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AN ANALYSIS OF THE MENTAL FACTORS OF VARIOUS AGE GROUPS FROM NINE TO SIXTY

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University Microfilms
300 N orth Z e e b R o a d
Ann A rb o r, M ich ig an 48106
A X ero x E d u c a tio n C o m p a n y
13-3019
LD3907
.E3
Balinsky, Benjamin.
1940
An analysis of the mental factors of
•B3
various age groups from nine to sixty...
New York, 1940.
iii,44 typewritten leaves.
tables.
29cm.
Thesi3 (Ph.D.) - lJev: York university,
School of education, 1940.
Bibliography’ p.41-44.
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Ann Arbor, Michigan 48106
THIS D ISSE R T A T IO N HAS BEEN MICROFILMED EXACTLY A S RECEIVED.
{ Ih sbi« aoeeptod
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AN A N A L Y S I S
VARI OUS
OF THE VENTAL
« . . . APR 5
FACTORS
AGE GROUPS FROV N I N E
S
enja v
.
in
S
a l i n s k
TO
OF
SIXTY
*
S u bmi t t e d in p a r t i a l f u l f i l l m e n t of t he r e o u i r e me n t s
f o r t he decree of d oc t or of Fhi l os ophy
in t he School o f Educat i on of Few York U n i v e r s i t u
1340
1940
PLEASE NOTE:
S o me p a g e s
ma y h a v e
i nd i s t i n e t
print.
Filmed
University
as
M icrofilms,
received.
A Xerox
Education
Company
T a 8l e
of
Contents
CHAPTFB
I.
Introduction
.
.
.
.
.
a. H i s t o r i c a l Background
1. D i s c u s s i o n o f t h e f a c t o r T h e o r i e s
a. The T h u r s t c n e Vethcd
P. The ° r o b l e m .
1. S t a t e me n t o f t h e Problem
?. The Heed of a S o l u t i o n
P. L i m i t a t i o n s o f t h e Ptudy
.
.
.
.
.
A 5 4 3 7 9
-i-
p
P
1?
IV. I n t e r p r e t a t i o n of t h e P e s u l t s
A. A n a l y s i s of t h e C o r r e l a t i o n V a t r i c e s
P. D i s c u s s i o n of t h e P o t a t e d F a c t o r s
C. Dr e s e n t a t i c n of F i n d i n g s Fased on t h e Study of
t h e P o t a t e d and U n r o t a t e d F a c t o r Le adi ngs
Piblicgraohy
p
c
ITT. P r e s e n t a t i o n of Data
A. The
Original Correlation Vatrices
P. The
CorrelationVatrices
wi t h t h e Sex F a c t o r
Fliminated
C. The U n r o t a t e d F a c t o r Leadi ngs
1. The Problem, o f How Vany F a c t o r s To Use in
the Potations
D. The P o t a t e d F a c t o r Le a d i n g s
.
A
p
p
I I . D e s c r i p t i o n of Sampl i ngs and T e s t s
A. The
Sampl i ngs
F. The
Tests
V. Summary and C o n c l u s i o n s
PAGI
1
1
rr
.
.
.
.
1F
1F
IF
1P
1P
17
?e
?p
CO
S4
?P
41
L ist
of
T ables
TABLf
1.
10
11
1?
1?
14
lc
IP
17
is
PASf
Age 9) I n t e r t e s t C o r r e l a t i o n V a t r i x ( O r i g i n a l ,
Removing Sex F a c t o r )
.
.
.
.
Age 1?) I n t e r t e s t C o r r e l a t i o n V a t r i x ( O r i g i n a l ,
Removing Sex F a c t o r )
.
.
.
.
Age i c ) I n t e r t e s t C o r r e l a t i o n V a t r i x ( O r i g i n a l ,
Removing Sex F a c t o r )
.
.
.
.
Pefore
.
Pefcre
.
Fefore
.
Ages SF-SP) T n t e r t e s t C o r r e l a t i o n V a t r i x ( O r i g i n a l ,
P e f o r e Removing Sex F a c t o r )
.
.
.
.
Ages PF-44) I n t e r t e s t C o r r e l a t i o n V a t r i x ( O r i g i n a l ,
P e f o r e Removing Sex ^ a c t c r )
.
.
.
.
Ages FO-FP) I n t e r t e s t C o r r e l a t i o n V a t r i x ( O r i g i n a l ,
P e f o r e Removing Sex F a c t o r )
.
.
.
.
Age P) Summary of T n t e r t e s t C o r r e l a t i o n s (Sex ^ a c t c r
Fel d C o n s t a n t )
.
.
.
.
.
.
Age 1?) Summary of T n t e r t e s t C o r r e l a t i o n s (Sex F a c t o r
Fel d C o n s t a n t )
.
.
.
.
.
.
Age 1?) Summary of T n t e r t e s t C o r r e l a t i o n s (Sex F a c t o r
Fel d C o n s t a n t )
.
.
.
.
.
.
Ages ?P-SP) Summary o f T n t e r t e s t C o r r e l a t i o n s (Sex
^ a c t c r Feld Constant)
.
.
.
.
.
Ages SF-44) Summary of T n t e r t e s t C o r r e l a t i o n s (Sex
f a c t o r Fel d C o n s t a n t )
.
.
.
.
.
Ages 5 0 - KP) Summary o f T n t e r t e s t C o r r e l a t i o n s (Sex
F a c t o r Fe l d C o n s t a n t )
.
.
.
.
.
Age P) C e n t r o i d F a c t o r Loadings and Communal i ti es As
Computed by T h u r s t o n e ’ s Ce n t r o i d Vethcd
Age 1?) C e n t r o i d f a c t o r Loadi ngs and Ccmmunal i t i es As
Computed bv F h u r s t o n e ’ s Ce n t r oi d Vethcd
Age l c ) C e n t r c j d F a c t o r Loadi ngs and Communalities As
Computed by T h u r s t c n e ’ s Ce n t r o i d Vethcd
Ages SF-S9) C e n t r o i d F a c t o r Loadings and Communal i t i es
As Computed by T h u r s t o n e ' s Ce nt r o i d Vethcd .
Ages SF-44) C e n t r o i d f a c t o r Leadi ngs and Ccmmunal i t i es
As Computed by T h u r s t o n e ’ s C e n t r o i d Vethod .
Ages FQ-F°) C e n t r o i d f a c t o r Loadings and Communal i ti es
As Computed by T h u r s t o n e ' s Ce n t r o i d Vethod .
-ii-
18
18
19
1P
50
51
SI
r*o
<r<
C'f*
<C
S4
S4
S4
SF
-iii
TABLE
( Age 9) P s y c h o l o g i c a l l y Veani ngf ul f a c t o r Loadi ngs
Obt ai ned A f t e r P o t a t i o n .
.
.
.
.
?0. (Age 1?) P s y c h o l o g i c a l l y Veani ngf ul F a c t o r Lo a d i ng s
Obt ai ned A f t e r P o t a t i o n .
.
.
.
.
?1. (Age 1?) P s y c h o l o g i c a l l y Vean i n g f ul F a c t o r L e a d i n g s
Obt a i ne d A f t e r P o t a t i o n .
.
.
.
22. (Ages PF-09) P s y c h o l o g i c a l l y Ve a n i n g f ul F a c t o r L e a d i n g s
Obt ai ned Af t er P o t a t i o n .
.
.
.
.
2c. (Ages PF-44} Ds y c h c l o g i c a l l y Vean i n g f ul f a c t o r Le a d i n g s
Ob t a i n e d A f t e r P o t a t i o n .
.
.
.
.
04. (Ages F0-F9) P s y c h o l o g i c a l l y Ve a ni n gf u l F a c t o r Loadi ngs
Ob t a i n e d Af t er P o t a t i o n .
.
.
.
.
PA3JT
1?.
OF
27
27
27
CHAPTER
I
I NTRODUCTI ON
A.
h i s t o r i c a l Eac k i r ouni
For many c e n t u r i e s , man has been concer ned wi t h t h e problem of
u n d e r s t a n d i n g h i s f e l l ow- ma n .
The a n c i e n t S o p h i s t s gave a new d i r e c ­
t i o n t o human t ho u g h t when t h e y t u r n e d from s p e c u l a t i o n about cosmol ­
ogy t o t h e c o n s i d e r a t i o n of human a f f a i r s .
They i n f l u e n c e d such l a t e r
p h i l o s o p h i c a l g i a n t s as S o c r a t e s , who b e l i e v e d t h a t he could o b t a i n
knowledge of t h e " s e l f , " and h i s d i s t i n g u i s h e d p u p i l P l a t o , who r e c o g ­
n i z e d i n d i v i d u a l d i f f e r e n c e s in man. P l a t e went sc f a r as t o pr opos e
an i d e a l s t a t e , t h e R e p u b l i c , where men were t o be chosen f o r s p e c i a l
d u t i e s , wi t h r e f e r e n c e t o t h e i r a b i l i t y t o per f or m them. A r i s t o t l e
c o n t i n u e d t h e emphasis on human m a t t e r s and " a d d r e s s e d h i m s e l f t o t h e
t h i n g s o f t h e mind i n much t h e same manner as t o a n y t h i n g ' e l s e i n t h e
m a t e r i a l o r d e r . 1,1
Some of t h e Creek o h i l c s o p h e r s even c o n s i d e r e d c l a s s i f i c a t i o n s
f o r t h e v a r i o u s t y p e s of man. T h e o p h r a s t u s pr o po s ed t h e schemat a of
some t h i r t y t y p e s , i n t o which he t h o u g h t he coul d f i t a l l i n d i v i d u a l s ;
and H i p p o c r a t e s d e s c r i b e d a l l men i n t e r ms of t h e f o u r "humors" which
he had d e v i s e d .
Vor eover , t h e Hindus i n v e n t e d a c a s t e system, t h e
r i g i d i t y of which i s s t i l l f e l t i n I n d i a .
Thi s d e s i r e t o c l a s s i f y and t o u n d e r s t a n d man i s ver y s t r o n g , and
t h e t endency has p e r s i s t e d t h r o u g h t h e c e n t u r i e s t h a t have p a s s e d .
The p e r s i s t e n c e i n d i c a t e s a d e f i n i t e need f o r a s m a l l e r number o f ter ms
i n which t o d e s c r i b e so complex an animal as man. At p r e s e n t t h e r e a r e
many schemes of c l a s s i f i c a t i o n , u s i n g such d e s c r i p t i v e t er ms as i n t r o ­
v e r t and e x t r o v e r t , and puhni c and a s t h e n i c , each of which b r i n g s t o
mind a c e r t a i n k i nd of b e h a v i o r .
We a r e h e r e c on cer ned wi t h t h e c o g n i t i v e f u n c t i o n s as measured by
t e s t s of i n t e l l i g e n c e .
I t i s wel l known t h a t t h e r e e x i s t i nnumer a bl e
t e s t s p u r p o r t i n g t o measure t h i s a s p e c t o f man. The f i r s t t e s t s or
o b j e c t i v e measures were s p e c i f i c a l l y d e v i s e d by P a l t c n and C a t t e l l t c
measure such "mental a b i l i t i e s " a s memory, mental i magery, and a s s o c i a ­
tion.
When compared wi t h e t h e r r a t i n g s , such as s chool marks, t h i s
t y p e of mental t e s t i n g was found t o have c e r t a i n d e f i c i e n c i e s .
1. l?dna H e id b re d e r, Seven P s y c h o l o g i e s -
-1-
I t was n ot u n t i l about 1905, when Al f r ed F i n e t d e v i s e d h i s t e s t
o f " g e n e r a l " i n t e l l i g e n c e , t h a t t h e f i e l d of mental t e s t i n g began i t s
g r e a t e x pa ns i on .
F i n e t c o n c l u d e d , a f t e r some e x p e r i m e n t a t i o n , t h a t
no s i n g l e p e r f o r ma n c e c o u l d be us ed as a j u s t i n d i c a t o r of i n t e l l i g e n c e .
From t h i s p c i n t on, t e s t s of i n t e l l i g e n c e i n c r e a s e d r a p i d l y i n number.
Vany group t e s t s were p u b l i s h e d , and t e s t s cf a " p e r f o r ma n c e ” n a t u r e
were s t a n d a r d i z e d .
Turing t h i s t i m e , s t a t i s t i c a l t e c h n i a u e s were be i n g f o r m u l a t e d f o r
t h e e v a l u a t i o n of t h e t e s t s which had been dev i s e d.
They had t h e i r
b a s i s i n t h e m a t h e ma t i c s o f p r o b a b i l i t y , which were f i r s t s e t f o r t h
about t h e y e a r 1*00, and were more t h o r o u g h l y f o r mu l a t e d by such mat he­
m a t i c i a n s as P e r n o u i l l e , Ce F' oi vre, La p l a c e , Oauss and C u e t e l e t .
It
f e l l t o Oa l t c n t o a p p l y t h e methods of s t a t i s t i c s t o an t h r o p o me t r y ,
and he h i m s e l f added o t h e r t o o l s f o r t h i s work. With t he i m p o r t a n t
c o n t r i b u t i o n s of Karl P e a r s o n , s t a t i s t i c s became a powerful and u s e f u l
t o ol for the purposes of a n a l y s i s .
Turi ng t h e p r e s e n t p e r i o d of ment al t e s t i n g , a g r e a t d e a l c f a t ­
t e n t i o n has been p a i d t o t h e n a t u r e of i n t e l l i g e n c e , and t h e r e has
been much d i s c u s s i o n a s t o what s p e c i f i c t h i n g s t he t e s t s of i n t e l l i ­
gence were d e s i g n e d t o meas ur e.
I t was t h e ext r emel y i m p o r t a n t p r o ­
p o s a l by Spearman1 on t h e t w o - f a c t o r t h e o r y , in 1P04, t h a t s t i m u l a t e d
a g r e a t deal of r e s e a r c h in t h i s f i e l d .
This t h e o r y p r o v i d e d an e x ­
p l a n a t i o n f o r c e r t a i n common f i n d i n g s i n mental t e s t i n g , such as
p o s i t i v e i n t e r c o r r e l a t i c n s , and l e n t s u c c or to t h e t e s t s of " g e n e r a l "
i n t e l l i g e n c e , l i k e t h a t of F i n e t .
Fut was t he t w o - f a c t o r t h e o r y a
b r o a d enough means o f e x p l a n a t i o n f o r o t h e r p r o c e d u r e s i n ment al
t e s t i n g ? App ar en t l y i t was n e t .
Thomson,? Spearman' s s e v e r e s t c r i t i c ,
propounded t h e t h e o r y c f group f a c t o r s , which o f f e r e d an e x p l a n a t i o n
f o r t h e f a c t of lew i n t e r c o r r e l a t i c n s among p a r t s c f a t e s t b a t t e r y ,
and which was more s u i t e d t o s e r v e as a t h e o r e t i c a l b a s i s f o r voca­
tional testing.
The t w o - f a c t o r t h e o r y c f Spearman f a i l s t o e x p l a i n why t h e b e s t
b a t t e r i e s of t e s t s a r e t h o s e i n which t h e p a r t s show low i n t e r c o r r e l a ­
t i o n s with each o t h e r and h i g h c o r r e l a t i o n s with t h e e n t i r e b a t t e r y .
For , i f t h e e n t i r e b a t t e r y meas ur es a q u a l i t y t o be d e s i g n a t e d as 9,
i t f o l l o w s t h a t each p a r t of t h e b a t t e r y , i n o r d e r t o c o r r e l a t e h i g h l y
1 . C h a r l e s Spearman, "The P r o o f an d M easurement o f A s s o c i a t i o n b e tw een Two T h i n g s , "
American J ournal o f P s y c h o l o g y , XV ( t 9 0 4 ) , 7 P—1 0 1 #
u
Pi w i l l i a m Brown and
frhomaon, The F s s e n t t a l s o f Mental Measurement •
wi t h t h e e n t i r e s c a l e , must be somewhat s a t u r a t e d wi t h 9.
Thi s b e i n g
sc, t h e i n t e r c o r r e l a t i o n s among t h e p a r t s w i l l a l s o have t o be h i g h ,
f o r t h e s e c o r r e l a t i o n s a r e i n p r o p o r t i o n t o t h e i r s a t u r a t i o n wi t h 9.
Thomson' s g r o u n - f a c t o r t h e o r y does g i v e an ad e a u a t e e x p l a n a t i o n
f o r t h e low i n t e r c o r r e l a t i o n s among p a r t s o f t h e t e s t s .
Ee assumes
t h a t t h e r e a r e many e l e m e n t a r y a b i l i t i e s , and t h a t each t e s t sampl es
a c e r t a i n range of these.
