1n3 tvrtt a? sibnlfiu1nee were run comparing the errors ob- tained from each of the three methods. Average errors for each of the three methods were then grouped into ten-month intervals in >rder to show the average error for the different methods at lifferent chrono— 0) Cf logical ages. Te s 0f significance were run to see in which ten-month interval the errors were statistically different from the mean error for e1ch method. Five cases were selected 1t random, and the theoretical line of growth for each of the three methods was compared with the actual measurements. Judgements were made concerning the dynamics of the growth pattern found through this proce- dure. CHKPTEH IV ANALYSIS U? D131 The one hindred cases used for this study were adminis— tered a totil of 878 mentel tests. The mdjor ruroose was to find which of the three methods used wonld most accnretely fit the sctual test scores obteined. Tible V shows the average error oni the standard deviation for the Conrtis multi—cycle equations, for Helnis equations, and for equa- tions derived by using tne teen 1.1. as tte rate of mental growth. The average deviation from tne wctusl mentsl test scores was 4.7 months using multi—cycle equotions, 7.4 months using Heinis equetions, 1nd 3.2 months usinm the ween I.Q. as rote. A test of the significnnce of the difference of means, stowed thet the error obtained for multi-cycle eqzn- tions was lower, qt the one percent level of confidence, then the error for the other two methods. The difference between the error obtained from Heinis equwtions wss not signifiantly different from the error obtained by using mean I.Q. es rate. Figures 4, 5, and 6 show the frequency distribution (If the errors obtained for the one hundred cases by each of the three methods of describing mental growth. Since s general look at the date obteined from the turree methods of descrioing growth showed that mdlti-cycle SPCNvth equations had described the date most closely, further Fmalysis was undertaken to see if there was any psrticuldr ETCthh period when errors from the three methods used were TABLE V AVERAGE ERRQRS HULTI-CYCLE 134API“HS, EEIJIS E: E3 AJD SJAJDAED DGVIAIIUHS ..1. T 1.1 Ufi T" NIT " “*5/‘1‘TC‘ :1-5. 1‘ LLK’Jvh) , Method Average Error Standard Daviqtinn 4.7 months 7-4 8.2 Multi—oycle equwtio 1 months2 Helnis eqaations 3 monthsv I.Q. —_._. equations 1 Significantly lower "" fit til-3 be] S me 0d 0 '1 (\r, ‘. \J 2 Signif t ifiXlS . la 3 SignifiCfifltly than average error owe percent level of con? .utly hiflher than malt: not sixnlficantly ilffcrent frgu dawn error from I.Q. of othar two idence. but .3'1’ ~ .. ””43 -cycl° FPFHP, H ghar tnwn mean srror of multl—cycle eaaations, but not significfintly fiifferent frgm main arror of H91118 equations. in greatest. Figure 7 shows the mein error of each of the three methods daring ten-month intervals from 60 months through 190 months. A study of this figure shows that multi— cycle equations best describe the data during each ten-month period except for the period from 60 to 00 months, when I.Q. was the best indicator by a margin of .2 of n month, a sta— tistically insignificant difference. More imoortnnt is the pattern of average errors of the Heinis equotion and of meqn I.Q.'s. It may be noted that the mean error for the Heinis equntion increases ench ten— month period from 130 through 180 months. fable VI shows the mean error of each 0’ the three methods dnring ten-month intervals from 60.5 to 200 months, as well as the number of measures wittin each ten—month period. Statistical analysis was made to determine dnring what time oeriods th=re mi ht be significant deviations from the mean error over all time periods for each of the methods used. For the mnlti-cycle method, the menn error of 7.0 months obtained between 80.5 and 90 months wds signifioontly higher than the mean error of 4.7 months obtained for multi-oylce equations ising all the measures. Also, the error Obtained on the malti—cycle method between 180.5 and 190 months of 2.3 montns Hos significantly lower than tre over-ell error of 4.7 months. For Courtis multi-cycle equations, no other ten—month period showed an wverage error significantly dif- ferent from the over—all average error. There is nothing intrinsic in the date which can TABLE VI CUI‘ilr‘AHISUA HF 33310113 19011 I‘lULTI-CYCLE 131111.911‘10328, HEINIS EQUATIONS, AND I.Q,. EQUA‘BIUI‘iS DU R I i Ur '1‘1‘31'1— MON TH FROM 31.41“! [AOL-.7 INTERVAL-S ‘i‘iiS TU 'fi‘JU—HUNDRED 1101158528 ”-0 Age Range Number of henn Error Mean Error than Error in Months Measures hulti-cyclo Heinis. I.Q. 60.5- 70 9 2.5 5.8 6.3 70.5- 60 18 3.6 6.3 10.0 50.5- 90 21 2.9 6.3- 7-7 90.5—100 £9 4.0 4.6 5.3 100.5-110 41 3.0 4.7 5.8 110.5-120 52 “.0 7.1 6.5 120.5-130 92 5.3 6.0 6.8 130.5-1NO 110 u_g 6.1 6.8 luO.5-15O 125 4., 7.0 7,0 150.E~150 151 4.6 5.5 5.6 160.5-170 117 5.5 10.3 