I f two t e s t s happen t o sample many c f t h e
same a b i l i t i e s , t h e y w i l l have c e r t a i n t h i n g s i n common, and w i l l
t h e r e f o r e c o r r e l a t e t o a c e r t a i n de gr e e , dependi ng on t h e number c f
common a b i l i t i e s measured.
The v a r i o u s p a r t s c f t he t e s t s may sample
smal l numbers c f t h e same a b i l i t i e s , and t h u s have low o r d e r c o r r e l a ­
tions.
Put a l l p a r t s sampl e some of t h e e n t i r e number c f p o s s i b l e
a b i l i t i e s , and t h u s each p a r t of a t e s t b a t t e r y c o r r e l a t e s t o some
e x t e n t with t h e t o t a l .
Ccnc er n i ng t h e t h e o r e t i c a l e x p l a n a t i o n s f o r t he p o s s i b i l i t y of
v o c a t i o n a l t e s t i n g , G u i l f o r d has w r i t t e n 1:
In the f i r s t Dlaee, i f Spearman'3 3 - f a o t o r e are r e a l l v s o n f i n e i t o o n e t a s k a l o n e , 33 he i n s i s t 3 , t h 9 r e i s n o way o f p r e l i s t i n g from t 9 s t s an i n d i v i d u a l ' s s ta n d in g in h i s 3 - f a o t o r s
f o r v a r i o u s o o o u p a t i o n s . I t i 3 l i k e l y , 3 i n e e many o c c u p a t i o n a l
a c t i v i t i e s h a v e a low c o r r e l a t i o n w i t h t 9 s t 3 t h a t m e a s u r e 3,
t h a t o c c u p a t i o n a l t a s k s d e p e n d l a r g e l y u p o n t h e i r own s - f a o t o r s ,
w h ich c o u l d n o t be m e a s u r e d w i t h o u t a s k i n g a n a p p l i c a n t t o p e r ­
form the t a s k 3 t h e m s e l v e s . . . . V o c a tio n a l guidanoe would t h u s
b9 n 9 x t t o i m p o s s i b l e w i t h o u t a l l o w i n g t h e i n d i v i d u a l t o t r y
o u t t h e d i f f e r e n t a l t e r n a t i v e s . • On t h e b a s i s o f t h e s a m p l i n g
t h e o r y , ho w e ver, b o th v o c a t i o n a l s e l e o t i o n and v o c a t i o n a l g u i d ­
anoe become l o g i o a l l . v p o s s i b l e .
Fpearman h a s come t o a c c e p t t h e e x i s t e n c e of f a c t o r s o t h e r t han
G. Pe and h i s a s s o c i a t e s have a d mi t t e d t h a t i n many i n s t a n c e s t h e
t a b l e s of i n t e r c o r r e l a t i o n s may i n c l u d e some c o r r e l a t i o n over and
above 3. Thus t h e y r e c o g n i z e d as group f a c t o r s v e r b a l a b i l i t y , nu­
m e r i c a l a b i l i t y , me c h a n i c a l a b i l i t y , and a p o s s i b l e f a c t o r of ment al
speed.
Pi nce Poearman f o r m u l a t e d t h e t w o - f a c t c r t h e o r y and d e v i s e d t h e
method o f t e t r a d d i f f e r e n c e s f o r d i s c o v e r i n g t h e f a c t o r s , o t h e r p r o ­
c e d u r e s have been i n v e n t e d .
These al lowed f o r t h e e x t r a c t i o n o f more
t h a n one f a c t o r , as Fpearman h i m s e l f a dmi t t e d t h e p o s s i b i l i t y o f
several facto rs in t e s t b a t t e r i e s .
K e l l e y / T h u r s t o n e , 8 and F o t e l l i n g '
each d e v e l o p e d t e c h n i q u e s of f a c t o r a n a l y s i s .
1.
J . P.
%\ L
f c
408 4? •
O o m fc w m tS *
3u
i l f o r d , P s y c h o m e t r i c Methods, p. 467.
S r s t o a e ^ ^ M u l t i B l t ^ i o t o ^ A a a l y a i s ” " P s y c h o l o g y R e vi en , XXXVIII ( l 9 8 l > ,
intf, "An A n a l y s i s o f a Complex o f S t a t i s t i c a l V a r i a b l e s i n t o P r i n o i p a l
J o u r n a l o f F d u c l t i o n a l P s y c h o l o g y , XXIV fl9 8 8 > , 417 -441 , 4 9 9 -5 5 0 .
-4-
We s h a l l co nc e r n o u r s e l v e s wi t h T h u r s t o n e ’ s method of f a c t o r
a n a l y s i s , s i n c e i t i s t h e one chosen f o r use i n t h i s s t u d y .
Thi s
method o f a n a l y s i s a l l o w s f o r t h e e x t r a c t i o n o f many f a c t o r s , which
a r e c a l l e d wei ght ed group f a c t o r s , i n o r d e r t o d i f f e r e n t i a t e them
from t h e group f a c t o r s o f Thomson’ s sampling t h e o r y .
Whereas Thomson
p o s t u l a t e d i n n u me r a b l e e l e m e n t a r y a b i l i t i e s , T h u r s t o n e 1 has p o s t u l a t e d
a l i m i t e d number, no t y e t f i x e d .
The Thur st one m u l t i - f a c t o r t h e o r y ,
l i k e Thomson’ s s ampl i ng t h e o r y , s e r v e s as an e x p l a n a t i o n f o r low
i n t e r t e s t c o r r e l a t i o n s , a s wel l as hi gh t e s t c o r r e l a t i o n s wi t h t h e
e n t i r e b a t t e r y , and a l s o as a b a s i s f o r v o c a t i o n a l g ui d a n c e .
T h u r s t o n e ’ s c e n t r o i d method of f a c t o r a n a l y s i s , r a t h e r t h an any
o t h e r method, has been chosen f o r s t udy h e r e , b e c a u s e i t i s t h e most
wi del y a c c e p t e d and t h e most t h o r o u g h l y r a t i o n a l i z e d .
/ l e x a n d e r ?'
s e l e c t e d t h i s method f o r us e a f t e r comparing s e v e r a l t e c h n i a u e s , and
wr ot e c o n c e r n i n g h i s c h o i c e :
For p r a c t i c a l p u r p o s e s i t i s our o o in io n t h a t the method of Thur­
s t o n s i s t o be p r e f e r r e d b e o a u s e o f i t s G r e a t e r s i m p l i c i t y an d
3 p e e d i n a p p l i o a t i o n . T o r t h a t r e a s o n we p r o p o s e t o a d o p t t h i s
method t h r o u g h o u t t h e work t h a t f o l l o w s .
V o r r i s 5 a l s o employed t h e t e c h n i a u e , s t a t i n g t h a t ’’T h u r s t c n e ’ s c e n t e r
of g r a v i t y t e c h n i q u e i s t h e g e n e r a l c a s e c f which a l l o t h e r s a r e but
s p e c i a l . c a s e s . ” Tn a c r i t i c a l compari son of t h e Th u r s t o n e t e c h n i a u e
wi t h t h e F o t e l l i n g method, VcClcy, Vet hi ng and T n c t t 4 found t h e Thur ­
s t o n e method s u p e r i o r .
3 u i l f o r d K has w r i t t e n about t h e f a c t o r a n a l y ­
s i s t e c h n i q u e s i n t h i s ve i n :
The m e t h o d s o f K e l l e y a n d F o t e l l i n 2 a r e m a t h e m a t i c a l l y a n d
s t a t i s t i c a l l y r ilo r o u s , but they freau e n tly lead to u n itary
a b i l i t i e s t h a t a r e d i f f i c u l t t o i n t e r p r e t . I t would be impos­
s i b l e t o d e s c r i b e a l l t h e a l t e r n a t i v e methods in u s e f u l d e t a i l
i n t h e s p a c e o f o n e c h a p t e r . Th e w r i t e r i s c o m p e l l e d t o d e p a r t
from th e p r e v i o u s custom of p r e s e n t i n g a l t e r n a t i v e p r o o e d u r e s .
The c h o i c e i n t h i 3 c a s e f a l l s u p o n T h u r s t o n e ' s m e t h o d s . T h e s e
methods have been s u p p lie d w ith 3 very com plete r a t i o n a l b a s i s
i n t h e m a t h e m a t i c s o f V a t r i x T h e o r y a n d t h e y o a n be made t o
lead to s ig n i f i c a n t , m eaningful v a ria b le s.
L. L. T h u r a to n e , V e c t o r s o f Mind.
W. P. A le x a n d e r, " I n t e l l i g e n c e , C o n o re te and A b s t r a c t , " B r i t i s h J ournal o f P s y ­
c h o lo gy , Monograph S u p p le m en t, 1935, p. 75.
3 . C. M. M o r r i s , "A. C r i t i c a l A n a ly s i s o f C e r t a i n P e rfo rm a n c e T e s t s , " Journal o f
G e n e t i c P s y c h o l o g y , LIV ( 1 9 3 9 ) , ? 5 - 1 0 5 .
4 . C. H. YoCloy, ®. M ething and J . K n o t t , "A Comparison of t h e T h u r s to n e Method of
M u l t i p l e F a c t o r s w it h t h e H o t e l l i n g Method of P r i n o i p a l C o m p o n e n ts," P s y c h o m e t r i k a ,
1939, 361-367.
5 . J . P. S u l l f o r d , P s y c h o m e t r i c Methods, p. 4 7 1 .
1.
8.
Wilson and W o r c e s t e r , 1 i n a d i s c u s s i o n of f a c t o r t e c h n i q u e s ,
j u s t i f y t h e T h u r s t o n e method.
They have w r i t t e n :
The H o t e l l i n g a n a l y s i s h a 9 t h e a r i t h m e t i c a d v a n t a g e s o f
i e t 9 r m i n a c y and of r e a d y m e ch a n ical a p p l i c a b i l i t y . Those a d ­
v a n t a g e s may b r i n S i n w i t h t h e m v e r y r e a l d i s a d v a n t a g e s . T h e r e
i s p e r h a p s n o t h i n g m o r e l i k e l y t o c o n v i n c e o n 9 t h a t h e ha B
something of value th an the a b i l i t y to execute a meohanical
a r i t h m e t i c a l p r o c e d u r e . Tor t h a t r e a s o n 3uch c o n s i d e r a t i o n s
a s h a v e b e e n o f f e r e d i n t h i s ’ N o t e ' w i l l n o t be w i t h o u t u s e ­
f u l n e s s i f t h e y seem o n o e more t o d i r e c t a t t e n t i o n t o t h e n e e d
of examining a formal s o l u t io n for i t s p sy ch o lo g ica l su b stan ce .
Tt w o u l d b e a p i t y i f Wu n d t h a d t a k e n P s y c h o l o g y a w a y f r o m h e r
m o th er P h i l o s o p h y and m a r r i e d h e r t o S c i e n c e o n ly t o have h e r
d e s e rt to a paramour M athem atics.
T h u r s t o n e ’ s method o f f a c t o r a n a l y s i s , l i k e a l l t h e o t h e r s ,
s t a r t s from t h e i n t e r c o r r e l a t i c n s c f t he v a r i o u s t e s t s i n c l u d e d i n
the battery.
These t e s t s may be p a r t s c f a s i n g l e s c a l e , or t h e y may
be t e s t s s e l e c t e d from wh at ev er s o u r c e .
When given t o t h e same s ub ­
j e c t s , t h e i n t e r c o r r e l a t i o n s of every p o s s i b l e p a i r of t e s t s can be
calculated.
As happens i n v a r i a b l y , t he c o r r e l a t i o n s between t h e p a i r s
o f t e s t s a r e al mo s t a l l p o s i t i v e , i n d i c a t i n g some t h i n g or t h i n g s
■common among them.
Thu r s t o ne h a s d e v i s e d a r a t i o n a l method of o b t a i n i n g t h e number
o f e l e me n t s common t o t h e t e s t s , and t hen i d e n t i f y i n g and naming them.
The common e l e m e n t s a r e c a l l e d f a c t o r s or a b i l i t i e s , and a r e e x t r a c t e d
from t h 9 o r i g i n a l c o r r e l a t i o n s u n t i l t he r e s i d u a l s of t h e c o r r e l a t i o n s
no l o n g e r can gi ve up s i g n i f i c a n t f a c t o r s .
A f u l l e r d i s c u s s i o n on t h e
m a t t e r of hew many f a c t o r s t o e x t r a c t i s r e s e r v e d f o r a l a t e r s e c t i o n
o f t h i s i n v e s t i g a t i o n , ' where t he problem w i l l a c t u a l l y a r i s e .
These f a c t o r s and t h e i r l o a d i n g s or wei ght s have no p s y c h o l o g i c a l
meaning. They merely r e p r e s e n t c o r r e l a t i o n s between any t e s t and one
o f t h e r e f e r e n c e axes , and may be p o s i t i v e or n e g a t i v e .
The r e f e r e n c e
ax e s a r e t h e u s u a l x and y axes of a c o S r d i n a t e system.
Any t e s t has
p r o j e c t i o n s on t h e two a x e s .
The c o r r e l a t i o n between any two t e s t s i s
t h e sum of t h e p r o d u c t s c f t h e f a c t o r l o a d i n g s c f each t e s t , i . e . ,
pab=a 1b l + a 2b 2+»»?nb n.
To make t h e f a c t o r s p s y c h o l o g i c a l l y meani ngf ul , t h e r e f e r e n c e
axes must be sc r o t a t e d t h a t t h e y p a s s t hr ough or near by t h e m a j o r i t y
of the leadings.
Th i s may be done as o f t e n as i s n e c e s s a r y , each t i me
wi t h t h e newly found r o t a t e d l o a d i n g s , u n t i l t h e number of zer o l o a d i n g s
i s maximum and t h e number c f n e g a t i v e l o a d i n g s minimum.
1.
(June,
I.- B. Wilson- and J . W o r o e s te r,
19391, p. 149.
"Note on N a o to r A n a l y s i s , " P s y c h o n . e t r i k a , V o l. IV
Tn t h i s way c e r t a i n t e s t s w i l l have s i g n i f i c a n t p o s i t i v e l o a d i n g s
i n c e r t a i n f a c t o r s , and o t h e r s w i l l have i n s i g n i f i c a n t p o s i t i v e l o a d ­
i n g s . 1 Fy s t u d y i n g t h e t e s t s with s i g n i f i c a n t l o a d i n g s i n t h e v a r i o u s
f a c t o r s , one may a r r i v e a t t h e e l ement s common t o t h e v a r i o u s t e s t
g r o u p i n g s and t h u s name t h e f a c t o r s .
An e x a mi n a t i o n o f t h e t e s t s with
i n s i g n i f i c a n t l e a d i n g s w i l l ai d i n t he naming of t h e f a c t o r s , by i n d i ­
c a t i n g p o i n t s which a r e not i n c l u d e d i n t h e s e t e s t s , t u t a r e i n c l u d e d
in the e th e r s .
F i n e s t h e r o t a t e d r e f e r e n c e axes a r e p e r p e n d i c u l a r t c
e ach o t h e r , or o r t h o g o n a l , t h e f a c t o r s or a b i l i t i e s a r e i n d e p e n d e n t of
each e t h e r .
5.
The Problem
T h i s s t u d y u n d e r t a k e s t o an a l yz e t h e ment al f a c t o r s a p p e a r i n g e ver
a wi d e s p r e a d p e r i o d c f y e a r s , i n o r d e r t c n c t e any s i g n i f i c a n t changes
which may oc c ur d u r i n g p e r i o d s of growth and d e c l i n e .
These changes
may o c c u r i n t h e f a c t o r s t h e ms e l v e s , so t h a t some w i l l appe a r and o t h e r s
d i s a p p e a r a t d i f f e r e n t p e r i o d s c f time; or t h e t e s t s t h a t f a l l i n with
c e r t a i n f a c t o r s a t one t i me may e n t e r i n with d i f f e r e n t gr oups a t a n o t h e r
time.
A dynamic p i c t u r e of mental o r g a n i z a t i o n may a l s o be o b t a i n e d from
t h i s study.
The o p p o r t u n i t y t o c a r r y cut such an i n v e s t i g a t i o n as t h e p r e s e n t
one
is
afforded
by t h e s t a n d a r d i z a t i o n c f t h e W e c h s l e r - F e l l e v u e I n t e l l i ­
gence S c a l e . 2 Thi s i s a p o i n t s c a l e which can be used e v e r such a wide
span o f ages a s from n i n e y e a r s t o s i x t y . ? Fy means of t h i s r e s e a r c h ,
i t w i l l be p o s s i b l e : (1) t o i s o l a t e t he mental a b i l i t i e s a t each age
l e v e l ; ( ?) t o n c t e t h e i r s t a b i l i t y from age t c age; (S) t o s t u d y t h e
t e s t s as t h e y a r e acc o un t e d f o r by each f a c t o r a t each age p e r i o d ; and
( 4) t o o b t a i n c e r t a i n f a c t s as t o mental o r g a n i z a t i o n .
T h u r s t o n e , 4 i n a d e s c r i p t i o n of what he c a l l s t h e p r i ma r y a b i l i t i e s ,
r e c o g n i z e s t h e need f o r s t u d y i n g v a r i o u s age g r o u p s . Fe g i v e s as an
i l l u s t r a t i o n t h e s o l u t i o n c f t h e simpl e a r i t h m e t i c a l problem F x l i . Fe
states:
To a n s w e r a e o o r e o f s u o h i t e m s q u i o k l y a t t h e a g e o f f i f t e e n
i s i n d i c a t i v e o f t h e f a c t o r V, b u t a f o u r - y e a r - o l d who s o l v e s
3uoh i t e m s r a t i o n a l l y
may r e v e a l l o g i c a l f a c u l t i e s , p e r h a p s i n i u o t i v e , r a t h e r t h a n s u p e r i o r i t y i n t h e f a c t o r N. T h i s i s a n
e x a m p l e o f what m i g h t be t a k i n g p l a c e .
1.
I t a a v happen
t h a t a f t e r s e v e r a l r o t a t i o n s a n e g a t i v e l o a d i n g w i l l s t i l l be fo u n d .
If it
is
w ith in th e
l i m i t o f - . 1 0 , i t may be o o n s id e r e d as i n s i g n i f i c a n t l y n e g a t i v e . J . P.
3 u i l f o r d , P s y c h o m e t r i c Methods, p. 507.
2 . D. W e o h s le r, Measurement o f A d u l t i n t e l l i g e n c e .
s A f u l l e r d i s c u s s i o n o f t h i s s o a l e w i l l be g iv e n i n C h a p t e r I I .
4 * L. L. T h u r s t o n e , Pr i ma ry Mental A b i l i t i e s , P s y o h o m e tr io Monograph No. 1, 1 9 8 -, p . . 7 .
)
-7-
Pe goes on t o p o i n t o ut t h a t " t h e s e r e l a t i o n s have no t been a d e q u a t e l y
r e c o g n i z e d i n r e c e n t s t u d i e s o f t h e changes i n ment al o r g a n i z a t i o n with
a g e . " to any r a t e i t i s " a d v i s a b l e t c i s o l a t e t h e ment al a b i l i t i e s
separately
a t each age l e v e l and t c irove wi t h c a u t i o n i n e x t r a n o l a t i n g
t h e f a c t o r i a l i n t e r p r e t a t i o n o f a t e s t f o r wi del y d i f f e r e n t a g e s . "
P e l l e y , 1- i n a r e c e n t c r i t i q u e of f a c t o r a n a l y s i s s t u d i e s , s t r e s s e d t h e
need f o r q u a n t i t a t i v e s t a t e m e n t s c f s t a b i l i t y c f f a c t o r s as age and
group changes.
Ds y c h o l c g i s t s have been wont t c d e s c r i b e i n d i v i d u a l s on t h e b a s i s
cf th e ir te s t r e s u lt s .
Put t h e y have not al ways been a b l e t c a g r e e as
t o t h e s p e c i f i c q u a l i t i e s measured by t h e v a r i o u s t e s t s .
Vurphy, ? i n
s t u d y i n g t h e r e l a t i o n between t e s t s c f mechani cal a b i l i t y and v e r b a l and
n o n - v e r b a l t e s t s of i n t e l l i g e n c e , found much c o n f u s i o n o f t e r mi n ol o gy
e x i s t i n g i n t h e f i e l d of measurement of mechani cal a p t i t u d e .
Wor t h i n gt o n8
n o t e d t h a t t h e P i c t u r e Completion T e s t , C a n c e l l a t i o n c f J and Kncx Cube
were t e s t s of s p e c i a l a b i l i t y and s houl d be f u r t h e r a n a l y z e d . P i n t n e r
and Anderson4 d e s c r i b e d t h e P i c t u r e Complet ion Te s t a s b e i n g a measure
o f t h e c h i l d ’ s a p p e r c e p t i v e a b i l i t y , " t o s ee how wel l he i s a b l e t o meet
t h e r e q u i r e m e n t s o f each s i t u a t i o n by g r a s p i n g i t s m e a n i n g . " L o u t t i t 6
has w ritten :
J u s t what a b i l i t i e s a r e m easured i n f o r m - b o a r d p e r f o r m a n c e s i s
not a t a l l c l e a r . V arious w r i t e r s have claim ed t h e i r u s e f u ln e s s
i n m e a s u r i n g for m p e r c e p t i o n and d i s c r i m i n a t i o n , m a n i p u l a t i v e
a b i l i t y , motor c o o r d i n a t i o n , e t c . , b u t t h e r e h a v e b e e n no a t t e m p t s
t o e s t a b l i s h a d e q u a t e l y t h e i r v a l i d i t y i n any of t h e s e f i e l d s .
The same d i f f i c u l t i e s i n i n t e r p r e t a t i o n have been e x p r e s s e d wi t h r e g a r d
to other t e s t s .
The r e s e a r c h by means of f a c t o r a n a l y s i s has made a g r e a t c o n t r i b u ­
t i o n t oward t h e i s o l a t i n g c f t h e ment al f a c t o r s i n v o l v e d i n t h e t e s t s of
i n t e l l i g e n c e , and towar d a d e s c r i p t i o n of t h e v a r i o u s t e s t s i n t er ms of
these factors.
Ft ephenson^ found t h e v e r b a l f a c t o r u, and Al exander 7
e s t a b l i s h e d as a s e p a r a t e f a c t o r i n c e r t a i n t e s t s t h a t he c a l l e d f , a
p e r f o r ma n c e f a c t o r .
Vorris® r e c e n t l y a na l y z e d "a group o f t h i r t y - f o u r
1.
T. L. X e l l e y , "M ental v a o t o r s o f Vo I m p o r t a n c e , " l o u r n a l o f E d u c a t i o n a l P s y c h o l o g y ,
XXX^No. ^
1 "The R e l a t i o n b e tw e e n M e o h a n ie a l A b i l i t y T e s t s and V e r b a l and NonV e r b a l I n t e l l i q e n o e T e s t s , " J ournal o f P s y c h o l o g y , 1 9 8 8 , 8 , 85 8-3 6 6 .
nf
p. M. R. W o rtb in S to n , "A S tudy o f Some Commonly Used P e r f o r m a n c e T e s t s , " l o u r n a l o f
A p p l i e d P s y c h ol o g y , X (i9 P 6 > , 5>18-P?7.
.
_
4 . P. P i n t n e r and M. V. Anderson, The P i c t u r e C o m p l e t i o n t e s t .
5. C. M. L o u t t i t , C l i n i c a l P s y c h o l o g y , p . 67.
6. W. S te p h e n s o n . " T e t r a d D i f f e r e n c e s f o r V e r b a l S u b t e s t s R e l a t i v e t o N o n-V erb al Sub­
t e s t s , " J ou rn a l o f e d u c a t i o n a l P s y c h o l o g y , XXII (1 9 8 1 ^ , 884 -8 5 0 .
7. W. P. A le x a n d e r, op., c i t .
S. C. M. M o r r is , Op. c i t .
_p_
o f t h e most commonly used per f o r ma n c e t e s t s " and found them t o be des c r i b a b l e i n t e r ms o f onl y t h r e e f a c t o r s , c a l l e d v i s u a l i z a t i o n , p e r ­
c e p t u a l speed and i n d u c t i o n .
Wr i g h t 1 made a f a c t o r a n a l y s i s of a p a r t
o f t h e o r i g i n a l f t a n f o r d - P i n e t T e s t , e x t e n d i n g from t h e s e v e n - y e a r
l e v e l t o t h e f o u r t e e n - y e a r l e v e l , and i d e n t i f i e d s i x f a c t o r s , c a l l e d
number, s p a c e , imagery, v e r b a l r e l a t i o n s , i n d u c t i o n , and one i n v o l v i n g
reasoning a b i l i t y .
Cf c o u r s e , T h u r s t o n e ' s a n a l y s i s ? o f f i f t y - s i x
p s y c h o l o g i c a l t e s t s must be i n c l u d e d i n any accou nt of f a c t o r a n a l y s i s .
As i s g e n e r a l l y known, he found seven f a c t o r s , which he c a l l e d primary
a b i l i t i e s , among t h e f i f t y - s i x t e s t s .
Th‘ j s t udy n e c e s s a r i l y h a s i t s l i m i t a t i o n s .
I t does not a t t empt
t o i s o l a t e a l l t h e p o s s i b l e mental f a c t o r s a t each age l e v e l i n v e s t i ­
g a t e d , or t o s t u d y each y e a r p e r i o d from n i n e t o s i x t y .
I t w i l l , how­
e v e r , e x t r a c t and name as many f a c t o r s as t he t e s t d a t a w i l l al l ow.
Fix r e D r e s e n t a t i v e age gr oups have been chosen f o r d e t a i l e d a n a l y s i s .
These a r e t h e f o l l o w i n g : n i n e y e a r s , t we l v e y e a r s , f i f t e e n y e a r s ,
twen ty -five to twenty-nine years, t h i r t y - f i v e t c fort.v-fcur years,
and f i f t y t c f i f t y - n i n e y e a r s . An a n a l y s i s
c f t h e s e age p e r i o d s may
s e r v e t o t h r e w l i g h t on t h e pr obl ems under c o n s i d e r a t i o n .
1.. R. W. W riS h t, "A m ao to r A n a ly s is o f t h e O r i g i n a l S t a n f o r d - B i n e t S c a l e , "P s y c h ov , e t r i k a , IV ^Septem ber, 13P9).
2 . L. L. T h u r s t o n e , Op. c i t .
\
CHA°TEg
De s c r i p t i o n
of
I I
S a v i p l i n 3 s and T e s t s
A. The Sampl i ngs
As p r e v i o u s l y s t a t e d , t h e p r e s e n t s t u d y de e s n o t att.eir.pt t o i n ­
v e s t i g a t e each s u c c e s s i v e age y e a r . \Tor does i t e x t e n d t h e i n v e s t i g a ­
t i o n below t h e n i n t h y e a r , s i n c e t h e s c a l e was not d e s i g n e d t c measure
c h i l d r e n below t h i s age.
At t h e n i n t h y e a r s i g n i f i c a n t s c o r e s , i . e . ,
s c o r e s b e t t e r t h a n z e r o on any s i n g l e t e s t , c o u l d s Y / / /
be o b t a i n e d .
The age gr oups s e l e c t e d f o r s t udy a r e , as i n d i c a t e d above: n i n e y e a r s ,
twelve years, f i f t e e n years, twenty-five to twenty-nine yea rs, t h i r t y f i v e t o f o r t y - f o u r y e a r s , and f i f t y t o f i f t y - n i n e y e a r s .
These v a r i o u s p e r i o d s ir.ay be b r i e f l y c h a r a c t e r i z e d . -Nine y e a r s
i s d e f i n i t e l y a p r e - p u b e s c e n t age. Twelve y e a r s can be r e g a r d e d as an
age when p u b e r t y b e g i n s f o r many i n d i v i d u a l s .
F i f t e e n years i s th a t
p e r i o d where t h e cur ve of mental Growth i s known t o appr oach a maximum.
Asch1 has s t u d i e d t h e c h a r a c t e r of mental o r g a n i z a t i o n i n t h e two age
l e v e l s n i n e and t w e l v e .
In a study of t h e age f a c t o r i n mental o r g a n ­
i z a t i o n , G a r r e t t , Eryan and P e r l ? used t h e age l e v e l s n i n e , t w e l v e and
f i f t e e n , which t h e y s t a t e d were " f a r enough a p a r t on t h e growth cur ve
t o make age a r e a l f a c t o r . " Tw e n t y- f i ve t o t w e n t y - n i n e y e a r s i s gen­
e r a l l y a c c e p t e d as t h a t p e r i o d of l i f e i n which a l mos t ever yone has
co mp l et ed h i s e d u c a t i o n and t r a i n i n g , and has embarked on some d e f i n i t e
a c t i v i t y or c a r e e r .
Thi s age p e r i o d was c o n s i d e r e d t h e o p t i ma l age
group i n t h e s t a n d a r d i z a t i o n of t he T e c h s l e r - F e l l e v u e Ec al e, and was
us ed
as a b a s i s f o r compar i son with o t h e r age p e r i o d s .
Thirty-five
t o f o r t y - f o u r y e a r s can be c o n s i d e r e d as ap e r i o d when t h e r e i s t h e
b e g i n n i n g o f a n o t i c e a b l e d e c l i n e i n t h e cu r ve c f ment al growtf.. The
p e r i o d from f i f t y t o f i f t y - n i n e y e a r s t a p s t h a t p a r t o f t h e c u r v e o f
ment al growth and d e c l i n e where t he d e c l i n e i s d e f i n i t e l y n o t i c e a b l e .
Thi s p a r t i c u l a r age group was s e l e c t e d i n p r e f e r e n c e .to any o t h e r of
t h e o l d e r age g r oups, b e c a u s e more c a s e s wfere a v a i l a b l e between t h o s e
years.
All of t h e i n d i v i d u a l s used i n t h e v a r i o u s s a mp l i ng s were s e l e c t e d
from
t h e f i l e s used i n t h e s t a n d a r d i z a t i o n o f t h e E e l l e v u e Ec al e, and
were
made a v a i l a b l e by Dr. Wechsler. None c f t h e s u b j e c t s were p a t i e n t s
1. S. f .
Asch,
"A Study o f Change i n V e n ta l O r g a n i z a t i o n , " A r c h i v e s o f P s y c h o l o g y , No.
O a r r e t t , H. J . Bryan, and F. ?.. P e r l ,
A r c h i v e s o f P s y c h o l o g y , No. 176, J a n u a r y , 19SE.
-9-
"The Age F a o t o r i n M en tal O r g a n i z a t i o n , "
-10-
in the h o s p i t a l .
All t h e s u b j e c t s were t e s t e d by e xami ner s who had
become q u a l i f i e d t o a d m i n i s t e r t h e s c a l e a f t e r a t r a i n i n g p e r i o d under
Wechs l er .
The i n v e s t i g a t o r h i m s e l f examined many o f t h e i n d i v i d u a l s
during the course of s t a n d a r d i z a t i o n cf the s ca l e.
Fach age sampl i ng was s e l e c t e d t c comply as n e a r l y as p o s s i b l e
wi t h K e l l e y ’ s c r i t e r i a c f homogeneity from t h e s t a n d p o i n t c f m a t u r i t y ,
sex, r a c e and g e n e r a l s c h o l a s t i c t r a i n i n g .
Thi s b e i n g a s t u d y c f d i f ­
f e r e n t i a l t r a i t s , i t i s n e c e s s a r y t h a t as many f a c t o r s as p o s s i b l e be
held constant.
The r e s u l t s must not be marred by v a r i a t i o n s which a r e
a t t r i b u t a b l e to extraneous f a c t o r s .
Fcrrcgenei ty c f s amp l i ng s w i l l
avoi d s p u r i c u s c o r r e l a t i o n s .
Kel l ey has w r i t t e n on t h i s p o i n t 1:
r e a d e r ean r e a d i l y s a t i s f y h i m s e l f t h a t r a e e h e t e r o g e n e i t y ,
p r o v i d i n g t h e i n d i v i d u a l s o f t h e on e r a c e a r e on t h e a v e r a g e l o n e r
as a d u l t 3 in b o th t r a i t s c o n s i d e r e d t h a n t h o s e of the o t h e r r a c e ,
o p e r a t e s t o i n t r o d u c e c o r r e l a t i o n , iu3t a s do u n e q u a l l e v e l s o f
m a t u r i t y . S i m i l a r o b s e r v a t i o n s a p p l y t o s e x a n d n u r t u r e . We ma y ,
t h e r e f o r e , c o n c l u d e t h a t ev e n i f t h e s e l e c t i o n of t h e two m e n t a l
t r a i t s i s e x c e l l e n t in the 3en3e t h a t th e m ental c a p a c i t i e s a r e
i n t r i n s i c a l l y independent, p o sitiv e c o rre la tio n s w ill n ev erth eless
commonly be f o u n d b e t w e e n t h e m , owin5 t o t h e h e t e r o g e n e i t y o f t h e
p o p u la tio n employed.