0.7 170.5—180 86 5.7 12.3 18.6 180.5—190 20 2.3 17.8 1H.5 190.5-200 3 .7 15.0 15.5 explain the relatively high error for multi-cycle equwtions during the period from 60.5 to 90 months. A possible factor might be tie Kuhlmnnn-Anderson test series itself. A study of tne over—lapping test booklets will show that the first and second crude booklets are lerysly concerned with non- rending; tusks. However, by the third mr'fle, the FQ‘Ill'lé, skill becomes mach wore of a fdctor in determining the test score. Pius, 1 child who starts late in beginning to read, might show considerable test fluctuuticn during this period. Greenshields} in studying the relati;nshin between consistent I.Q.'s, decreasing I.Q.'s, and reading scores, conclided that individuuls' inability to soore on the verbal subtests of the Kihlmnnn-Anderson at the SQWD level at which they scored on the non-verbal subtests resulted in a drob of their 1.4. soures. An explunqtion for the significuntly low error found in multi-cycle equations from 160.5 to 190 months muy come from the flexibility found in the Courtis technique. Between the ages of fifteen wad sixteen there is mlch individual difference in flatterns of mental growtt. Some individuals hqve slrewfiy leveled off and fire making very little gain, while others are nroceeding at u rwoid rate which may extend for several more years. Of tie three methods used, only the COJPtlS techniq1e can tuke into account these individual 1 C. h. Greenshields, "The deletionshib Between Con- sistent I.Q. Scores, Decreasinm 1.1. Scores, and Reading Scores Combured on d Deve10bmsntul Basis," Unbiblished master's Thesis (East Lensium, hicniyun: hichigun St te University, 1055) 1 mi differences. Especially in cases where the individual has clearly begun to level off in his mental growti, the indi- vidual's theoretical growth curve will come very close to the final actual mental growth score. The mean error of the heinis equations of 10.3 months from 160.5 to 170 months, of 12.3 from 170.5 to 180 months, and of 17.8 months from 180.5 to 190 months were all sig- nificantly higher, at the five oer cent level of confidence, than the over-all mean error for the Heinis equations of 7.u 1 month. It may as noted that the average error for the Heinis SqdetIOQS increases from 130.5 through 190 months. The errors obtained by using mean 1.0. as rate resemble the error pattern obtained from Heinis equstions in showing an upward trend after 130 months. However, in using 1.1. as rate, only the errors of 18.5 months from 170.5 to 180 months, and 14.5 from 180.5 to 190 months are significantly Cf different a the five per cent level from the over-all error of 5.2 months. Figure 5 shows the distrihition >f the range of the I..g.'s for the. h .12"fil""7‘~" coses used. The mean range of I.:{. was 18.h I.u. points. A detailed summary of the data can be found in Apnea— dix A. Courtis first and and second cycle equations end the mean error for each ones are rresented. Also u sammery of CHeinis equations includes the high Personal Constant ratio, the low Personal Constant rstiO, the range of the ratios, the medn Personal Constant, and the mean error for each case. h.) The summarnr'ltt€1”’l wofld seen to timbre the concept 0f 11 (Scnnfiriit 1.5 difficmlt to defend. Case 23M is Wfl exwmple o? 1 boy shoviir on errvtic tern. He was given a totdl o? ten intellirence tests .1. “qq C31 tires CMMTISlOflS his rvartal one felJ.1Melow the n \D ntwl ()0 ‘fi3¥ (Dotwined on tie Frevious testin"r Children showinfi SIGN '3 ... . ‘ o w ' *1 ”lrflilalxrirwtterns vuiibi seen tC>rN?;fUOl s nyects fnr"l tire \I Hot .L V] P“? '1' . v ' e iTCG work. In 23h it Cdn be seen that the Heinis eqa tion used u not b lwnce the errors ddove and below the theoretiuwl of growth. A stxd; of the Hentql Growth Units used in '9 LPersonil Constmnt s ous thdt in do erratic pattern, low (Jress wt in early age will iufluence tte mean more than low 3+3es at u later use. To illustrlte soecificnlly, if an n? ividnsl hws :1 mental. of‘ five 'dt =1 Ci.I‘<)"’21)1C).."710-’11Hg“ ~"ix years, the rwtio in mental growth units is 254/228, ‘3 I.C. of .3900. If the Same individlnl “is n mentdl age ten at 11 ca.ronolc,§:,icnl 215:9. of twelve years, the ratio ’ v- au-b“inL‘ ~ 9 9} T T“ Q‘- ’ E I owe. ‘ FL ‘ . . V . . ~ . . . . . . _ . . . . . . . . . . . . . . . . . . . . , . . . y . . V . . o . . . . . . . . . , . . . . . . . . . . . . . , . i . . . . . . . . . . . , . n . . . . . . . , . o . v , . , . . . v . . . . . - . . . . , . . . . v . . . . . . . . . . . . . . . _ . . . a . . . . . . . y . . . . . . 4 i . . . . . V . . . . . i . . . . . . . . . . . . . . . . . . i . . . . . . . ‘ . . . . . . . . . . , . i . . t t . . . . i . . . . . . . . . 4 , . . . . . . S. L. t; n 5‘. -14.... I . ll 1"!!qu ii 2-45.15.55.— ,‘ll 4% Elflol II.