Although sex d i f f e r e n c e s were s t a t i s t i c a l l y i n s i g n i f i c a n t f o r any
o f t h e s u b t e s t s o f t h e f e c h s l e r - F e l l e v u e Ccale us ed i n t h i s s t u d y , what­
e v e r d i f f e r e n c e s might have s t i l l e x i s t e d were removed by o a r t i a l l i n g
o u t t h e f a c t o r c f sex i n every i n t e r c o r r e l a t i c n c f two s u b t e s t s f o r
e v e r y age l e v e l .
The v a r i o u s sampl i ngs were s e l e c t e d randomly w i t h i n
t h e r e t i r e m e n t s s e t f o r t h by K e l l e y .
The group o f n i n e - y e a r - o l d s c o n s i s t e d c f s e v e n t y c a s e s r a n g i n g from
n i n e y e a r s and z e r o months t o n i n e y e a r s and e l e v e n months.
All t h e
c h i l d r e n were w h i t e , Ameri can-born, and a t t e n d e d cne o f t h r e e el e me n t a r y
s c h o o l s l o c a t e d i n m i d d l e - c l a s s s e c t i o n s o f vew York C i t y .
The group o f t w e l v e - y e a r - o l d s c o n s i s t e d c f s e v e n t y - f i v e c a s e s
r a n g i n g from t h e age of t we l v e y e a r s and z e r o months t o t h a t of t wel ve
y e a r s and e l e v e n months.
All t h e c h i l d r e n were w h i t e , Amer i can-bcr n,
and a t t e n d e d one c f t h r e e e l e me n t a r y s c h o o l s l o c a t e d i n m i d d l e - c l a s s
s e c t i o n s of New York C i t y .
The f i f t e e n - y e a r - o l d s compr i sed a group o f n i n e t y - t h r e e c a s e s
r a n g i n g i n age from f i f t e e n y e a r s and zero months t c f i f t e e n y e a r s and
e l e v e n months.
.All t h e c h i l d r e n were wh i t e , Amer i can- bcr n, and a t t e n d e d
one c f t h r e e g e n e r a l h i g h s c h o o l s i n m i d d l e - c l a s s s e c t i o n s c f New York
City.
1.
T. L. K e l l e y , C r o s s t o o i § i n t h e Mini o f Man, p. ?S.
-1 1 -
The age group t w e n t y - f i v e t o t w e n t y - n i n e y e a r s i n c l u d e d one hun­
d r e d and t h i r t y - f i v e s u b j e c t s .
*11 were w h i t e , Amer i can-bor n, and had
had some hi gh s chool t r a i n i n g , r a n g i n g from t he f i r s t y e a r t o g r a d u a t i o n .
They were employed i n o c c u p a t i o n s which were c o n s i d e r e d t o be on a
s i m i l a r l e v e l i n t e r ms of t h e a b s t r a c t i n t e l l i g e n c e r e q u i r e d .
They a l l
be l o n ge d t o Cat egor y TV c f t h e "Six C a t e g o r i e s c f A b s t r a c t I n t e l l i g e n c e "
o f t h e V i n n e s c t a O c c u p a t i o n a l Ra t i n g S c a l e d e s c r i b e d by F i n g h a m. 1 Some
o f t h e o c c u p a t i o n s d e s c r i b e d i n t h i s c a t e g o r y a r e t h e s e cf aut o mechanic,
s t a t i o n a r y e n g i n e e r , f i l e c l e r k and t y p i s t .
The age group t h i r t y - f i v e t c f o r t y - f o u r c o n s i s t e d c f one hundred
and t we n t y - o n e i n d i v i d u a l s .
*11 were w h i t e , Amer i can- bcr n, and had had
e d u c a t i o n a l t r a i n i n g r a n g i n g from t h e s i x t h y e a r c f e l e me n t a r y school
t o t h e f i r s t y e a r c f hi gh s c h o o l .
Thi s group was employed i n o c c u p a t i o n s
s i m i l a r t o t h e s e c f t h e t w e n t y - f i v e t o t w e n t y - n i n e y e a r group. Cn t h e
a v e r a g e , t h e o l d e r a d u l t gr oups have n e t r e c e i v e d as much e d u c a t i o n as
t h e younger .
Ci de r i n d i v i d u a l s wi t h l e s s e d u c a t i o n have been employed
i n o c c u p a t i o n s s i m i l a r t o t h o s e of younger p e r s o n s wi t h mere e d u c a t i o n .
The age group f i f t y t o f i f t y - n i n e y e a r s ol d c o n s i s t e d c f s i x t y - n i n e
oases.
*11 were w h i t e , and were e i t h e r Ameri can-born, or e l s e had been
i n t h e Uni t ed S t a t e s f o r a t l e a s t f o r t y - f i v e y e a r s .
They had a l l a t ­
t e n d e d school i n t h e Uni t ed S t a t e s , and t h e i r e d u c a t i o n ranged from
t h e f i f t h gr ade of e l e me n t a r y school t c t h e e i g h t h .
They were a l s o
employed i n o c c u p a t i o n s s i m i l a r t c t h o s e of t h e two younger a d u l t gr oups.
No a t t e m p t was made t o c o n t r o l r a c i a l d i f f e r e n c e s i n t h i s s t u dy ,
b e c a u s e i t was p e r m i s s i b l e t c combine gr oups of d i f f e r i n g r a c i a l o r i g i n .
I t was, of c o u r s e , n e c e s s a r y t o assume t h a t t h e s e r a c i a l gr oups had, a t
any gi ven age, t h e same mean l e v e l of a t t a i n m e n t wi t h r e g a r d t o t h e
t r a i t s in question.
Cn t h i s p o i n t , Wechsler h a s w r i t t e n 55: "We b e l i e v e ,
however, t h a t t h e d i f f e r e n c e s t h a t might be found bet ween t h e E n g l i s h s p e a k i n g whi t e gr oups i n t h e Uni t ed S t a t e s of d i f f e r e n t ' r a c i a l ' o r i g i n
would not be ver y l a r g e . " ^ e l l e y s a y s 5 : "Fere i n America we can throw
t o g e t h e r a number of r a c i a l s t o c k s and ap pr o xi ma t e t h i s c o n d i t i o n ”
[ e q u i v a l e n c e of means a t any a ge ] .
The groups s e l e c t e d had aver ag e T . C . ' s on t h e We c h s l e r - P e l l e v u e
S c a l e a p p r o x i ma t i n g 100.
These were as f o l l o w s :
1 . w. V. Bimjhaai, A t t i t u d e s and A t t i t u d e T e s t i n g .
<?. D. W eo hsler, V e a s u r e v e n t o f A d u l t I n t e l l i g e n c e , p.
£. T. L. X e l l e y , o t . c i t . , p. ?9.
110.
Chronological
9
vean
I. a.
100.1
S ta n d a r d D e v ia tio n
wi t h
from
each
us ed
14. 19
12
99. a
13.44
As e
15
1 0 3 .5
1 1 .4 ?
25 -2 9
35-44
5 0 -5 9
104.1
1 0 3 .9
1 0 4 .5
11.1®
1 1 .3 2
1 3 .4 5
The agr eement i n a v e r a g e I . C. i s r e l a t i v e l y good when compared
s t a n d a r d i z a t i o n g r oups where t h e a v e r a g e I . C . ' s r a n g e s i m i l a r l y
age t o a g e . 1 Cn t h e b a s i s c f t h e c l o s e n e s s of a v e r a g e I . C . Ts t o
o t h e r , as not ed i n t h e t a b l e above, i t can be s a i d t h a t t h e grcuDS
i n t h i s s t u d y a r e of s i m i l a r i n t e l l e c t u a l l e v e l .
T’ha Te s t s
The F e c h s l e r - F e l l e v u e F c a l e used i n t h i s s t u d y i s an a d o l e s c e n t
and a d u l t t e s t of i n t e l l i g e n c e which i s i n d i v i d u a l l y a d m i n i s t e r e d .
It
i s a Doi nt s c a l e c o n s i s t i n g of t e n d i f f e r e n t s u b t e s t s , f i v e v e r b a l and
f i v e n o n - v e r b a l , b e a r i n g t h e f o l l o w i n g names: (1) I n f o r m a t i o n ; (?) Com­
p r e h e n s i o n ; ( ?) A r i t h m e t i c ; (4) Vemcry ?Dan f o r D i g i t s ; (F) S i m i l a r i ­
t i e s * ; (P) P i c t u r e Arrangement; (7) Di c t u r e Comol et ion; (?) Cb.iect As­
sembly; (9) F l ock Desi gn; (10) D i g i t Fymbcl ( S u b s t i t u t i o n ) .
The t e s t of I n f o r m a t i o n c o n s i s t s of t w e n t y - f i v e i t e m s a r r a n g e d i n
o r d e r , from t h e l e a s t t o t h e most d i f f i c u l t .
Cf t h i s t e s t Wechsler
h a s w r i t t e n * : "The f a c t i s , a l l o b j e c t i o n s al l owe d f o r , t h e r a n g e of
a man' s knowledge i s g e n e r a l l y a very good i n d i c a t i o n c f h i s i n t e l l e c ­
t u a l c a o a c i t y . " Thi s t e s t i s one of t h e f i v e v e r b a l t e s t s .
The t e s t o f Ccmnrehension has t e n i t e ms , each s c o r e d on a two,
one, and zer o s t a n d a r d a c c o r d i n g t o d e f i n e d c r i t e r i a .
These i t e ms a r e
a l s o arranged in the order cf t h e i r d i f f i c u l t y .
About t h i s t e s t , Wechs­
s.
l e r has wr itten*:
P r e o i 3e l y w h a t
i i f f i o u l t t o 3 a.v.
s e n s e and i t i 3 so
seem ingly depends
tio a l inform ation
enoe.
fu n e tio n 3 the Comprehension Test in v o lv e s is
O f f h a n d i t m i l h t b e t e r m e d a t 9 3 t o f s ommon
o a l l 9 d o n t h e Army A l p h a . S u o o e s s o n t h e t e s t
on t h e p o 3 3 9 3 3 i o n o f a c e r t a i n a m o u n t o f p r a o and a G eneral a b i l i t y t o e v a l u a t e pa3t e x p e r i -
Th i s i s a l s o c o n s i d e r e d a v e r b a l t e s t .
1 . L. M. Terman and V. A. M e r r i l l , M easuring I n t e l l i g e n c e , p. BE. I n t h e T a b le o f
I . a . means by age f o r t h e s t a n d a r d i z a t i o n c r o u p , t h e means (fro m Form L o f t h e l a v e
r e v i s i o n o f t h e S t a n f o r d - B i n e t S c a l e l v a ry from a h i c h o f 10 9 .9 a t a a e two and a b a l f
t o a low o f lOO.^ a t t h e aCe o f f o u r t e e n . F o r F o r m V, th e y v a ry from a h i g h o f l O. J ?
«+ t h e ac e o f two and a h a l f t o a low o f 101. P a t t h e age o f f o u r t e e n .
p. The s i m i l a r i t i e s t e s t i s n o t in o lu d e d i n t h i s s t u d y , b e c a u s e i t wae i n t r o d u c e d
l a t e in th e s ta n d a rd iz a tio n
o f t h e s o a l e , and many
o f t h e s u b j e c t s u sed i n t h e , v a r i o u s
s a m p li n g s had n o t b e e n g iv e n t h i s p a r t i c u l a r t e s t . See D. W e c h s le r, Measurement 07
A d u l t I n t e l l i g e n c e , p.. ?.
p. W e o h sle r, ot>. e x t .
A t e s t o f A r i t h m e t i c a l Reasoni ng, c o n s i s t i n g o f t e n i t ems r anged
i n o r d e r o f d i f f i c u l t y , i s t h e t h i r d t e s t i n t he b a t t e r y .
Thi s t e s t
was d e s i g n e d t c be i n t e r e s t i n g to a d u l t s as wel l as t c c h i l d r e n , and
i s a l s o i n c l u d e d under t h e s u b - h e a d i n g c f Verbal T e s t s .
Cf t h i s p a r ­
t i c u l a r t e s t , Wechsl er ha s w r i t t e n 1:
Th9 a b i l i t y t o 9 o l v e a r i t h m e t i c a l p r o b l e m s h a s l o n g b e e n
r e c o g n i z e d a s a s i g n o f m e n t a l a l e r t n e s s . Even b e f o r e t h e i n ­
t r o d u c t i o n o f p s y c h o m e t r i 0 3 , i t wa s u s e d a s a r o u g h a n d r e a d y
measure of i n t e l l i g e n c e .
The f o u r t h t e s t o f t h e v e r b a l group i s t h e Vemory Span f o r D i g i t s .
The f i f t h , S i m i l a r i t i e s , was n e t i n c l u d e d , as not ed above.
The Vemory
Span f o r D i g i t s h a s b o t h t h e f or war d and t h e backward s e r i e s combined
i n one t e s t , and so a l l o w s f o r a wider r ange of s c o r e s .
In d i s c u s s i n g
t h i s p a r t i c u l a r t e s t , Wechsler has w r i t t e n 1 : "The a b i l i t y i n v o l v e d [ i n
t h i s t e s t ] c o n t a i n s l i t t l e o f ' g ' and as Snearman h a s shown
i s mere or
l e s s i n d e p e n d e n t of t h e g e n e r a l f a c t o r . "
The f i r s t c f t h e s e r i e s of n o n - v e r b a l t e s t s i s t h e P i c t u r e Ar range­
ment T e s t , c o n s i s t i n g c f a s e r i e s c f p i c t u r e s , which, when p l a c e d i n t h e
proper seauence, t e l l a story.
There ar e s i x such s e t s of p i c t u r e s t h a t
go t o make up t h i s s u b t e s t .
The f i r s t f o u r a r e s c o r e d f o r accur acy
a l o n e , and t h e l a s t two f o r bot h accur ac y and t i me .
The l a s t t h r e e of
t h e p i c t u r e s e r i e s have mere t h an one s c o r a b l e s o l u t i o n .
Wechsler not ed
concerning t h i s t e s t t h a t 1:
Tt i s t h e t y p e o f t e s t
a b i l i t y t o c o m p r e h e n d and
j e c t must u n d e r s t a n d
the
b e f o r e he i s a b l e t o
3et
which e f f e c t i v e l y m easures a s u b j e c t ' s
3 i z e up a t o t a l o f s i t u a t i o n . T h e s u b ­
w h o l e , must g e t t h e " i d e a " o f t h e
story
himself e f f e c tiv e ly to the task .
The P i c t u r e Compl eti on Te s t c o n s i s t s of a s e r i e s o f f i f t e e n p i c ­
t u r e s , each wi t h some i m p o r t a n t p a r t mi s s i n g .
The s u b j e c t h a s t o d i s ­
c o v e r and name t h e mi s s i n g p a r t .
Thi s t e s t , a c c o r d i n g t c W e c h s l e r , 1
o s t e n s i b l y "measures t h e i n d i v i d u a l ' s b a s i c p e r c e p t u a l and c o n c e p t u a l
a b i l i t i e s i n so f a r as t h e s e a r e i nv o l v e d i n t he v i s u a l r e c o g n i t i o n
and i d e n t i f i c a t i o n of f a m i l i a r o b j e c t s and f o r m s . "
The Fl ock Design Te s t i s a m o d i f i c a t i o n c f t h e Kohs s e r i e s , and
c o n s i s t s of s even d e s i g n s , none of which a r e found i n t h a t s e r i e s .
In t h e W e c h s l e r - F e l l e v u e Fcal e a l l t h e d e s i g n s a r e i n t h e two c o l o r s ,
r e d and w h i t s .
Wechs l er 1 d e s c r i b e d t h i s t e s t as t h e " b e s t s i n g l e
p e r f o r ma n c e i t e m , " and i t seems t h a t t h e " r e p r o d u c t i o n o f t h e t y p e of
d e s i g n d e v i s e d by Kohs i n some way i n v o l v e s b o t h s y n t h e t i c and ana­
lytical ability."
t . W e c h s le r, Ot>. c i t .
-14-
The Ob j e ct Assembly Te s t i s not a s i n g l e i t em.
Tt c o n t a i n s t h r e e ,
f i g u r e f o r m- b o a r d s : a Vani ki n, a F e a t u r e P r o f i l e and a Pand. The Vani k i n i s t h e one made f a m i l i a r by t h e P i n t n e r - P a t e r s c n Scal e.
The Fea­
t u r e P r o f i l e i s s i m i l a r t c t h a t cf the P i n t n e r - ^ a t e r s o n Feature P r o f i l e ,
b u t i s t h e p r o f i l e o f a f emal e i n s t e a d o f a male, has a t w c - p i e c e e a r
i n s t e a d of a f o u r - p i e c e one, and ha s an a d d i t i o n a l c u t o u t a t t h e base
of the s k u l l .
The Pand i s a new f i g u r e f or m- b c a r d , which has been
m u t i l a t e d by c u t t i n g o f f t h e f i n g e r s and a l a r g e s e c t i o n of t h e palm.
Th i s t e s t was i n c l u d e d in t h e S cal e b e c a u s e , a c c o r d i n g t c P e c h s l e r 1,
’’i t t e l l s us somet hi ng about o n e ’ s mode o f p e r c e p t i o n , t h e degr ee t c
which one r e l i e s on t r i a l and e r r o r met hods, and t h e manner i n which
one r e a c t s t o m i s t a k e s . "
The l a s t t e s t , t h e D i g i t Symbol or S u b s t i t u t i o n T e s t , i s t h e f a m i l ­
i a r /'rmy P e t a D i g i t Symbol T e s t .
The t i T e al l owed f o r t h i s t e s t has
been r educed from two mi n u t es t o one and o n e - h a l f .
T e c h s l e r has n o t e d 1
t h a t t h i s t e s t r e o u i r e s t h e s u b j e c t " t c a s s o c i a t e c e r t a i n symbols with
c e r t a i n e t h e r symbols, 3nd t h e soeed and a c c u r a c y with which he does i t
s e r v e as a measure c f h i s i n t e l l e c t u a l a b i l i t y . "
1. W eohsler, o t .
cit.
CHAP T E R
Presentation
I I I
of
D at a
Fach cne c f t h e age s a m p l i n g s has been t r e a t e d s e p a r a t e l y .
All
p o s s i b l e c o r r e l a t i o n s bet ween s u b t e s t s were c a l c u l a t e d by P e a r s o n ’ s
prcduct-moment method, and t h e r e s u l t s were p u t i n t o t he form cf c o r ­
r e l a t i o n matrices.
These m a t r i c e s a r e i n c l u d e d i n Tabl es 1-*. Tn
o r d e r t o e l i m i n a t e c o m p l e t e l y any i n f l u e n c e t h a t might have been due
t c t h e grouping t o g e t h e r c f t h e s e x e s i n t h e v a r i o u s sampli ngs, each
s u b t e s t was c o r r e l a t e d a g a i n s t t h e s e x e s by t h e b i - s e r i a l method and
t h e p a r t i a l c o e f f i c i e n t s were c a l c u l a t e d f o r t h e s i x c o r r e l a t i o n
m a t r i c e s . 1 These new s e t s c f i n t e r t e s t c o r r e l a t i o n s were f a c t o r e d by
T h u r s t o n e ' s c e n t r o i d method, and a r e shown i n Tabl es ^ - 1 f .
An a l y s i s c f t h e v a r i o u s c o r r e l a t i o n a l m a t r i c e s was c a r r i e d c u t t o
t h r e e f a c t o r s f o r age n i n e , t c f o u r f o r ages t we l v e , f i f t e e n , t h i r t y f i v e t c f o r t y - f o u r and f i f t v t o f i f t y - n i n e , and t c f i v e f a c t o r s f o r
age t w e n t y - f i v e t c t w e n t y - n i n e .
The numbers o f f a c t o r s e x t r a c t e d f o r
each age p e r i o d ar e i n each i n s t a n c e cne mere t h an t h e number o f f a c t o r s
used in t h e r o t a t i o n p r o c e s s e s .
I t seems t o be t h e acc e p t e d p r a c t i c e c f
i n v e s t i g a t o r s employing t h e method o f f a c t o r a n a l y s i s t o e x t r a c t mere
f a c t o r s c u t of t h e c o r r e l a t i o n t han w i l l be used i n t h e r o t a t i o n s .
Cf c o u r s e cne c o ul d c o n t i n u e t c e x t r a c t as many f a c t o r s as t h e r e
are t e s t v a r i a b l e s .
Put t h i s would be an u n s c i e n t i f i c pr o c e d u r e , s i n c e
t h e o r i g i n a l p u r p o s e has been t o r edu ce t h e number of v a r i a b l e s .
Tf
cne c o n t i n u e d t c e x t r a c t f a c t o r s up t o t h e l i m i t of t h e t e s t v a r i a b l e s ,
one would e v e n t u a l l y be e x t r a c t i n g a r t i f a c t s due t o sampling e r r o r s and
t h e u n r e l i a b i l i t y n e c e s s a r i l y a s c r i b a b l e t c any c o r r e l a t i o n f i g u r e .
There ar e s e v e r a l c r i t e r i a u t i l i z e d i n t h e d e t e r m i n a t i o n c f t he
number cf f a c t o r s t o be removed from any c o r r e l a t i o n m a t r i x . Vone of
t h e s e a r e " f o o l - p r o o f " or m a t h e m a t i c a l l y r i g o r o u s . P u i l f c r d w r i t e s 55:
Ona c r i t e r i o n f o r t h e 3 t o p p i n g p l a c e i a t o P i n ! t h e e t a n i a r l
d e v i a t i o n o f t h a d i s t r i b u t i o n oP r e s i d u a l s i n t h e t a b l a a n d t o
c o m p a r e i t w i t h t h e s t a n d a r d e r r o r oP t h e a v e r a g e " r " i n t h e
o r i g i n a l c o r r e l a t i o n m a t r i x . . . . T h e w r i ’t e r i s i n c l i n e d t o
b e l i e v * t h a t t h i s c r i t e r i o n i3 to o cru d e .
Tn d e t e r m i n i n g t h e number of f a c t o r s t o be e x t r a c t e d i n a sample
problem, D u i l f c r d s ays a g a i n 3:.
1. I t i s t o be n o t e d t h a t p a r t i a l l i n S o u t t h e se x f a c t o r produced v e r y s l i g h t
o h a n ? e 3 i n t h e o r i g i n a l c o r r e l a t i o n s , t h e maximum c h a n g e b e i n g . 0 ®, t h e r e b y i n d i c a t i n g
t h a t th e s e x d i f f e r e n c e s were i n s i g n i f i c a n t , as had a l r e a d y b e e n p o i n t e d o u t by W e o h sle r.
2. J . p . C u i l f o r d , P s y c h o m e t r i c V e t h o i s , p . 4 9 4 .
3. I b i d . , p. 435.
-15-
-1"When we c a r r y t h r o u g h t h e a n a l y s i s f o r t h e t h i r d f a c t o r , we
f i n d t h r e e f a c t o r s of r e a s o n a b l e s i z e , two of which c o n t r i b u t e
m o r e t h a n . 1 0 0 t o t h e o o m m u n a l i t y . We r e t h e r e o n l y o n e s i g n i f i ­
c a n t f a c t o r l o a d i n g h s r e , we s h o u l d b e s k e p t i c a l o f t h e r e a l i t y
of t h e t h i r d d i m e n s i o n . 5 u t when a t l e a s t t h r e e of t h e e i g h t
t e s t s h a v e s o much i n c ommon o v e r a n d a b o v e t h e c o m m u n a l i t y i n ­
v o l v i n g f a c t o r s o n e a n d t w o , t h e n we f e e l j u s t i f i e d i n a d o p t i n g
the th ir d fa c to r as r e a l .
Thur s t one has a l s o c o n s i d e r e d t h i s problem, and has s e t f o r t h s e v ­
eral possible c r i te r i a .
They a r e as f o l l o w s 1 :
(1) C o n tin u e u n t i l one c a n a s c e r t a i n by mere i n s p e c t i o n of
r e s i d u a l s t h a t mors th a n enough f a c t o r s have been removed.
(2) A 3im ple p r o c e d u r e i s t o compare th e d i s p e r s i o n of the
r e s i d u a l s w ith th e p r o b a b l e e r r o r s of g iv e n c o e f f i c i e n t s .
(3) Another i n t e r n ? s t a t i o n i s t o c o n s id e r the c o n t r i b u t i o n s
t h a t e a c h new o o l u m n o f f a c t o r l o a d i n g s m a k e s t o w a r d t h e c o r ­
relation coefficient.
I f th e two l a r g e s t a b s o l u t e v a lu e s in a
ne w c o l u m n a r e , s a y . 2 0 a n d . 3 0 , t h e n t h e ma x i mu m c o n t r i b u t i o n
o f t h e new f a c t o r i s t h e p r o d u c t . 0 ? t o o n e o f t h e g i v e n c o r ­
r e l a t i o n s o r t o o n e o f t h e g i v e n r e s i d u a l s . Tf t h e r e a r e o n l y
a f e w s u c h v a l u e s i n t h e new c o l u m n , i t s e e m s r e a s o n a b l e t o
s u p p o s e t h a t t h e new f a c t o r i s a t l e a s t n o t o f m a j o r s i g n i f i ­
cance in the system .
(4) A v a r i a n t o f ( 3 ) i s t o e x a m i n e t h e l a r g e s t p o s i t i v e and
t h e l a r g e s t n e g a t i v e e n t r i e s i n a new c o l u m n o f t h e f a c t o r i a l
m a t r i x . Tf t h e s e a r e , s a y + . 2 0 a n d - . 3 0 , t h e n t h e t h i c k n e s s o f
t h e c o n f i g u r a t i o n d o e s n o t e x c e e d . 5 0 i n t h e new d i m e n s i o n a n d
t h i s 3 h o u l d b e t h e maxi mum p r o j e c t i o n t h a t c a n b e o b t a i n e d by
r o t a t i o n fo r the minor dim ension of the system .
(5) A n o th e r method f o r d e t e r m i n i n g th e p r o p e r number of f a c ­
t o r s to e x t r a c t would be t o c o n s i d e r t h e o b t a i n e d d i s p e r s i o n s
o f t h e r e s i d u a l s f o r t w o s u c c e s s i v e f a c t o r s t h a t w o u l d be e x ­
p e c t e d i f t h e v a r i a n c e i n t h e t a b l e s w e r e a l l due t o c h a n c e or
to v a ria b le e r r o r s .
A c r i t e r i o n of t h i s ty p e would i n v o l v e th e
number o f d e g r e e s o f f r e e d o m in t h e f a c t o r i a l m a t r i x a f t e r de­
term in in g each f a c t o r . T hurstone has s ta te d th a t a s a t i s f a c t o r y
c r i t e r i o n of th is 3 o rt has not yet been developed, but T ucker'3
em p iric method, a l t h o u g h not yet r a t i o n a l l y proven, seems to
give t h i s r e s u l t .
the
The u n r o t a t e d f a c t o r s e x t r a c t e d from t h e c o r r e l a t i o n Beatrix a r e
p r e s e n t e d i n T a b l e s 1? - 1 8.
Cn s t u d y i n g t h e s e f a c t o r s f o r each age
l e v e l , i t i s found t h a t t h e t h i r d f a c t o r e x t r a c t e d f o r age n i n e has
no f a c t o r as high as . 2 1P ( t h e coi rmunali t y c f which i s i t s square and
t h e r e f o r e about . 1 0 0 ) .
Age t w e l v e h a s no f a c t o r l o a d i n g i n t h e f o u r t h
f a c t o r with a ccmTunal i t y as hi g h as . 100.
The t h i r d f a c t o r h a s one
l o a d i n g as h i gh as .
and s e v e r a l a p p r o a c h i n g . C1P. The same o b s e r ­
v a t i o n s can be made f o r age f i f t e e n .
The f o u r t h f a c t o r c f age t we n t y f i v e t c t we n t y - n i n e h a s l o a d i n g s o ve r .81®, b u t the f i f t h has none a t
all.
Age t h i r t y - f i v e t o f o r t y - f o u r p r e s e n t s a mere d i f f i c u l t problem.
i . L. L. T h u r s to n e , Pr i ma ry Mental I h i l i t . i e s ,
pp. 6F f f .
P s y o b o m e tric VonoSraph, Wo. 1, 19P3,
-1 7 -
Fer e b c t h t h i r d and f o u r t h f a c t o r s have no l e a d i n g s of t h e o r d e r .
Pu t s i n c e t he age group f i f t y t o f i f t y - n i n e has t h r e e f a c t o r s t h a t a r e
s i g n i f i c a n t , i t was f e l t t h a t t h e t h r e e - d i m e n s i o n a l system s ho u l d be
r e t a i n e d f o r t h e age group t h i r t y - f i v e t c f o r t y - f o u r ,
further j u s t i f i ­
c a t i o n f o r t h i s p r a c t i c e was o f f e r e d by a c o n s i d e r a t i o n c f t h e f a c t t h a t ,
i f t h e t h i r d f a c t o r were r e a l l y i n s i g n i f i c a n t , i t would shew up as such
in the r o t a t i o n s .
Cn t h i s p o i n t Thur s t one has w r i t t e n 1:
A fte r s o i m l a t i n a t h e r o t a t i o n s , the t h i r d f a o t o r would drop out
as i n s i g n i f i o a n t and m e a n i n g l e s s . T h is s i t u a t i o n oan be b r o u g h t
a b o u t b y t h e f a c t t h a t t h 9 o e n t r o i d m e t h o d a d d s new d i m e n s i o n s a s
f a r as p o s s i b l e i n t h e o o m m o n -fa c to r s p a c e , and as f a r as p o s s i b l e ,
o u t s i d e t h e e r r o r s p a c e . I t may h a p p e n t h a t t h e s u c c e s s i v e o e n t r o i d
a x e s a r e n o t e n t i r e l y i n t h e o o m m o n - f a c t o r s p a c e and t h a t a t h i r d
f a c t o r i3 c a l l e d f o r in t h i 3 problem in o r d e r to give r o t a t i o n a l
f r e e d o m f o r e l i m i n a t i n g t h e e r r o r s p a c e prom t h e f i r s t t w o f a c t o r s .
A p p l i c a t i o n o f T u c k e r ’ s e m p i r i c a l method t c t h e v a r i o u s c e n t r o i d
l e a d i n g s a l s o i n d i c a t e d t h a t t he numbers c f s i g n i f i c a n t f a c t o r s t o be
used i n t he r o t a t i o n p r o c e s s s houl d be two f or age n i n e , t h r e e f o r ages
t we l v e , f i f t e e n , t h i r t y - f i v e t o f c r t v - f c u r , and f i f t y t c f i f t y - n i n e , and
f c u r f c r ages t w e n t y - f i v e t c t w e n t y - n i n e .
The u n r o t a t e d f a c t o r l o a d i n g s were t hen r o t a t e d f c r each age p e r i o d
t o make them p s y c h o l o g i c a l l y me a n i ng f ul . This was done by t h e g r a p h i c a l
method d e s c r i b e d by O u i l f o r d . 9 Twc f a c t o r s a r e d e a l t with a t one t i me,
" r o t a t i n g them about a t h i r d a x i s as a c i v e t , computing new f a c t o r l o a d ­
i n g s a f t e r each r o t a t i o n , and r e p e a t i n g t he p r o c e s s as many t i me s as i s
n e c e s s a r y " — t h a t i s , u n t i l f u r t h e r r o t a t i o n s no l o n g e r d e c r e a s e t h e num­
b e r of n e g a t i v e l o a d i n g s .
The r o t a t e d l e a d i n g s a r e p r e s e n t e d i n Tabl es
1P-F4. All c f t h e f a c t o r s i n each age group ar e . p s y c h o l o g i c a l l y meaning­
f u l and, b e i n g o r t h o g o n a l t c each e t h e r , a r e each i n d e p e n d e n t c f t h e o t h e r .
The s u b t e s t s c f t h e We c h s l e r - De l l e v u e S c a l e a r e l i s t e d by number i n
the various Tables.
They a r e : (11 Comprehension; (?) I n f o r m a t i o n ; ( c)
A r i t h m e t i c a l S e a s o n i n g ; (4) E i g i t Span f o r w a r d and Fackwar dl ; (Fl P i c t u r e
Arrangement; (Pi Di e t u r e Compl et i on; (7) Cb.iect Assembly; (P) Flock Design;
(Pi E i g i t Symbol ( o r S u b s t i t u t i o n ! .
The c c mm u n a l i t i e s a r e p r e s e n t e d t c
show how much o f t h e t o t a l v a r i a n c e of each t e s t i s acc ou nt e d f c r by t he
various f a c t o r loadings.
The ccmmunality i s merely t he sum c f t h e s q u a r e s
o f t h e f a c t o r l o a d i n g s f c r each t e s t , r e g a r d e d as p e r c e n t a g e s .
The communa l i t y minus 100 p e r c e n t r e p r e s e n t s t he u n i q ue n e s s o f t h e t e s t , i . e . , t h e
s p e c i f i c f a c t o r and chance and e t h e r f a c t o r s due t c p o s s i b l e e r r o r s of un­
reliability.