“ \2 p ..II..I..NI¢OU.. .n . .5 4 woobi be :358/333, or a P.C. of .9302. TH:us, in tus Heinis Personal Constqnt, if the ratio oetweezi nentfil uni chronological age is lsss th1 one, and coast 1r1t , ta? FhCI.‘Hill imuyruass vdnjv-aga. If the IV1tiO betws:=r1 ..sntnl qnl chronological age is nors than on: out rsnniris constant, P.C. will decrstse with age. xklthoqgt lsss cleir-cut than in 1F, 23H olso shows n Chqnfif* in rats from the first to the ssc»nd oyols, It mqy ...: F >8 fi¢>“eed thit tbs mean 1.4. for tin first dive nsnsnrss of 13 ‘- - - ‘ v ‘4 v r‘ - 9 ~ ’ . 1~v93¥12L_sncs sVPrngs J7, nhils tbs {verdgs »? the lwst five I.;."§ 8 "vii . H. The graph of the line described by the mesa I.w. com- 7Yh39fi. with tis notisl isdsarss also shows more deviation above toe ]_ine than below the line, although the difference is much less than on tin“- sir-{p}: of tns Personal COI.'1f§t'1(.lt. In the Urocfiriure of averaging I.Q.'s, 13 in nvsrafiinfi P3P503dl Con— Starltés, soures at an early axe may be given a slightly heavier u, in terms of number of months deviation from the main For example, if in individadl had an 1.4. of 90 it “ JVEHrs J: age and an I.w. of 110 wt twslva years of qgs, uuean I.%. would bs 100. Howsvsr, n grnhh of tne actual ...-Jr‘s: : fi ., 0 1 , ’. .1 . . 1”arse: dguiist the mean line UOJlfi su»u 1H error of seven $10 1 t IL .57 -S oslow 34? noon line at six years 1nd Fourtssn ”ontt QDOV‘t the msnn line at twelve vsqrs. Note ttdt in tts ex— givsn, ttP amount of srror per unit tit:n is sqnwlly L'led uUM)ve 'uri belumz his nssu1 line. 7 Case 32? shows rabid montwl growth daring the first f1 .lw'MH‘VIHmJWiMh *1“; .u .. u -..L. In-n Fun... + .... 'I. I. M “‘51! '3 i9“. , . . v a 5’3 cycle, but in early sscond cycle maximum which the Coxrtis . c . o 7 (a 1 I vq1-, i “q: . WjYHAC‘ f- ‘ ,’ mél‘la ee(_1._,1..1tion predicts to be (m. in s C re, ”terms a ..., o ccnistiant I.&. ttnn do most of the cases, since on the nine tesst:s administers}, the high I.Q. was 113 enfl the low I.= w’qs 102. However, attention shoxld be yiven to tte toqr «ventral --.,~;:e sc' res FiClllf‘v'ef‘l beta-men 11+va wonths of rage 'mcl 157 , l ' / ‘ , ' morltskms. Tnese scores were 152 mOUtLS, lol mOfltLS, 160 Months, ..M. "mi-n“ - . fflvi 113 months. Duns, on four tegts COVgpiqy , pgriofi fin more *‘Eiim :2 year, ‘il!’;Q:‘:t no "l”.‘fltill .{f'lizi was ~ 0 O O W g to LI‘t219 equation for this case indicates a "econr cycle maxi— . nuns cxf 175 nontus, which will mein thwt this inflividuil w. | ..h l .4 }._J h: . 8001’! :fifillli-lw 1.1). Case jofi‘lnus two HMHHJal age scores winjfliifiall below - Escores 3f greceding tests, although the COlPtlS equation 18 ‘1k319 to fisscribe the rest of the growtt fattern very aCOzll”fit€lI. The C01rtis egnwtion fiescrihes the first cycle ‘8 .Ewelativelv slow, with w very rnnii seconi cycle. 01 both dse iieiqis equation an} the 1.4. etnwtion, the error is b“]¥3?10e& filmost e;islly above find below the line. Agein, ‘ <3tinnge in rote is ooafirmpfl by the average Uf-the first 0 ‘1V‘3 II.Q.'s which averwfie 11M cooofirvd with the lost I.Q.'s w' ' " n 1C ‘] vI'EVJLDP'v-15;H 132 o 53 P1 some sitqwtion is *veq more flrnstically ill~strnte8 -,‘u,'i case n tiny stows shirextremely Iwnrvl second . L-Le 1.1. 1""z'l);.‘? for 13:31.0 c'ftse is 35 roints, e'r'i there is -. , k ‘ZLS?)‘eiiLle_rnnge in tpe Personal C>nstants obtained on “iifferent tests. As before, the change in rote is shown 60 l f. 1.31...." .. .4: .. 4. --. -. .14.-..”4 .. 1:34..” . q . .__ 4 f 2.4.7“. H H . 1- S; 4 - . 4:71.144 .4. . ..NWH .. Mm“ g...” ... . .429 4 e .4. 114 4 . 11- . .114 - .. . q .T... -. - . 8.. .... 1. . . H 4 . .- .. . ..L .. . . . .. .. - .. . 4 4 . . 4 .44: :4 .74.\ 114 ... H 4, 4. .3. r3 4. W 4. 11-11-.“ 1... -..-f4 4. . 4 . / . .. . .- .... . . e P tl.1| .II.. '11 I 1 1H 4 41.. . 4 1 - ,4-.1-.x-. . 1 . 314-3- 1111+-24 1.1: Ta!-.1111--Tn4111111...1-t1..--21.111 In . . fl 4 4 l.- 1. .4 WI.- .. .A :- _. 4. 4 . 94....» .1. . . .. . 4 4 , , H ., 4 4 4 - . ..l-i 4. 1 . 4 H 4 _ -_ I 4 z .- 4 4 ,4 4 lfio 4 4 4 4 4 .4 . H . . .1:-1-1L1-1- . -llr; 13:1;1f- :---1 . T ltd-ix- 1-11 -1. .--1. 1. I .11l4s1-pf1- -. ..-1 l /._ 4 ... U 4 4 4. 1.. 4n” 44 4 4 . . . 4 4. 4 4 x, 4 w H 4 _ 4 n .3 Mn 4 n1. 4%. 4 F .41111l-1-r-2-111L . . . _ . y a h b‘l‘l‘il .1 .. I. - . c. 4 1 1 H r. 4 11111.11- 4 . _ H O z. 4 _ ...1 . . 4. . . H 4 4 . / . t. 4 _ . .14.... (J. . 4 .... N. 4 . . 4 . 4 n H v..- _-.x- . .. . 4 1 t _- iii-1* . 4 -. -24«um-«Wigiif .. 1 - - 1 - . .1 ..1 111.“. I #1.“ a. 1. H - I 4 ... 4 4 4 4 e 1 l 3 4 M1... Ru 4 4 4 4. .- 4 :1? -. . . H 4 m mm P 0 T. 4 , 4 L .1 . . m ,r. -. 41 1 J. QM 1.1.. 4. . ... 4 .. .. 4 4 4 4 f -; _ 4. 4 e to 4r 4 4 I WWW 4 _ H 4 .4 4 . 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T. 1.4 0.‘ ... .m u 1.109. ?£.t .& ‘ 1 . . 1 . . o . . 1 . . ¢ . v . . . on 1111' n» . l.‘ n... .1.0+ .. 1.1 4.. o W 0 v6 0 ... 0‘. .y.. .. n. .. .. ..- .v .. .. t 11.1. .. 9.1. o .- -. . .0. v 0‘ w o. .. . f4. . a . ... ... do >.. 1.. . . . . o . ... r. .- ... 0‘ .V #11. ...t .‘ . . 1.1a ... § ... co. . b C. 9.0. v c c o 3 4 o o ‘ V . o o . . . . . . o. . t . . 4v 0 o . . ... . o .0 1 - . . . . . u u . y y . a q . . c . . u 61 . u . c . . . . v o $ ... .11 1.. ..o .1. 0v 91+.» -11. ¢A§ 01 .v 49?. 4 o p .... Orb ... 4 . 1 ...... . . . . . . ....- a . r . . 11. 1 . .... .. .1. . . .- ‘A t O .04 Av. 01?.- .q-o .o. .. .¢.¢ 0... -‘Il . ..o. ....1 ...; .... 1... .1.. .o .-.. . .... .1 ... .... ... ... .... ... ....1 .. .... 111. ... o... ... ...o .... . .. .... .... .-.. 111... .11.. .1. 111. ..1 11. ...9 ...v ... . .t .1. ..y. ... 1... .1.. .1 .... .... . . .... . .... . .. .. .... .. .-. .. .. - .. . .. .... .1.. .... .... .. . . .- ... .. .. .‘u. 1.. .oo.. .... ,1... 4 1.1 ... . . . 4 1 . .+. ..1 . .9; 1 r .... .. a- .... o... o... ... . 71¢ 634 .... 4 .... $1.10 .... .A . .... ... ..6 -o o . . . . . . . . . . . . . . g . . o v . i 1 l . . . . ..1 ... . . v 1. ckl’ o o .. ~§v u 1.? . .61.. ..A. b) . 14.4. ... ... .... ... . . O 1 . . . o u . . ¢ . . I A . . . . . .?9 Of. 1..» o. .. ... ...1 ..v v ..4. .34 v9.0 C‘.‘ 1. 99¢ .11 .- . § . n . . . . 1 v 1 1 1o. .1.- . o ... 0 .4 o . Q‘.’ + n . . o *¢ . 1 . . . . . a 01$ 1 . Y. . . u . o v c . * . n . Voco 1 . . . . u n 1 . . . o . . . 1 p o 1 . . v u . 3 9. . ... q a v . c. . o o . . . ... . l5 . < ...... . b . V Jr1 v . . : 1 VI. .... 9O 4 0.. ‘.~ I... <.o .t 11. .. . . Y. ... r.- n 1 VI». .oo .1. oi. 1.4 ?v 1?. 70. ’1 ... 5.:- Jpn. T..1. 96 0.1- v. 4., 'n .1.- .1 ..k. 9 . V 94 $11.. 04‘ .... 09+ 1.. -#o o 01.1 .1.. If. 1.. .... v1.1 .-. 1... .... .1.. .... .1 411 .... .1.. 11. ... .. ‘1'. ...vv . o O r... .0.- - 1. 0.... 4. . 1!. ... ts. c? ...-... ...O ...1 o .406 .1.. . ..1. .... .+ . 1 . Q1. 1 I. ... ... £10 .1 v. 0.1.. v. .0 in 9Q ... '.. '. 9.‘ ... .V‘ .3. t'n .1 I. . v A. utl .... I .7. 6.91. . u 0 o . . » . . P9. 1.1: ...v .1 50. ¢.‘ 1:1. ..1 n. .o t ’0. 0 c. {v.. O... 9 0.0 Q.1.§ ...) A399.‘ 00 .o.. co... .a 11. J. Vt to . o o u a 1 .5 1 VI. 114. T 9 a 1 o 1.1. 121 o 4 1 . 1 1 1 . 1 $ 1 1 1 1 1 1 1 . 1 w . 1 1 4 1 . 1 1 1 o 1 . 1 9 . . 1 1 1 1 1 . 1 1 1 o .0 o 1 .1 10 1o ...! 1.0 11 ‘1‘. 0. 1,017 10.9 111 LA 1 1 O 1 0 1 1 1 1 ).1 1 1 . 1 1 1 1 .1. .1. 100 0 I11 111 .1411 0. . o .1 O OI 111 ?.r1111 "§ 1 1.... >111 6.11. . 1 1 es ‘bYtne wean I.Q.'n for th; |ir9t foar tésts which average 108 3 waile the wverqu I.q. for tte lfiSt three tests jumvs A“. r_- rm ILF l‘fiflmun all "-3 CED Z I 131}. V CONCLUSIONS AND IMPLICKTIONS FOR FURTHER RESEAQCH ONCL IS I 0'31 S C} I. Two major oonolisio s are apparent from the wholysis cm"the data: (1) multi—cyole equtions derived by using the CRDHI’ClS taobniqie were significantly suoarior to tha other tz-z. r*152tl.<_)sls of‘ describing; ”12:11:71.1xjr'swtl'u; «fl, (2) the error dEI‘ifiled by using the mean Parsonwl Constint ns rate and by \AS 1 11 ' {__, meqq I.Q. as rwto showed 1 s rni?icwfit increase at 'K these two outcom s mwy 3e fl) E7) C ; ‘) “‘3 C. ’1 Oldffl‘ a“? lévels. Bhe r.' foixafl in the fun: that milti-cycle oqlatioqs hi7? 1 iifferéat affix rnore accurate theoretical basis than the theor/ underlying the JP9rconwl Constant or tLo Intelligence Quotient. Both tho Moiqis Persoqwl Coast at find to: Intelligence Quotilent are bnsoi on thase two qss1mptlons: (1) that thare is ‘1 fline of normal mantql ”rowth which can fiesoribe the averakjg person from. birth to n:i1t~.1r-ity; 'mrl, (2) that #1 (jivpn indeV’iduql's mental growth awn be test describe} by 1 ratio 0 ' . l v a 1 f ' 1.3 mentql :rowtn to toe line CI av;r1:e mrowtn. A multi-Cycle conoewt, on the OtIRP hnnl, implies th‘it , , 1 .. , c .. 1 .6» .. ‘ . 'm 1111 ivrl..1'11 s: _?.I‘i)".‘«'tl] cannot on. dPSCI'lDI‘3'1 :33! any 0:19 11"}; fl “ ? or carva :rom birth to notarity, nnfl that the indiv1dual's h .va: ‘ , , tférn will Change at flifferent growth stwg:s. Sinoa tnis 1)‘1t ‘ V o "\ 14“ra of connge may ilflor in 987¢rwl ways in terms of ? “56} . . ‘ . . ' czlifio indiVdefll, tuan an ratio optw92n a limo of wverages q. “(1 1“ v1 line derived for an individual qu truly fissoribe growth. c7 While the Psrsonal Constwnt cnl the Intelligence Quotie‘nt consiier rats as the only variable in the mental {mouth of individuals, the multi-cycle theory consiicrs two m”@r parameters of growth. One of these is incipiency or Stfirting noint. While the I.Q. anl ths P.C. nssgme thwt grwnvth stwrts from zero and proceeds it w coastwat rats, the rnlltsi-cycls concspt ussumss tnit rate may CHQng in a new f_fi?