The sum of t h e s a u a r e s of t he f a c t o r l o a d i n g s c f each t e s t
i s r e p r e s e n t e d by TT
/ P and - ~ - i n d i c a t e s t he r e l a t i v e p e r c e n t a g e s c f each
f a c t o r , t h a t i s , t h e amount of v a r i a n c e which i s a t t r i b u t a b l e , cn t he
average, tc the variou s f a c t o r s .
1. L. L. T h u r s t o n e , ot>. c i t . . , p. «7.
s>. J . P. S u i l f o r i , ob. c i t . , p.
-1?I
TA=LS
]
( A3E
9)
.......................
I ntertest Correlati on Vatri x (Or i g i n a l , Before Revovi ns Sex c actor)
COVPRE­
HENS I ON
INARITH- D13 IT
FORVA- VET 10 SPAN
T ION
PICTURE
ARRANGE­
MENT
OBJECT
ASSEM­
BLY
PICTURE
COVPLETION
Com prah a n s io n
,.5 0 7
+.3=0
A r it h ­
m e tic
It OpK
c .
1 .0 7 ?
,.441
± .0 3 5
. 49?
± .3 = 1
. 445
± .0 = 4
. 44?
± .0 5 5
° ic tu re
A rra n g e ­
ment
. 391
±. 0*5
.4 0 5
±. 057
. 204
± .0 7 7
. 551
±070
P ic tu re
Comple­
tio n
, . ?71
i . 075
,.3 0 ?
i . 072
oco
± .0 7 4
. • 097
±0=1
,. 354
± .0 7 2
.42=
±.3==
. 405
±. 057
.2 7 9
+ .0 7 4
. 409
+. 057
. 4=9
+. 0=4
. 227
+.37=
Bloclc
D e3i5n
,.444
±. 055
,.414
±. 0=7
.2 ? ?
+ .0 7 4
. 40=
+. 0=7
..5 7 9
+. 054
.2 3 7
+. 07=
. 494
+.0=1
O l3 it
Symbol
. 2*7
±. 075
. 437
± . 0=5
.5 2 1
+ .0 7 2
.9 7 2
+. 070
. 4=4
+. 0=3
.0 9 ?
+.3=3
. 395
+. 059
O b.ieot
Assem bly
DIGIT
SYMBOL
N=70
T n fo rm ab io n
D i4 it
Span
BLOCK•
DESIGN
.5 0 4
+. 0=0
Y3T5: R’i J u r e s in e a c h box r e o r e s e n t o o r r e l a t i o n betw een tw o t e s t s ± th e o r o b a b le e r r o r .
TA = |_S ?
(&3E
12)
I ntertest Correlati on Vatri x (Or i g i n a l , S efore ? evovi n 3 S ex - actor)
COVPREHENSION
ARITH­ DI3IT
IN­
FORMA­ METIC SPAN
TION
P IOTURE
ARRANGE­
MENT
PICTURE
COMPLE­
TION
OBJECT
ASSEM­
BLY
Oom preh e n s io n
M^75
In fo rm a ­
tio n
,. 595
+. 051
A r ith ­
m e tic
.4 7 5
+ .0 9 0
.5 2 1
± .0 4 ?
O iS i t
Span
,.4 1 5
± .0 5 5
.4=9
±. 059
. 3=7
+.33=
P ic tu re
A rran g e­
ment
.2 3 7
+ .0 7 4
.3 0 2
± .0 7 1
.1 3 0
± . 077
. 29=
± .0 7 1
P ic tu re
Comple­
tio n
,.3 5 0
± .3 3 =
.2 9 2
±. 071
- . 022
± .0 7 =
.3 4 9
±. 03=
,.3 3 5
±. 0=9
.3 0 1
± .0 7 1
.2 3 5
+ .0 7 2
.1 4 1
± .0 7 =
.0 1 5
± .0 7 ?
±! 072
. 130
± . 075
91 oc Sc
0 e 3 i4 n
,.3 4 3
± .0 5 9
,.4 0 1
± .0= 5
.. 239
± .0 7 2
,.2 5 0
± .0 7 3
,.2 5 9
± .073
307
± .071
,. 433
± .0= 3
O iiit
Symbol
,.4 5 0
±. 031
.5 0 1
+. 05=
.4 5 1
+. 051
+Io=o
± . 074
,.221
,. 329
±. 070
,.2 9 ?
±. 071
O b.iect
Assem bly
BLOCK
DESIGN
,.4 3 1
+.0=1
DIGIT
SYMBOL
-1C TABLE ?
( A3 e IE')
I ntertest Correlation Vatrix (Or i g i n a l , Before Removing Sex F actor )
COMPRE­
HENSION
IN­
ARITH­ 0 I 3 1T
FORMA­ METIC SPAN
TION
PICTURE
ARRANGE­
MENT
PICTURE
COMPLE­
TION
C o n o ra h 9 n 3 io n
OBJECT
ASSEM­
BLY
block
DESI3N
DI3IT
SYMBOL
M=93
T n f o rn a ­
tio n
, . 33*
1. 059
A rith ­
m e tic
.3 4 5
±.0 5 2
,.4 1 5
1 .0 5 °
D ifit
Span
. 159
i.0 ? 0
. 1 aa
t . 05°
.1 5 2
+. o ? °
P ic tu re
A rranfanent
. 24s
±. 0 a ?
.2 0 5
± .0 5 7
. 449
± .0 5 5
,. 091
±. 0 a 9
P ic tu re
Comple­
tio n
,.2 ° a
±. D?4
,.2 9 7
±. 054
,.1 4 7
1 .0 3 9
-011
1.0 7 0
,. 3 4 9
1.0 5 1
O b je c t
A33embly
,.1 4 2
±.D a 9
, . 195
i . 0a7
-.3 1 9
1 .0 7 0
.1 2 3
+ .0 a9
,.1 9 1
1 .0 3 7
.3 4 4
1.0 5 2
?lo ck
D e e if n
.° ° 2
1 .0 ? 4
, . 3a P
±. 0a l
.2 4 3
+. Da ?
. 01a
1.0 7 0
,. l a 9
1 . 3 aP
. 357
1 .0 5 1
,.4 1 3
1 .0 5 °
D ifit
Symbol
.2 4 0
± .0 ? a
. 153
+. 03=
.15 1
+. 0 5 °
.127
+. 059
.157
+.Da ?
. 277
+ .05 5
.1 1 2
+. Da 9
TABLE 4
(A 3E S
. 133
+. 039
?E -?9)
I ntertest Correlation Vatrix (Or i g i n a l , Before Removing S ex cactor)
COMPRE­
HENSION
ARITH­ D 13 IT
IN­
FORMA­ METIC SPAN
TION
PICTURE
ARRANGE­
MENT
PICTURE
COMPLE­
TION
OBJECT
ASSEM­
BLY
Compre­
h en sio n
inform a­
tio n
BLOCK
DES+3N
V=135
..4 2 4
1 .0 4 ?
Ar i t ti­
met i o
,.2 2 7
1 .0 5 5 1
030
± :?S 4
D ifit
Span
.030
1 .0 5 9 0
.0 4 1
±. 059
.2 2 3
+ .0 5 5
P io ta re
A rr a n f o ­
ment
. 194
1 .0 5 5
,.2 9 0
1 .0 5 3
,.2 0 5
1 .0 5 3
, .0 0 4
1 .0 5 9
P ictu re
Comple­
tio n
.1 2 5
± .0 5 7
.2 4 5
± .0 5 5
.2 2 1
±. 055
,.0 3 2
± .0 5 °
,.1 9 2
±. 05?
Ob.ieot
Assembly
. 0?4
+. 05P
.142
1 .0 5 7
-.0 9 0
1 .0 5 °
-.1 1 1
1 .0 5 7
.0 5 3
1 .0 5 ?
.3 2 9
1 .0 5 2
P lo o k
D e 3 if n
t. 244
1 .0 5 5
,. 2 3 4
1 .0 5 5
,.0 9 4
1 .0 5 ?
T. 0 1 a
± .0 5 °
,.3 5 7
±.050
.. 310
1.0 5 3
,.5 1 7
1 .0 4 3
D ifit
S.ymbol
.2 2 3
± .0 5 5
.2 1 1
«L055
.0 9 5
± .0 5 9
.2 0 7
± .0 5 3
.1 5 0
+ .0 5 7
.1 0 9
1 .0 5 7
.195
± .0 5 5
.2 1 7
± .0 5 5
DI3IT
SYMBOL
-? 0 TABLE 5
(A g e s
B 5-44)
I ntertest Correlation Vatrix (Or i g i n a l , Before Bemoving Cex F actor')
COMPREHENSION
ARITH­
IN­
FORMA­ METIC
TION
DI3IT PICTURE PICTURE OBJECT BLOCK
SPAN ARRAN3E- COMPLE­ ASSEM­ DESIGN
TION
BLY
VENT
Oompreh ansion
D IS IT
SYMBOL
^=121
T n fo rm a b io n
.5 7 4
+. 041
A r ib h m abia
. 331
±. 055
. 4?7
+ .04 7
D i2 ib
Span
.2 9 3
± .3 5 *
.3 5 =
L 053
.347
+.054
P iab u re
A rr a n 4 e manb
. 172
± .0 5 0
. 9*3
+ .057
.291
± .0 5 5
.1 7 1
± .0 5 0
^iab u ra
Oomolab io n
. 373
±. 053
.327
±. 055
.4 1 3
±.3*1
.15?
+ .0*0
. 41.4
+. 0*1
Ob.ieab
433embly
.1 3 7
+ .05 9
. 2=5
+ .053
. 327
+. 055
.153
+.0*0
. 39F
+ .0 5 5
. 33c
+1054
S lo e*
D aai4 n
. 33*
+ .0 5 5
. 31?
+. 055
+’. 057
.1 5 3
+. 050
. 435
+. 050
. 3*7
+. 053
.5 4 1
+.043
O i3 ib
Symbol
. 273
+ .0 5 7
. 34 a
+. 054
. 40?
+.051
.3*3
+ .05 3
. 333
+. 055
. 179
+. 054
.1 * 3
:• 350
( ages
k0 - 5 9 ')
TA °L^
*
. 351
±. 054
I ntertest Correlation Vatrix (Or i g i n a l , Before Bevovin 3 Bex c actor')
COMPRE­
HENSION
AR ITH— DI3IT PICTURE P 1CTURE OBJECT BLOCK
IN­
SPAN ARRANGE­ COMPLE­ ASSEM­ DESIGN
FORMA­ MET 10
BLY
TION
MENT
TION
Oomprah an3ion
M=*9
T n fo rm a b ion
,.* 2 7
+ .0 49
A r ib h m abia
35*
± .071
.5 4 7
± .0 5 7
O iS ib
Span
,.1 7 0
+. 079
,. 3 0 9
+ .374
.4 0 0
+. 039
P iab u ra
A rran4amenb
. 444
+ .0 * 5
. 473
+ .0 3 3
.5 * 7
+ .3 5 5
.3 5 3
± .0 7 1
P iab u ra
Oomplab io n
.411
+ .0 * ?
,.4 1 0
+. 039
<309
£ 039
.3 0 5
+.074
.5 9 4
+.054
Ob.jeab
Aasembly
.2 4 7
+ .0 7 *
.1 7 3
+ .3 7 9
.3 9 9
+ .0 * 9
.193
+. 079
.4*7
t.o s s
.455
± .3 * 4
S lo ak
D a3 i5 n
,.4 0 1
± .o * e
, . 519
±. 059
,. 3 2 1
± .0 5 0
. 299
± .0 7 4
,. 535
±. 055
,.* 2 7
+ .0 4 9
,.4 * 7
±. 0*4
D ilib
Symbol
,. 455
± .0 * 4
, . 357
±.071
,. 492
± .0 3 2
. . 307
± .0 7 4
,.-555
± .0 5 3
x. 433
± .0 3 3
,.5 * 1
± .0 5 3
..5 4 9
± .0 5 7
DIGIT
SYMBOL
-?1TABLE 7
(A3E
o)
S ummary of I ntertest Correlations (S ex F actor Held Constant ')
COVIPRE­
HENSION
Comprah a n 3 io n
T nfo rm atio n
INARITH- 0 13 IT PICTURE PICTURE OBJECT
FORVA- VETIO SPAN ARRANSE- COMPLE­ ASSEM­
T ION
VENT
TION
BLY
.539
.5 3 9
.3 1 3
•
^
. 4=2
;
. 412
. 445
.2 2 0
.335
.412
. 413
. 452
. 235
.2 5 =
.2 4 4
. 283
. 27?
.3 7 4
. 34p
.3 5 9
.4 2 1
.2 9 1
. 339
. 471
. 581
• 3=7
• 23P
. 23P
.3 5 1
. 535
.3 2 2
.433
40?
A rith m e tie
.3 1 3
. 445
D ig it
Span
. 4=2
. 453
.4 1 3
P ia tu ra
A rra n g e ­
ment
. 392
. 43?
.2 3 5
.374
P ic tu re
Comple­
tio n
.227
.3 0 5
.
2*®
. 34?
. 339
3b .j e a t
Assembly
.4 1 2
. 412
.2 4 4
.3 5 9
.4 7 1
. 233
P lo a 'i
D e sig n
. 445
• 41?
. 2 PS
.4 2 1
. 5°1
.2.3®
• 505
C u b s t.
.2 2 3
. 4=2
. 27?
.2 91
• ?®7
.3 5 1
. 322
.4 1 9
P r o b a b l e e r r o r s r a n g e from . 3 Q1 f o r r = 0 . 33 t o .3 5 4 f o r r = . 551
TABLE a
SUBST.
. 227
. 392
k
BLOCK
DESI3N
U se
. 53?
.5 3 ?
»
I?")
Sum.mary of I ntertest Correlations (Bex r ACTOR ueld Constant ')
COMPRE­
HENSION
Compre­
h e n s io n
ARITH­ DI3IT P ICTURE PICTURE OBJECT
IN­
FORMA­ METIC SPAN ARRANGE­ COMPLE­ ASSEM­
BLY
TION
MENT
TION
. 5=2
BLOCK
DESI3N
SUBST.
. 47=
. 411
. 233
. 343
• 292
. 341
.4 5 9
. =22
. 4=5
• 23=
. 2=3
. 259
.3 9 9
.5 1 3
. 387
.1 3 3
- . 32?
.141
. 2=7
.4 9 4
.2 9 3
. 343
.3 3 4
.241
. 495
. 321
.2 7 5
.2 5 9
.191
.1 3 3
.3 0 3
.2 7 7
. 432
. 254
Inform a­
tio n
. =°2
A rith m etia
. 47?
. =22
D ig it
Span
.411
. 495
. 397
p io ta re
A rrangemant
.2 3 3
. 29°
. 133
. 293
P io tu ra
Comple­
tio n
.3 4 3
.2 8 3
- . 32=
. 343
.3 2 1
O b je c t
Assembly
. 292
.2 5 9
.1 4 1
.3 3 4
.2 7 5
.1 3 3
PlooK
D e sig n
.3 4 1
.3 9 9
.2 5 7
.2 4 1
.2 5 9
.3 0 5
. 432
P u b st.
.45®
.5 1 3
.4 9 4
.4 9 5
.1 9 1
.2 7 7
. 234
P ro b a b le e r r o r s r a n g e from . 3 7 7 ffor r = 0 . 33 t o . 3 4 8 f o r r - . 322.
.4 7 9
.4 7 9
-? ? T A 3 L E
9
( A
g e
1 5 )
S ummary of I n tertest Co rrelations (S ex cactor Helo Constant )
compre-
HENSION
Compre­
h e n s io n
IN­
ARITH­ DISIT PICTURE PICTURE 09JECT BLOCK
FORMA­ METIC SPAN ARRANGE­ COMPLE­ ASSEM­ DESI3N
TION
MENT
TION
BLY
.3 9 5
suesT.
.345
.1 5 3
.2 4 5
. 2=9
.140
.2 9 2
.24®
.419
.1 3 1
.2 0 4
. 275
.1 = 9
. 35=
. 10=
.1 5 7
. 449
. 149
-.0 1 9
.2 4 7
• 155
• OP?
-.0 1 3
.115
- . 01?
.0 1 4
• 352
.190
.1 5 =
• 173
• 345
• 353
. 252
.4 1 5
.1 0 0
In fo rm a ­
tio n
.3 9 5
A r it h ­
m e tic
.3 4 5
.4 1 9
D ilit
Span
.1 5 3
• 131
. 157
P ic tu re
A r r a n la mant
.5 4 5
. 204
. 449
P io ta re
Comple­
tio n
.2 8 =
.2 7 5
.1 4 9 -.0 1 9
O b je c t
Assem bly
.1 4 3
• 199
S lo c k
D a s iln
.2 9 2
S u b 3 t.