“‘ csnslug and that one factor in plotting this new cycle will be thee incipiency. Thus, 3 child who grows rqoidly flaring the II fir~siz 0v 3: may Fave a high starting point misc he enters a y 03%; :zycls. If his Pit? slows down in ths new cycle then he Willi Show a filling I.Q. Stifiec of physical growth tivc shown the possibility Of' a chls brssk whint the time tint most chilireq enter SChCDOl. Since Host stidiss bqsnfi on longituniqal data stwrt rFt~3¢ the Chi‘fl is ilrssfly in school, thsn the initicl score Obtgiismsi for the child may be bassd on 1 Giffsrent starting boiflt in terms of tbs growth pattern is will follow for the ”53t7 fsu yewrs than 79rd. 3 tVTfPC l/lto C(nnrirsrrytinn ~ Aqottcr chtc by the COirtis ". C . ~ C s 9 -\ ' . ‘h '. I ’ h [1 1mg 15‘: t‘. -=3 {T121 1:'::i:;1 LL; :‘LlC'u 131:? 133 i\’ 151 1.1711 iS BrOWj-‘lé’f' child with a low rots 1nd 1 low incipiency may reach U T '0 all {All Tiltii'gdlli} })I'O'v'i(lz¥e-‘i {E f;;ll;1t‘11ns his raltp for. fl 1011;; igh 'erion of time. On the otiwr band, a chili with A ¢-~ rwte, NEH/‘¥?_jflild toward a lxnirmixinnm, whictaiKEtvill 3. i u-. 1 ’ v ‘ét- in a start Mario} 01 time. By cocsiflering the tnrce o‘«\ -. 0'0 -: A n . , ,- -.r , 1‘ . - ~ . 2r-,:rg ale t‘-\ooar%31s StylltlA)fl--T‘ftr, iicigvisruxg, :uid W;- ..3 -q:'-_g-—r ~“rim“111121], it 1:: Op 1'1 tr . OWth pattern. 3.13 (it 1‘," a l‘lCI‘E‘lSlllé: Io‘ao “S C possible to exvlein a f' Tn a nntnril function oi on Consideration should be given to the fact allin“ I.Q. ‘(J inlividuel's that data I‘ Q q . O 0 ' b’eed on firolp stanonrdized tests, Sicn as tne data wnicn to lye free from errors. scores ictnnll {Titsi no theoretic-ll :"rz-meI-Iork What) sswch q sitlstion occnred, ony of the methods iesnieioe the finttrrn mo 1% show error, althszqt t 18 '11Jnost certainl Since the Heinis 3 - _£scz‘lb1mgawntwl “.‘ v'. :T‘- W I'. :5. v obharents thit hulfllS aSe .L.’ Li. utzflil bus? I. ':l l V"- I‘ P “"- ig‘J‘BS 01 bills 'u: »firowth pattern—-a bittern in which cnmned.the raw material for this stqdy, cannot be For the oxrposs of this expected 1— ‘.. stsidgr, .,Le ' T#-" , 47‘ ‘- mi- . .g o nxaiaed ;.r01 TJ~3 thrbR P119 ccri- Lfi‘lelt‘l *rortn. tviicn can assimilate'nn H"tel age scores ootiihefl A ,. ,- .L‘. ‘igrd‘c. Lu; , 3.;18'1r'53 Personal 5' if? one ALT-1‘51. , A . ~ ~‘-‘ a , o ‘ ‘ ¢-'-, ‘0 son: a: the 73JJQJ1gCS r may be consilerei. One scores no? 77 L? nowsver, there is erratic men— ievel at W eerlisr. wsei to ! Cunstnnt was found in this as slinI’Jtlj-r more "1CCIT'1N'3'? thnzi the mean In. in 1nd disni- of th? s in wivoonting thQ Personal Constnnt g. is bisel.cm1 his coinion tint lNF? I.Q. "ifg ixflnueen infiivifihrils is twuv lnrge. ‘3? Ioints <)rt that Y ‘g‘M-‘L vs a. , . L‘\3L;«b rln’f of n laree “15 be onlf twenty i- ggru)nj; o1 lobes, w ile the I.Q. re ‘“3 fflryuyrwt/ he eifihty or tore “Oidtfi- It 33 tile - I9snnenre1 Constants :fi‘ragnnvy) nf infliviflnfils Adults selectefi it ran— :39 For the trae that will Show :11 1 ' “(3h smaller range nnu‘zericnlly tnrm wonlfl I.Q.'s flerived he true error upw- '6‘ rom the same tests, Exit it mist be refierflrnwyi thit the range (:)"‘ a a , I 133/ Sgrigs .3; rnquglreflozlts nauericnlly is 'l ILTOdllCt '31 t1“? #3 Q. It of {nee‘aszzrenaent 1189:”? nngs of ndnlt height, for ex- qmgl ‘ e, could be more hnn doubled numerically simply by using Oflfltimete's rather than inches is the znit Of measure. The Personal Constant can he consiflerefl to be 1 rs— Tirrefifient over the 1.1. in tLe sense that it actually nttemrts to Flesscribe o curve of mental nrowth which is assumefl to be I "‘ 'A ' v~ -\ . c ,. “ ' ‘ ' ' . ~ I \ ‘ . t5? ‘Fvattsrn which n~ntil grouty ‘rtnelly follows. AlVOCfitPS k ‘. D . . ‘ ‘ . w , . l". , . ‘- T .‘\ ‘ . J‘ y - - R I r , ’- - .~ ‘ 4 - 0n , *0 n * ,O . ' ‘- VL x CCL1:-diu i.%. A}? not r9111; ffbdlflh tha. ,entil firing t3 1 st-ligit line wrocess, hit r ther that in ihiividiil , Will. rrzintnin n no stwit Titld to the vein mentwl “routh A? a _ a ‘ ' - ( ‘ L-‘ . ' 1" ., ’ W1, .Ufl‘on , 1w 1 07—4 th» 1 ~1rt tn .ntt .' o L' zxnnt 3 . ths, Ll amen: thwt qn infiividlul wctuilly si us mire :mentwl Ixywt! in ter 9 '4 *1 mercentige :n‘izis nfiult CQPfifiiity Letneen zero 131 five years of age thqn he doe. be— the ages oi ten and fifteen years. In terms of 1.1. a ye‘b's mental growth can as ’lefinei as the :werve increment :Fa,’ ‘ .— a '1 ’ v7 0 ‘ ‘ "\ ‘ ‘ 1" 7:13.; .;:1~ yerzflr‘ to the {Ir-PA by {1 large nnnoer of 33.20016 0 *5 m ‘iven fifiP takinj the test. The situation is further Corl‘ ' m33~13845i my at the fact thot the tfisks or test items used ‘1?) early nfie levsl are not the same tnshs or test items :at a liter are. If one nmress that an individnwl mikes 'v ,~_ u?‘ \' J. i _ ‘ ,J..._, - .- ‘-‘-. L‘ ' 7‘ J- .’ ‘ r ' fl . ~ ,‘ Tbewl-t‘% til .iwrwth bet-rr~n the -nges (n Five yeinw; find a u D ‘ Q l i L r, q‘ '-,\ l - " *‘v A Ll‘, ' .v‘ ’\»" 5‘ “$- _- ‘ .,, b’ei : ,hln ne Woes hetleen the 15es -1 liiteei Years wnl } L-‘ , L, . -- . ~ .' 4" CHPW the mentil n,e concsut from nFich the ‘ is derivefi is reelly Colihrotefi 1n Fifferpnt Inits at 70 <\ . *1, v" . - , ...! _- ‘ . .1 ... , ‘1 ,_ 5 ,3 ‘ ' ‘ «ier it uses. nor this rsnsoi, .srufiz firssmfln an» otnsrs (D --‘t‘,. -kl ' v“ ‘ “~' "1‘ L.’ “ T .\. '" V '— l' ,. ' ' Din-,1? for tuz" CunSqva}! of‘ l.~'..., messnt -: snub—c5033 he “iiivsly accelerated curve fls tie t;;s;r=9tic'11 rental growth Q. )‘b ‘V q \ Heiuis, t.:r-;.:t1“n ti??- ..1 a, ..f' piss gruv-"ch mitts: «mi the L) 'r I‘ t! Persn-mril Constxmt, attempts to r-resent the actual "mttsro of Cisntril ztrrn-«Iti‘. In terms m" ‘.-is units of' msntwl y'rr‘m't'u, '1 "u’s‘ 3 ‘3“... ’~ . n" h . :-' \ ‘ «D '. fl ‘ A. r f‘ ¢‘\ y _ r ‘ Q I r L A l ”a /‘\ m 11r1 .rom live to 913, in »;lvr ts miictwiu a riuiv 0. “Us, YW)1113 gain 28 mentil mromth uwits. To maintain the same I / rat 10 from fifteen to sixteen years, he wo 11d sin only o 5'; meat-'11 growth units. The ti.:a:_)ra:t cal f‘r'arauework (’levfélTJgF’fjl by Courtis liff‘srs frcnn that Lfi‘itsinis in that Chxuctis WdVOCitss '1‘liffersnt 10(3T‘1.tkynic <3;ucve sis ctwst (iszxxrf.,izi; ¢;rtwrth, all: tipzt 1»? ft?» “£30555 the malti-cycle concept. ?Le results of this stuly 1‘!“ v: 0 g i . ~. ~ -\ v» ' -«'\’ ~~ L”-1-- 1nd11r1te that inia {:1Lretixwil f1“vm9uorfi. W V int-J '-f {D c é' COLPTSis better renrsssuts h-w growth actually takss yloos. II. IhYLICA?ICNS FOR FUR? if RTSTARCH J ‘ ‘b F ' I’r’ ' o v' .;blfl" sa:g,est rsJVer'fl crusas ia l. The ft Lliflgs of C?” y 0 1:1. 6') :0. ‘s‘ ‘3 r \‘ I " I" '. .~ . 3‘ f1 V -\ .' art wr lassirct is 1d-jcatrd . The results heir to ixvt tLe wxlti—cyclio concept of mental growth in children tbs time of school entrance into .ic aflolsscsnt gsriofi. ”? is ‘Viieane to s! {9st ttfit Another growth ,ynls is V ’ rticg wround birtp an: I L p...‘ C.— H. ..3 } J. I ) --.: ‘ V H. “,JJ 5; r- —J ’J’\ 2’) C. ) I J- .. ' COflhlhulCd fi . . I, H i. , ._ . t- ., - ~ it V *—l. gnoqt ty-~rus% of Six. .1L fiF?SJ'WZ‘tuBPP is JJJJUIQ lon¢i~ (pr F #3 ,4 1111 fintu available for thi. mzs rants which wollfl mnkfi ".1 (4.)" il~ . . “10331219 to check wusrtsr such c301 c:3 , H q ¥;i?ou17, IIES€.UWN in bzlg; arfi‘ TI (1)01 01-28 of Item to Start c:il”““* t:> L1? iI‘st g'frmh “ml how t.) int—’arrrst :2 0h11df;fifl Acct} fig? 0 a“? f'lctor Mick; sigoglr'l Dee ss is ental grow ; iy.t shed lig.t o3 scuooi, Writ to -'_—‘.'v: act ontnl test scores 0? stxiisfi ix2:uy¥ar to :3t 22 31 yrs" Sict2r: oi tbs RC ‘“ Pattern of msitsl "rowth LII—Trimmfi‘ is the aim. of sentgzl "ngc ".8 it is 1“‘°ese'zitl;' :‘le";::s"‘~. ‘13: Itffkairent 25a levels. Since it is now gsnernllv agreed that a V13£1*‘ of mentjl ugwnvth i3311M§ li‘rsrwrt t id%:3riacii?fsrent ChPCHfl<>logicql ages, an attempt should Se made to Firfi on If” instrument or 52 an; of Cir-TCE‘iiJgfi in which the Ul€’i.“€ill‘lil§j sc-ils " 370311"? 9min. construct. 511.4109 voc;_2l):2l'2r3' has. Tiber) Nana”. to COPP€312ts tigtly Witw wistsvcr is moasnred by intelligs2te I'\ J ruf izhe ‘JOC 2li Jumif"r' of indiviziils w02lfl bc fruitful. ale! 3 stawy 00413 ”Old t?” task to be berforuei constant, thus kecning the ”337‘," 0 . v ,v ' ' ; 2.2r212 i.wtr&'“nt Coos fl; turo2gnoit UP? stul . Tbs uiole ares oi growth icter—rslatic sai 5 needs mac": _ 1 , .1 g. a. 1 .0 r) ‘ ilflitiowqi : wdv Millqrq 3 study o; 2“ ctildrsn SIV" i \ ~ ' ‘ U' 953, in gs2¢rxl, tnwt Cwildren wnoss Lr02xtt01rves in Var . . . . 1‘3 18 areas vars coordinated in terns o~ tns timing of two eye 3\ w I . 1.:53 wire jidpeu to Live better social-auctionql adjirtment *1 UL: ifl .V. -...L in ”a ,. ..l.‘ a. . l .1 . i»srP iliren Mud lobertn o2 bro ;« Suowsfl more JiV, 1C3}. -‘ ‘ r7 ‘. "‘ . ' 1 7’. L‘ , A —‘ g. l ." p‘ " r'1. ‘. ‘: ’1; , . EL9IH,, Eli“ pat” '.111x'uufP15k-tJlJMOio, lye fh7lfi. :Cwuuixtion ' r ‘ ' f‘ I. f P 0‘ ant," Lulx fir} as \ A ~ "’ l ‘1'- ." . ' '7 w ,. 1. A '~ '1 ..'-1- A. Eichurn, H. u. '-u€ Jrhuta-uefirolucliln Cycle," urowun, ad: 2b1_gt 19:6 1) g .2 , _ ./C H 0 V- . T ' . ’ 5.51115, ..{0 So ’ " Elle .51 ‘HYS (J J. fifidja," ?srcholqu Bull~’ Al N For-1n, I‘. "bay-y Pull-21‘5“? Review: 9;" tbs Const my 0: tie I1— ligermwa-taotient," (lwtholic {Luivarsit1_;gllhlgrict Eflucwaion Research Bulletin, H, l¥37. Foster, ”1]? r27, "Physiologic:1 Age ~s w quiq ?nr the 014331- ficwtiuu a? Plyils Entering Hlbh 5(h0)l—-R,lwtivz of Pubwsoéncs to Ihight," PsycholqglCfll Clinic, #:83—1, 1930. Friuk, Iwrwmwmwa;i. "The Prob »:::n?Wfi?n§Ju :11}, ‘lhflj. ...- 5min “my" 0 l 77 Freehlich, Gastav, "Mental Development During the Erenfiolescent Periods," Review of Educational Resenrct, lhzbfll-lZ, 1044. “.— Gesell, Arnold, "The Anpraisal of Mental Growth Coreers," Journal 9; Cons11t gg_xsxcholog1, 3:73-Gj1339. Garnett, H. 3., "A Develcnmental fiheory of Intelligence," American Psycholorigt, 1:372-77, lfibé. 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M., "Mental Growth," Journal 9; Aunlied Psychology, 14:517-Bl, ngr Kwtz, Evelyn, "The Constancy of the Stanford—Binet I.Q. From Thflee to Five Years," Journal 9; Psychology, 12:159-81, 19 1. King, Irving, "Physiological Age and School Standing," Psycho- logiqgl Clinic, 7:222—29, 1914. Knezevich, Stephen, "The Constancy of the I.Q. of tteSecondnry School Pupil," Journal 9: Educational Research, 39:50/- 16, 1946. ‘ Krogman, Marion, "Trends in the Study of Physical Growth in Children," Child Develonment, 11, 1940. " A I f". I U Lincoln, Edward A., "A Stidy of Changes in tie Intelligence Quotients of Superior Chiliren," Journal 9: Eiicqtiggll Hegearch, 29:272-75, 1935- 33 Luh, C. W., "Note on the Relwtion Between the Constancy of the I.Q. and the Rst of Fentsl Growth," Journal 9: Genetic Psychology, 36: 185-87 l/L/o Mil-s, C. C. and W. R. hiles, "'[me Correlwtion of Intellirence Scores qnn Cr2ronological l e from Early to Lite nltlrlty," Tie AmoriCin Journal of Psycholo~v ’“z41-73, 1932. 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Olsen, jillqrd and Byron Hughes, "The Concept of Organismic Age," Journal of decstiongl Resenrch,3§:525-27, lCfl O'Neill, H. C. ”Variations in the Intelli» Tenoe Quotient of 105 Childre n," Chili Develggpent, 3:357-63, 1937. Pearl, Raymond and Lowell Reed, ”Skew- ~growth Curves," Pro— ceedings 9: the National Acaiegl g: Sci-nee, ll: 16— 22, 1925. Peterson, Joseph, "The Growth f Intelligence and the Intel— ligence Quotient," The Journll of Edlcntional Psychology, 12:145—5u, 1921. Pintner, Rudolf, ”Intelli; ence and Its Measlremem1 A Sym- posiim, Che Journal of .dlcitional Psxciolqyi , 12:139- 43,1921. I‘m-.2...“ . NH #— 79 Ileithnrd, Suzanne, "Mental Organization and Age Level," Archives 9;,Psychology, 295:5-30, 1944, Piichards, T. W., "Individual Variations in I.Q. and Analysis of Concomitant Factors," Psychological gulletin, 37:442— .UB, l9h0. Iiiley, Gordon, "A Comparison of the P.C. and the I.Q.," Egycholorical Clinician, 18:261-65, 1930. 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Olson, W., Chili DevelQEW‘nt. Boston: D.C. Heath and Comnzwny, lgLC. Pieron, L., La Déveloremeut L,: tel at L'intelliqenoe. quisz Aloan, 1930. Pintaar, Rudolph, Intelligg z:oe Tettiqu. flew Iork: Henry holt and Company, 1931. Stofidqrd; Gaor~p 3,, The leanin' of In.e11ibggtce. New Iork: The 10mfi 11m Comznny, 1551». / Stronhi, ?ntr, An In Mro‘xotiLn to Child Stafll. New York: Pkg Macmillan Comrnny. 1C51o Tkrhddn, L. M., TLe Measurenmnt of Intelligence. Cumrrfige: Houthcn Hifflin Company, 1916. -... . «.Mwlvuu. k .3 82 Thorpe, Louis: P., 3111.37 ‘?‘{_£;i"‘l"l;\f in“. Developmqnfu New York: Ronwlfl Prpcs, 1046. ”931191”? DaVid. Outside 31831101; in Igy'ciology. Mm; York: 'i‘homc., Crowell Company, 1950. C. UNFUBLISHED NANUSC7IPTS DeLong, Arthr R., "The Ecwning of Individawl Scorcs on Gr01” Tarts." Pa“er ~r999.ntod to .hn Notional C 13011 on “tarxrcnncts, Atlantic City, New Jersay, February 18, 1057. ‘ ' x . , ‘1- ......z‘k Johnson, William, "The léfitil hroutr Curve of baconflary 7 School Stidents." Unrublishpd Doctor' the sis, The University of Chicxgo , Cl -H L., Kowitz, Gerald "An Explcr Physic-i]. Growth Pwttorns mentary School Chilfirer. " I'lCth' m at t3 COLL-159, E Kunkle, Faye L., "Growth iui went." Uniiolishad Hzfite 1e59, iist Liusiub, 1%1 ii Lee, Sigirfl, "The 97V°nt o” m Adolesceat thesis, Millard, C. V "An Analysis ' S mance in Smelling." on)uamli Eed Doctor'c thesis, Univer- sity of hicnififin, Ann Armor, .icnivan, 1037. Nally, Thomos P. F. "TM! 7 litionshih Betweon Achievo7 Growth in I eigflxt ’ nd ‘tu=- Begginxiin, or xflr(n'tii in 76 riith." {I1- publisted Doctor's thF9ia, Iichigan Stntp Coll.=g Eqst Lanai w;, hichiqtin, 1953. Kitsch, Reuben 17., "TSPFlal"wt‘1<)ns'rzim Jet: 19 ‘. }1"O'2'1 til 1 “'“1J’Tht qnfl Growth 1% weL rt." annhlisrefl H rt=r' th cs Qir Iiiciigyin Shiite CA) 1° '?ist wauiiig, Iiiccui:;r1, 1051: UflOI'I, ”It: «on (1390300), "Iielfitirmsmic o.” lien-wolf to Achieved Growth in Eeith." Unnuolirlefl Doctor'c thesis, Michigan State University, 110350, D-vslo;.1"t in leight." Universi:y of Lice ‘ ‘ 6 fl . 54st Linaia_ 1023. 113100 Ir‘itf) 13‘er Hal'ition-‘ghip Of 'nfl Classroom B”}1V10P in Ele- Uz11uilirh£d D)ctor'9 thesis, 5 rtrt Lansing, Licuigqn, 105“. E. .rfifiiction ia Acadiag Achieve— r's h‘si., Hichigaq State Col- lf’;'ll’], ICEOQ ~nstruwtion in Relwtion to Unr4blishefl Master's :igm, Ann Arbor, f‘liCi.l{jf’1fl, 193:5. of FWCtOTS Conditioning Perfor- ’- ,, I‘Lic'riig,'i‘:'1, 1‘55. ymtmu H FxJ H 33 m H iii-"JD S73 ,L‘lfl) C ICLC CC7V’TIfS WIZIAl‘IC'ZIS AND MEAN 323033 Average Case First Cycle Equation Second Cycle Equation Error 1F y . 16u(.37411t+3.24) y -.30(.du571-SU.70) 3.5 5M y - 122(.u3667t-8.85) y -‘32(.89813t-lll.28) 3.3 11m y - 1u5(.71036t-27.59) y - u5(1.3205o—1§6.o¢) 5.< 18H y . 17o(. 69550t- 36. 