.2 4 =
.OP?
. 3-52
.1 1 3
.1 9 3
. 345
.3 5 =
. 247 - . 3 1 ?
. 1a =
. 353
.415
• 19=
.1 3 5
. 17?
.2 5 2
.100
-.0 1 9
• 014
.0=2
.0=2
P r o b a b le s r r o r s r a n l e from . 3 7 0 f o r r=0. 33 t o .057 po r r=. 449.
T49LE
10
(A s e s
25-?°)
S ummary of I ntertest Correlations (S ex c actor weld Constant )
COMPRE­
HENSION
Compre­
h e n s io n
ARITH- D13 IT PICTURE PICTURE OBJECT BLOCK
IN­
FORMA­ METIC SPAN ARRANGE­ COMPLE­ ASSEM­ DESIGN
BLY
TION
MENT
TION
.42 1
SUBST.
.2 0 5
• 030
• 1=a
.1 0 3
.0 7 5
. 239
. IS®
,2 5 5
.0 3 3
• 284
. 235
.1 3 5
.2 2 9
.1 9 1
. 22 a
.120
. 1=8
- . 104
.0 7 0
-.0 1 1
.0 0 3
.0 5 2
-.1 1 2
-017
.2 2 7
.1 = 0
.059
.3 5 3
. 134
. 324
.3 0 5
.025
.•514
. 15?
In f o r m a ­
tio n
. 421
A rith ­
m e t ic
.2 0 5
.2 5 5
013 i t
Span
.0 3 0
.0 3 3
. 225
P ic tu re
A rrange­
ment
.1 = 5
.2 = 4
.1 9 0
.0 0 3
p ic tu re
Comple­
tio n
.1 0 3
.2 3 5
.1 ? =
.0 5 2
• ISO
Ob.jsat
Assembly
.0 7 5
.1 3 5
- . 134 - . 1 1 2
.0 5 9
. 324
S lo c k
D e 3 i ln
.239
.3 2 3
. 0 7 0 - . 017
oa3
. 305
.5 1 4
S u b st.
.1==
.1 9 1
.1 3 4
.0 2 5
.1 5 ?
- . 011
.2 2 7
•
P r o b a b l e e r r o r s r a n l e f rom . O' :o f o r r= o . 00 t o . 0 4 3 f o r r = . c 1 4 .
.2 0 5
.2 0 5
j
o^
IA « L E
11 T A q 'e s
? S - 4 4 ^ ------------------ ----------------
------
Eumvary of I ntertest Correlations (Cex caotor Held Constant ')
INCOVPRE—
HENSION FORMAT I ON
Compreh e n s io n
Inform a­
tio n
• c c«„cc. 535
ARITH­
METIC
D 13 IT PICTURE PICTURE
SPAN ARRANGE- COMPLE­
VENT
TION
OBJECT
ASSEM­
BLY
BLOCK
DESIGN
SUBST.
.3 3 3
.2 9 3
. 132
. 323
.1 7 3
. 257
. 231
. ^71
. 374
.24-5
.2 5 3
.2 3 2
. 2*3
. 354
. 344
. 251
. 397
.3 2 3
. 245
. 411
• 159
. 153
• 153
.1 4 5
• 352
.4 3 ?
.2 3 3
.425
. 334
. 322
. 33?
.1 3 5
. 53°
. 152
4r i t h -
m e tio
.3 3 °
. 471
D i2i t
Span
. 293
. 374
. 3*4
P ic tu re
A rrange­
ment
.1 5 2
. 2*5
. 231
.1 3 3
P ic tu re
Comple­
tio n
. 323
• 753
. 337
.1 5 3
. 43=
O b je c t
Assembly
. 173
. 23?
.323
• 133
. 239
. 322
P lo c k
De3 i 4n
.2 = 7
.2 3 3
. 24?
.1 4 5
• 425
.3 3 2
. 1a2
I
P r o b a b le e r r o r s r a n 2 e from . 3=1 f o r r = 0 . 03 t o . 3 4 ? f o r r= . 533.
S u b s t.
. 2=1
. 354
.411
.3 5 2
T A PLE
17
. 334
.1 = 5
(A g e s
*0-591
. 357
.5 3 3
.3 5 7
Summary of I ntertest Correlations (S ex c actor Held Constant !
compre ­
hension
Compre­
h e n s io n
OBJECT
ASSEM­
BLY
BLOCK
DESIGN
SUBST.
.3 = 3
.23=
. 40=
• 451
. 472
. 411
.171
.5 1 9
. 355
. 5=5
.3 3 3
. 3=7
.5 2 0
.479
. 353
.3 0 =
. 1=2
.2 3 7
• 305
.5 = 7
.4=5
• 5=5
.553
. 451
. =35
. 427
. 45=
. 55=
DIGIT 3 ICTURE PICTURE
SPAN ARRANGE­ COMPLE­
TION
MENT
IN­
FORMA­
TION
ARITH­
METIC
. =29
.3 5 2
.1 = 9
. 445
. 547
.3 3 7
.3 3 3
In fo rm a ­
tio n
.5 2 3
A rith ­
m e tic
.3 5 2
.5 4 7
3 i2 it
Span
.1 5 3
.3 3 7
.339
P ictu re
Arrange­
ment
. 445
. 472
. 5=5
. 353
P ictu re
Comple­
tio n
.3 = 3
.4 1 1
.3 3 3
.3 3 5
. 5=7
O b je c t
Assembly
. 23=
.171
. 3=7
. 1=2
. 455
.4 5 1
P lo c d
D e sig n
.4 0 5
.5 1 3
. 520
. 237
• 555
.5 3 5
.4 5 5
Sub3t.
. 451
.355 |
•473
.3 3 5
• 553
. 427
. 55=
Pro bab l e e r r o r s r a n l e from .3 = 1 f o r r = 3 .0 0 t o .3 4 3 f o r r=. 535.
. 54=
.5 4 =
-?4 TABLE
1?
9)
(A 3 E
Centroid Eaotor Lo a d in s s and Covmunalities As Computed by T hurstone ' s Centroid Vethod
Bubtest
1
1I
11
communality h?
. 295
. 537
i
O
tr
- . 214
?
. 717
- . 223
- . 199
• 533
3
.5 2 9
- . 35 4
- . 22 0
. 454
4
. 539
-.1 7 2
. 2 92
.4 = 9
x
• 592
. 253
. 137
.5 4 1
a
.3 7 4
-.1 3 2
-• 137
• 1*9
7
. *32
.1 ^ 3
. 134
.4 3 7
o
. 732
. 325
.3 7 3
.* 4 *
3
. 5*3
. 273
?34
. aa°
TK5
3. 432
3. 547
3. 353
r £
N
.3 9 1
.3 9 1
.3 3 9
•
l
TABLE 14
(A3E
1?)
Centroid c actor Lo a d in s s and Covvunalities As Computed by Thurstone ' s Centroid Vethod
Buetest
i
11
1 11
IV
COMMUNALITY h?
l
. 734
• 11 *
• 355
2
. 773
. 245
.1 3 3
.1 5 9
. 523
.* 7 9
3
• 591
. 599
. 4^3
. 443
. 424
.3 3 =
.* 9 =
3. 221
. 90?
.2 5 9
— 274
- . 239
- . 375
- . 291
. 137
3. 7°2
. 33"
- . 24=
. 295
. 234
• 399
- . 29*
- . 2*9
- . 1=1
3. 539
. 191
- . 242
. 13=
- . 233
. 212
- . 174
- . 334
3. 353
.733
.5 7 2
.3 2 2
.45*
.4 5 3
.55 1
.*3 1
. =5=
• 397
. 3*3
• 34?
&
5
*
7
c
9
5K2
Yl<^
N
TflBi_r >jR
Centroid caotor Loa dinss and Covvunalities AS Computed by T hurstone ' s C entroid Vethod
COMMUNALITY hC
IV
I 11
iI
i
SUBTEST
1
• 591
-.1 3 4
-.3 7 2
-.0 9 1
. 7*9
2
.5 9 3
- . 22*
- . 257
-.1 4 *
9
. 5*7
. 192
.5 4 1
. 54°
. 4dl
.'5 3 7
. °? 4
-.1 5 3
- . 492
- . 221
-.1 3 4
.3 1 1
. 4?9
. 274
.3 52
. 4=5
.5 9 5
.2 0 9
.4 5 3
. 432
. 493
.4 9 *
. 154
TK2
2 . 195
3 .7 3 9
3 .4 1 *
3 .3 4 3
.244
.3 7 9
.3 4 *
.3 3 9
3
A
C
7
o
.
IK 2
N
.1 3 3
- . 214
.3 * 1
.1 9 1
- . 22 ?
-.1 9 9
. 215
. 293
. 12*
-.3 4 1
. 233
- . 295
.3 3 5
,
rtr
£
TABL E
16
(A 3ES
? r- ? 9 ')
Ce ntroid c actor Load N3S AND Communal i t i e s As Computed 9 y Thurstone ' s Centroid Vethod
SU9TEST
1
11
l
. 4=4
.2 9 9
.1 7 3
• 189
.1 1 4
.3 9 4
2
. 572
. 329
. 173
. 457
. 453
. 49?
.3 2 ?
• 351
.3 2 3
.3 1 2
-.9 2 3
.1 5 3
-.1 2 *
- . 495
- . 297
- . 151
• 121
- . 375
.1 * 7
. 47?
.9 9 1
-.1 9 2
. 252
. 252
.1 1 3
.9 3 2
- . 95*
.3 2 *
-.1 7 2
- . 2*9
- . 29=
- . 27?
.421
- . 97°
-.2 2 *
- . 299
. 199
.2 4 9
-.1 7 2
-.1 5 2
. 357
.3 2 9
.3 * 9
.3*7
. 57*
.* 5 3
.3 * 2
ixs
1. 7?9
9. 5=5
9. 592
9. 545
9. 334
I X2
M
.2 9 9
. 973
.9 5 *
.9 * 1
.9 3 7
7
c
9
11
IV
I
•
CO
•tt
'O
3
4
5
*
i
TABLE
(ASES
17
V
COMMUNALITY H?
C5-A4')
Centroid c actor Lo a d in s s and Communalities as Computed by T hurstone ' s Centroid Vethod
SU9TEST
I
1
. 5*2
. 243
2
Q
.3 5 1
. 34?
• *3*
. 4*4
• 171
.3 1 ?
- . 2?5
a
c
i
3
. =34
. 547
7
. 545
c
.3 0 3
.5*1
2 .9 2 5
- . 293
-.3 * 9
-.3 9 2
.1 9 1
9. 754
.3 2 5
. 0?4
9
IX?
TX?
K
IV
COMMUNAL ITY H?
-.2 7 =
.2 4 2
. 512
- . 139
.291
• *92
.9 5 9
. 139
- . 973
- . 23?
.291
.1 5 ?
. 219
9. 2??
- .1 = 1
.971
- . 23*
-.1 7 9
. 24?
• 175
- .1 = 9
9. 3*4
.4 7 9
.34 1
. 443
. 423
.9 3 2
.9 4 9
i
1 11
,
TABLE I B
Ca s e s
•
.5 2 9
. 579
. 431
F 0-F 9)
Centroid c actor Lo a dinss and Communalities as Computed « y T hurstone ' s Centroid Vethod
i
11 1
IV
COMMUNAL I TY H?
.* 1 7
- . 533
- . 9**
-.9 7 ?
.3 7 9
. *73
- . 349
. 335
.92=
. 3?2
. 72*
• 45=
‘.1 9 9
.1 9 1
.2 = 9
.2 5 9
. *52
.3 9 3
. 579
.9 9 *
• 993
. 294
.2 1 7
.1 * 5
- . 93?
.91 1
-.3 7 9
.9 5 3
-.3 3 ?
-.9 5 3
.391
.* 5 2
.523
9
• 7?1
. 795
.1 3 3
-.9 9 1
.1 2 1
-.3 3 9
.5 7 7
.3 2 2
5X8
4. 9?9
9. 53 ?
9 .4 5 2
-.1 = 5
.9 3 ?
9. 317
.4 5 4
.9 3 9
.9 5 9
.9 3 5
SU9TEST
1
1
2
Q
4
5
3
7
o
IX?
N
. 7*5
.7 9 4
i
T A B L E
1 9
( A
9)
s e
PSYCHOLOGICALLY VEANIN3FUL p ACTOR L0ADIN3S OBTAINED AFTER POTATION
SUBTEST
A
8
1
.4 91
.4 3 0
. 459
2
3
3
IX 2
• 560
.S 3 ?
.4 9 1
• 7??
. ?93
. ®20
• 901
.6 2 6
.4 9 9
.541
. 412
. 030
. 247
.1 3 9
009
- . 017
. 5®3
.4 0 3
.4 0 1
.5 2 5
. 147
.4 0 4
• 342
.3 9 2
?. 921
1 .0 0 7
?X2
. 325
• 112
■ 4
9
7
c
T A4 L■E O')
COMMUNALITY HO
( A3 E I ? -)
°SYCH0L03ICALLY VEANIN3FUL ^ACTOR Loadings Obtained After Rotation
"N
COVVUNALITY HO
SUBTEST
A
3
1
. 5 °7
. 94®
.2 0 0
.5 0 =
2
Q
. 72=
.2 9 °
.19®
. 77=
.619
.1 2 9
. 129
. 03F
.2 4 4
-601
12?
. 365
.517
.5 3 9
. 253
020
.1 9 4
.2 2 0
-O F 4
.15®
015
.59®
. ®02
• 392
. ®57
. ®®9
.5 1 3
. 30°
. 419
2. 911
1. 225
1015
. 257
.13®
.1 1 3
4
a
7
Q
9
IX2
V<?
V
TAPLE 21
Cage
.4 0 3
.5 2 4
.5 4 1
151
°SYCHOLOS13ALLY VEANlNGFUL ^ACTOR LOADINGS 03TAINED AFTER ROTATION
r\
COMMUNAL ITY H2
SU9TEST
A
3
1
.2 4 5
.4 7 3
. 273
.2 5 9
2
.1 4 2
. 499
. 395
. 414
3
4
• 153
.7 2 9
-0 3 9
- . 12 ®
. 497
.2 9 5
.4 2 4
-.0 7 3
.5 3 0
.1 2 5
.4 3 9
.6 0 3
.1 1 7
.2 2 9
.4 3 0
7
o
.3 5 7
-.0 5 4
. 557
.4 4 1
.3 5 7
.1 4 0
.507
. 404
9
• 353
.1 6 9
-.001
.1 5 5
1 .1 1 3
1.3 1 9
• P°3
.1 2 4
.1 4 5
099
5
a
7X2
IK ®
N
• 169
-P777
T A SLE
(A 3E S
95-?9)
PSYCHOLOSICALLY VEAN1N3FUL FACTOR L0ADIN3S OBTAINED AFTER POTATION
rs
SUBTEST
A
6
1
3
3
4
5
a,
7
a
.5 4 0
.5 0 4
.0 3 4
.0 5 1
. 344
- . 095
.0 3 5
. 174
. 395
.059
.3 7 0
• 071
.0 1 9
.193
. 493
-• 097
.1 1 5
.0 01
-.0 4 9
.3 5 4
.1 3 5
-.1 3 7
-.1 0 9
. 349
. 379
. 739
. 7d3
. 309
.909
. *39
.4 1 5
.5 51
.1 3 3
. 391
.4 0 3
-.0 3 3
. 331
- . 101
.9 3 7
• 0°9
.0 4 9
.1 0 4
. 153
9
TX?
IX?
N
TA 9LE
5?
Ca 3 e s
D
OOVMUNALITY H?
.373
.4 4 3
. 354
. 379
.3 7 3
. 335
.5 3 9
. 539
. 343
1. 379
^ e - a a 1)
a SYCH0L03ICALLY Vea n in sfu l c actor Loadinss Obtained After P otation
r\
COWUNALITY H9
B
SUBTEST
A
.1 9 7
.3 1 9
. 505
. 453
3
. 397
. 313
.501
. 594
3
. 441
• 33?