07) y = 28(1.44588—1éo.55) 1.7 19? y - 150(.557g4t-17.33) y = 34(.818 5t-77.53) h.62 19m y - 155(.66727t-27.3o) y = 19.2(.75000t—77.47) ".ou 20m 5 - 180(.53411t-22.54) y = 53(1.54222t-219.33) 2.8 21F y - 155(.49259-11.25) y g u5(.70423-7u.63) 4.3 22F y = 136(.70115-21.63) y . éo(1.11600—113.35) 5.8 23m y a 127(.63953-32.52) y = 33(1.15000t—138.28) .86 24? y - ( 56083-3:.07) y - 52(1.16123—181.74) 7.7 25F y - 165(.35932+1.13) y g 80(.31320t-80.47) 3.0 25% y , lu3.5(.41544—.70) y = 12(.92923-¢1.77) 2.3 26K y - 3(.67166t—34.4f) y = UU(. 85257t 105.82) L.ul 27m y - 164(.3C250t-3.80) y g 50(1.30750—177.90) 2.72 25F y - 147(.‘6l75-53.EO) v = 51(.63100—5o.06) 3.7 231 y - 157(.53973t—1u.co) y a u2(1.M;7ooo-182.57) 2.5 29F y - 183(.60275c-23.15) y = u3(.71333t—79.26) 3.31 30h y - 175(1w12~~t 11.<6 y : 27(.2095ut—1C3.30) 7.2 31? y : 125(.960f5—5u.ou) y = u6(1.63793-52.12) 4.5 }ZF y = 1L3(.531C7t-10. “0) y = 30(.46354t-33.6.) 3.15 339 y = 139(.60083t-32.78) y = 60(.36309—3u.25) r.u 341 y = 169(.7277u—u6.3d) y = 39(1,o¢131t-1u2.11) 4.6 35E 3 = 153(.7 7o75ut- 2C. 75) y = 46(1. 0/388-1115 c ) 2,1 1‘ .'. - A iverw p Cuse First Cycle Eflililfin Seconfi C cl= 71: Jinn Error 36M y = 125(.66960— 35.21) y = u5(.93111t-118.15) 3.84 37F y - 1c3( 42 720t-8.33) y = 50(1.13250—134.07) 7.61 37M 7 = 1u4(. 31152t+5.72) y z 32(1.05391—117.66) 5.43 332 y = 150(.72967t—33.13) y z 55(62320t-60.79) 4.5 now y = l50(.jl780t+ll.30) y ; 80(.41181t-33.l6) 6.2 41? y = 55(.4576§t—5.12) y z 26(1.66714—215.371) 2.57 (1.1: 41M 7 = 160(.34100+9.54) y z 40(.96703—116.25) 4.73 . 422 y - 135 .,o,71.—24.Ji) y - uo(.51320t-52.71) 2.56 7 42m y = 170(.60522t-31.06) y z 60(.70509t—96.36) 4.07 i 432 y = 155(.#2762-?.76) y z 25(.¢r352—112.:7) 3.2 3‘ \. ) PTRSO;1L (1“ \I Mean 1.082“ .9382 1.0361 1.0577 1.0fl5: 1.116 1.0512 1.0094 1.0273 1.0300 1.0668 1.0061 1.0050 1.01203 .9921 K...) Case High low 3505? N900 Error 37F 1.1259 1.0716 .0583 1.095' 10.85 C) 03 UN; 0 ‘ n 0 37M 1.0197 .9567 .0630 .991 333 1.053 1.029 .0050 1.0633 5.2 how 1.065 1.000 .065 1.036 6.57 41F 1.0602 1.0197 .0005 1.0001 6.70 41m 1.0933 1.0187 .0746 1.0053 7.17 “2? .9946 .9095 .0051 .9693 3.8 42m 1.0669 .99M0 .0729 1.0371 J\ o 0 \Y‘k “ 1.0163 .9035 .0328 1.0011 b.83 3 Md 1.0654 1.’Jfl7 .0337 1.053,};f» 3.03 I 1 1 I.» .- 1 \n *1) 1.1050 1.0?78 .ON32 1-08231+ 6-33 4511 1.0563 . 970 .0553 1.0287' 0.53 1 46m 1.0736 1.0107 .0589 .3112r 5. » .usm 1.0101 .9553 .0538 .7955 5.38 #911 1.1345 1.007; ,fjm7 1.0503 13,17 5CXF 1.0736 1.0134_ .0602 1.0567 7.73 501% 1.0156 .5070 .4086 .0297 311,59 5 11‘. .1- . (“79,7 1 o q) r) no 0 ‘37‘ 7 l o 91;?!1 S o 5: O 5233 1.0517 .c502 .0075 1.0171 10.<3 ‘2}; 1 qr " r l (YM'H') Oiflr l n» 1 c ‘u y 1 . ’39,“ o :\&- o / '/ OVV‘O~L _, 0’7 .5419 1.00,; .9093 .0960 .c7u2 3.30 [-C / x , - ,‘ ., L“ 1.03 1‘ .337; .O:9L« l.OO§9 1’).23 .a t. o. .v... O\ N ’1] 9 ..1 Q L.) EL H O V‘ \ A) (,3 “u m H O L-IJ‘ 103E H H N ’J'J ljlfiz 1373 Mean .9917 1.0124 1.1141 1.0152 1. 02.69: 1.1203 1.1403 1.0bih 1.0177 1.0272 / ’1 1K) . D R '2 l: o _-- ,, 7.02 O C.) \1 \ 1) 1.0272 1. 0 ">511 1.9333 r’za -\ r’ y_ o 0 Cf. \_s.) \C‘ ch (.13 (‘3 .05121 ’14,:- o O :1 o 0111‘.“ . c p)’ . 04.)} A! “ 0,546 . (‘1405 51‘. ~ . 0:14“) . 03.19 7 o (1 \J .\-J 1: I“) 0 O \F‘t ’x} , . ’0' 3 091+ ‘i -.-')",(—‘ 1.”,“, 1 . 03-116 1.0183 1 . 012 <‘- 1.3116 . $562 .3. .71..) 1';l \J‘\ \m KR \) k1) III. 11161. 71111) LOW ILETI‘CLLLJI ”VJ-1313 aflJbfllfil‘lT32 31111603, MEAN , 11:17.-) ERROR Case High Low Bands M900 Error ‘1? 103 116 27 126 10,75 < 2.75 11M 118 102 15 111 $.13 ‘3 5M 90 81 9 . L J\ 1011 123 110 13 117 5.33 103 126 110 16 116 “.7 19M 123 103 20 111 5.75 20M 23 100 26 113 7.00 213 113 07 6 100 0.00 221‘ 11: 7 ‘30 17 1110 N \0 \j C“ C, l...) x) V) H \"1 \1 H N ‘T‘ I I J *z’ *W H r' u) U\ H ’1 H o ”.2 O O F" C\ 253 103 x 27 123 10.79 2 511 107 35' ’3 102 2.93 2311 12 103 9 108.0. 3.42 27h 123 103 20 111 9.50 25? 127 111 1 113 0.6 (‘0 \") J F.) J \ \‘r 1‘ ’J O P” 0 ‘3 \A} o ‘n .1\ \x‘) :3 H H H ('1) H H 11 H H D O C~ kg) 322* 11'} 1‘12 11 17"? -§ .f’ :73? 1‘31 8’,’ ll; (:1 5.;sz 314’11 11.3 {3 90 11,.) C .fi‘) U KR 0.” "J H ‘x \w 110 11 119 4.33 3511 02 80 12 80.6 7.53 - .2/ , 1 r. A .. 373 139 119 55 137.: 1:. 0 Q‘\ 104 91. 110 100 100 Range 14 23 26 17 10 \O 20 10 34 21 27 19 10.0 18.5 Mean 98.0 120 111 113.1 112.8 91.8 112.0 100.3 120.1 12¢.6 110.3 114.3 90.6 129.0 117.8 90.1 120.6 108.3 125.1 111.2 125.2 100.3 93.7 105. 100.9 100.5 93 Error 6.4M 7.3 8.00 6.115 0.87 3.16 7.02 4.50 12.01 6.73 11.42 7 7H 126 104 122 102 106 101+ 108 101 3'? 11,113 J 14 13 20 31 Low 81 100 91 101 7U 85 105 / O 13 11+ APP‘L'JU‘DIK B 99 4 A 44 4 4 4 44. 4 44 44 44 4 4 4 44 H 44 4‘ , 44 4 4 4 4 4 4 4 4 4 44]. 44.H 4... 4... .... .... .... 4... . . H4 .4...+ 4 . 4,... 4 .4 . 4 . .4.+0A+ 0 v. . . 4 .... . 4 . ... . .... . .. . 4. o... 0.Lo 4.4» «H40 H... .... .... .... 4.4- 0... .4.. . 4 4. 4,044. 4 4 4... 4 0 .o 4 . . 4 0494 4 .4 . o 4 .... . . 4... 4 . .... . .. . .. 4... 0... .4.. 04.0 4.4 .... .... .... .... .... .... . 4 .o o .... 4 . 4.44 o . 4. . . . o '40. 4 .4 . . . .... . o . .... 4 . 4... 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