. 3a e
4
5
a
. 4=3
.0 9 9
. 590
. 399
• 171
. 441
.3 3 3
.3 7 0
-.0 3 9
0
«p
o
1
.9 4 7
.4 0 1
. 473
7
c
• 001
. 341
. 530
. ?4=
. 33®
. 707
.0 0 4
.5 5 1
9
.5 1 9
.3 5 3
. 335
. 393
r< 5
TV5
T
1 .0 0 7
1 .9 1 3
1.15=
.1 1 3
.301
.1 5 9
TA3LE
94
U ses
E O - * ? ')
DSYCH0L03ICALLY Vea n in sfu l ^ actor Loadinss Obtained After P otation
"V
COMVUNALITY h 7
B
a
SUBTEST
1
3
3
4
c;
5
7
0
9
5X?
1X2
N
l
• 059
. 904
.171
.5 9 0
. 474
.5 9 3
. 414
.4 1 5
. 479
.1 5 1
. 579
.1 5 1
.5 7 5
. 959
.1 9 1
.391
. 351
.1 7 3
.3 5 7
.4 3 7
.091
.339
• 194
.531
.493
.599
. 439
.5 4 5
. 990
.5 7 5
. 343
.6 0 7
.5 3 0
.5 3 7
1. 533
1.939
1.750
. 159
. 303
.195
.5 4 6
.6 3 3
CHA°TE9
I nterpretation
of
IV
the
Re s u l t s
Tt i s e v i d e n t , unon i n v e s t i g a t i o n o f t h e i n t e r t e s t c o r r e l a t i o n a l
m a t r i c e s , t h a t t h e c o r r e l a t i o n s between t he s u b t e s t s o f what ever age
grouo a r e D o s i t i v e , e x c e p t f o r a few which, a l t h o u g h n e g a t i v e , ar e
i n s i g n i f i c a n t l y so.
The number o f n e g a t i v e c o r r e l a t i o n s a r e f ewer i n
t h e o r i g i n a l c o r r e l a t i o n m a t r i x t h a n in t he m a t r i x with t h e sex f a c t o r
eliminated.
Fut t hey a r e i n each c a s e s u f f i c i e n t l y c l o s e t o zer o t o be
called in s ig n if ic a n tly negative.
That most of t he c o r r e l a t i o n s a r e
p o s i t i v e i s t o be e x p e c t e d , s i n c e each o f t h e s e v e r a l s u b t e s t s was
i n c l u d e d i n t h e Fcal e b e c a u s e i t was p u r p o r t e d t c measure i n t e l l i g e n c e
o r some a t t r i b u t e o f i t .
The r a t h e r low o r d e r of t h e v a r i o u s i n t e r ­
c o r r e l a t i o n s i s i n l i n e wi t h t h e f a c t s found i n a l l mental t e s t s .
£
t e s t o f i n t e l l i g e n c e has low c o r r e l a t i o n s between i t s p a r t s , b u t each
p a r t c o r r e l a t e s t o a much h i g h e r degr ee with t h e e n t i r e s c a l e .
Fechs l e r 1 g i v e s t h e c o r r e l a t i o n s o f each p a r t of h i s f c a l e with t h e t o t a l .
They a r e a l l much h i g h e r t h a n t h e i n t e r c o r r e l a t i o n s among t he p a r t s .
Fut i t i s a l s o e v i d e n t t h a t t h e r e ar e changes i n t h e d e g r e e of
c o r r e l a t i o n from age t c age.
The t h i r t y - s i x i n t e r c o r r e l a t i o n s c a l c u ­
l a t e d a t each age l e v e l were a ve r a ge d i n o r d e r t o n o t e t h e s e changes
b e t t e r , wi t h t h e f o l l o w i n g r e s u l t s :
CHRONOLOGICAL AGE
A v sra 5 9 o ? t h 9
" r 's "
S ta n d a rd D e v ia tio n
9
1?
15
2 5 -2 9
P 5 -4 4
5 0 -5 9
.3 7
. 34
.2 3
• 28
.3 1
. 43
.1 0 3
. 1 28
.1 1 1
.1 1 0
.1 0 0
• 128
There i s , t h e n , a d e f i n i t e d e c r e a s e i n t h e aver a ge o f t h e s u b t e s t
i n t e r c o r r e l a t i o n s t h r o u g h t h e age grouc t w e n t y - f i v e t o t w e n t y - n i n e ,
f o l l o w e d by a d e c i de d i n c r e a s e f o r t h e c i d e r ages.
This s u g g e s t s a
g r e a t e r d i f f e r e n t i a t i o n i n a b i l i t i e s wit h p r o b a b l e s p e c i a l i z a t i o n , and
a l a t e r r e o r g a n i z a t i o n o f a b i l i t i e s due p e r haps t o compl et e m a t u r a t i o n
of a l l f u n c t i o n s , which would seem t c i n d i c a t e a g r e a t e r f l e x i b i l i t y
in the handling cf complex ities.
The t e n d e n c y f c r i n t e r c c r r e l a t i c n s of t e s t s t o d e c r e a s e wi t h age
h a s been n o t ed by O a r r e t t , Pr yan and P e r l , 1 who wrote c o n c e r n i n g t h e i r
1. P. W eohaler, Measurement o f A d u l t I n t e l l i g e n c e .
H. T. G a r r e t t . H. J . B rya n , a n i R. F. P e r l , - " T h e Atfe F a c t o r i n V e n t a l O rg a n iz a ­
t i o n , " A r c h i v e s o f P s y c ho l o g y , No. 176, J a n u a r y , 13PF.
<5 .
-ops t u d y " t h a t t h s r f i l e o f g e n e r a l a b i l i t y i s minimized i n f a v o r o f s p e c i a l
a b i l i t i e s a s age i n c r e a s e s . " P r e v i o u s i n v e s t i g a t i o n s on o t h e r groups
o f c h i l d r e n by T h o r n d i k e , 1 by P r y a n , 9 and by Anas t as i * have l e d t o e s ­
s e n ti a l l y sim ilar findings.
As ch, 4 in a s t udy of change in ment al o r ­
ganization, stated that:
T he r e e u l t e o f t h e o r e e e n t i n v e s t i g a t i o n 3how t h a t b e t w e e n t h e
a g e s o f 9 an d 1? t h e r e h a s o c c u r r e d i n o a r g r o u p a s i g n i f i c a n t
r e d u o t i o n i n t h e r e l a t i o n s h i p s b e tw e e n a number o f i n t e l l e c t u a l
f u n c t i o n s . The f a c t o r a n a l y s i s c o n f i r m s t h i s f i n d i n g and f u r t h e r
i n i i o a t e a t h a t a c o n s i d e r a b l e p o r t i o n o? t h e r e d u c t i o n h a s o c c u r r e d
in the f a c t o r of " g e n e r a l a b i l i t y . "
Vost o f t h e l i t e r a t u r e on t h i s s u b j e c t d e a l s wi t h t h e c h i l d o f school
age, b u t seme o f i t i s c o n c e r n e d a l s o wi t h t h e o r e - s c h c o l c h i l d .
Furfey,
Pcnham and F a r g e n t 5 a d m i n i s t e r e d a s c a l e of 17 i t ems t c 4P? new-born
i n f a n t s , r a n g i n g in age from 15 mi nu t e s t o c4 f h o u r s .
They concl uded
t h a t " t h e r e i s no ment al i n t e g r a t i o n i n t h e n e w- b o r n . " F a y l e y ' s 3 l a t e r
w o r k - s t u d i e d i n f a n t s from b i r t h t o t h r e e y e a r s of age, each c h i l d r e c e i v ­
ing a t l e a s t s ix t e s t s .
On t h e b a s i s of h e r f i n d i n g s , Fayl ey concl uded:
That th e b e h a v i o r grow th of th e e a r l y months of i n f a n t d e v e lo p ­
ment h as l i t t l e p r e d i c t i v e r e l a t i o n t o t h e l a t e r d e v e lo p m e n t of
i n t e l l i g e n c e — e v e n t h o u g h t h e l a t e r b e h a v i o r ma y d e p e n d i n l a r g e
p a r t on t h e p r e v i o u s l y m a tu r e d e l e m e n t a r y n e u r a l c o n n e c t i o n s or
behavior p a ttern s.
Very few such a n a l y s e s have been made of t h e a d u l t .
J o n e s and Con­
r a d 7 have d e s c r i b e d some s i g n i f i c a n t changes in per f or mance on t h e Army
Alpha of s u b j e c t s r a n g i n g i n age from 10 t c a0 y e a r s . They r e p o r t e d t h a t :
Tn t h e
s i x t h d e c a d e o f l i f e , a b o u t 40% o f t o t a l
Alpha s s o r e
i s d e r i v e d fro m tw o t e s t s ( T e s t s 4 and
a t age 10, t h e s e t e s t s
c o n t r i b u t e o n l y 2 5 # . As r e p r e s e n t e d i n m e n t a l t e s t s , t h e n , t h e
e f f e c t i v e i n t e l l e c t u a l p o w e r o f t h e a d u l t , much m o r e t h a n t h a t o f
th e 1 0 - y e a r - o l d , i s e v i d e n t l y d e riv e d from a cc u m u la ted s to o k s o f
inform ation.
Another i n v e s t i g a t i o n , t h i s one d e a l i n g with p h y s i c a l t r a i t s , o f f e r s
d a t a s t r i k i n g l y i n agr eement wi t h t h e s e found i n t h e p r e s e n t s t u d y . Peed
and Love3 examined c h a n g e s i n i n t e r r e l a t i o n s h i p s o f s l a r g e number of
1. F. T h o r n d ik e , "M easu ring Human I n t e l l l g e n o e , " H a r p e r ' s Magazine, 13 PO.
9. A. B rya n , " O r g a n i z a t i o n o f Memory i n Young C h i l d r e n , " A r c h i v e s o f P s y c h o l o g y , 1984,
No 10
*8. A. ‘ A n a e t a s i , "A Group F a o t o r i n Im m ediate Memory," A r c h i v e s o f P s y c h o l o g y , No. 19E,
Asoh, "A S tu dy o f Change i n M ental O r g a n i z a t i o n , " A r c h i v e s o f P s y c h o l o g y , No.
t 9 5 5 . MA^0H,. F u rfe y ? * M?"*A. Bonham and M. X. S a r g e n t, "The M ental O r g a n i z a t i o n o f t h e New­
b o r n , " C h i l d L e v e l o b m e n t , I (19 901 , 4S-51.
8 . N. B a y le y , "M ental Growth d u r i n g t h e F i r s t Three Y e a r s : A D e v e lo p m e n ta l S tudy o f
S i x t y - o n e C h i l d r e n by R e p e a te d T e s t s , " G e n e t i c P s y c h o l o g y Monograph, 1988, 14,. No. 1.
7 . H. F. J o n e s and H. S. C onrad, "Growth and D e o lin e o f I n t e l l i g e n c e : A S tudy o f a
Homogeneous Group b e tw e e n t h e Age3 10 and 8 0 , " g e n e t i c P s y c h o l o g y Monograph, V ol. XT II,
^ ° * 3 / , L ? aj ? ^ e e d ^ a n d A. 3 . Love, " B io m e tr ic S t u d i e s on 0 . S. Army O f f i o e r s — S o m a t o l o g io a l
Norma, C o r r e l a t i o n s and Changes w i t h A ge," Human B i o l o g y , IV (198 21 , E09-EP4.
p h y s i c a l t r e a s u r e s i n a group of 5999 Uni t ed S t a t e s Army o f f i c e r s .
These
o f f i c e r s had been examined . yearly and such treasures a s s t a t u r e , wei ght ,
c h e s t c i r c u m f e r e n c e , Du l s e r a t e , and s y s t o l i c and d i a s t o l i c b l ood p r e s ­
s u r e s had been t a k e n .
Changes were found i n t h e i n t e r r e l a t i o n s h i p s
bet ween p h y s i c a l t r a i t s .
The f o l l o w i n g c o r r e l a t i o n s bet ween d i a s t o l i c
ai S y s t o l i c b l oo d p r e s s u r e s houl d be not ed:
»
C H R 0 N 0 L 0 3 1CAL AS E
7 1 -7 *
?6-?5
68-45
46-55
56-64
C o rre la tio n
.2 3
.4 9
• 31
.7 3
.74
P ro b ab le 5 r r o r
.039
.0 1 3
.0 0 9
• 009
.0 1 4
I t becomes e v i d e n t , t h e n , t h a t t h e sstr.e a b i l i t i e s a r e not t apped
by t e s t s of i n t e l l i g e n c e a t v a r i o u s age l e v e l s , or t h a t t he a b i l i t i e s
t h e m s e l v e s a r e not c o n s t a n t .
Tt remains t o be seen what l i g h t t h e
a n a l y s i s of t h e ment al f a c t o r s can throw cn t h i s problem.
At t h i s p o i n t i t would be wel l t c name t h e i s o l a t e d , i n d e p e n d e n t
f a c t o r s f o r each o f t h e s e v e r a l age groups. F i r s t t c be ccn-srdered i s
t h e age group n i n e .
For p u r p o s e s o f d e t e r m i n i n g which o f t h e r o t a t e d
l o a d i n g s of t h e v a r i o u s s u b t e s t s a r e s i g n i f i c a n t i n each f a c t o r , us e has
be e n made of t h e c r i t e r i o n t h a t t h e i n d i v i d u a l l o a d i n g had t o "exceed
t h r e e t i m e s t h e s t a n d a r d e r r o r o f an o r i g i n a l c o r r e l a t i o n o f z e r o , " in
t h e words o f Woodrow.1 For age n i n e t h e f a c t o r l o a d i n g must exceed . F69.
Re f e r e n c e t o Ta bl e 19 (p.
w i l l gi ve t h e r o t a t e d l o a d i n g s f o r
age n i n e .
S i g n i f i c a n t loadings for the f i r s t f a c t o r are:
Comprehension
Inform ation
D i l i t Span
P i s t u r e Arrangement
=
=
=
=
.491
. 5a 0
. 491
.722
O bjeot Assembly
Plook 0e3iln
D i l i t Symbol
= .320
= . PCI
= .323
I t would seem t h a t t h i s f a c t o r c o r r e s p o n d s t o Spear man' s G, s i n c e
i t has s i g n i f i c a n t l o a d i n g s i n seven o f t h e t e s t s and r a t h e r s i g n i f i c a n t
l o a d i n g s i n t h e r e m a i n i n g t e s t s o f Ar i t h me t i c ( . ???) and P i c t u r e Ar range­
ment ( . ( 9 c ) .
S i g n i f i c a n t l o a d i n g s f o r t h e second f a c t o r ar e:
Comprehension
Inform ation
= .430
— .499
Arithm etio
D ilit
Span
~ .541
= .412
Thi s seems t o be t h e f a c t o r of v e r b a l i t y o r v e r b a l i z a t i o n .
I t might
a l s o be t h e f a c t o r of memory, s i n c e each t e s t i n v o l v e s t h a t t y p e of
1 . H. Woodrow, "The Common F a o t o r s i n F i f t y - t w o M ental T e s t s , " V s y c h o m e t r i k a , V ol. IV,
No. 2, J u n e , 1989, o. 99.
function.
Fut f o r age n i n e i t can be s a i d t h a t t h e a b i l i t y d e mo n s t r a t e d
in t h e s e t e s t s i s no t so t h o r o u g h l y r o u t i n i z e d as t o r e q u i r e mer el y memory.
For age t we l v e , r e f e r e n c e s houl d be made t o Tabl e ?0 (p. PP).
The
s i g n i f i c a n t l o a d i n g s a t t h i s age must exceed . Fd^. For t h e f i r s t f a c t o r
they are:
Comprehension
Inform ation
Arithmet io
= .597
= .725
= .77?
Digit
D igit
Span
Symbol
= .M 3
= . 5Q1
Thi s can be s a i d t o be a v e r b a l f a c t o r . The i n c l u s i o n o f t h e F i g i t
Fymbol Te s t in t h i s f a c t o r i s p r ob a b l y e x p l a i n a b l e by t h e f a c t t h a t t h i s
t y p e c f t a s k i s common i n t h e s chool system, and develoDS al ong with
e th e r verbal f unctions.
The second f a c t o r i n age t wel ve has t h e f o l l o w i n g s i g n i f i c a n t t e s t
loadings:
Comprehension
D i g i t Soan
= .3*7
Picture
Picture
= .355
Arrangement
Completion
= .517
= .333
Th i s f a c t o r very p r o b a b l y i s concer ned with t h e s e e i n g o f r e l a t i o n shios in s ocia l s i t u a t i o n s .
That F i g i t Fpan i s a l s o i n c l u d e d i n t h i s
f a c t o r would i n d i c a t e t h a t memory f c r s o c i a l s i t u a t i o n s i s r e c u i r e d be­
f o r e one can see r e l a t i o n s h i p s in them.
F a c t o r t h r e e i n age t we l v e has t h e f o l l o w i n g s i g n i f i c a n t t e s t
leadings:
O b ject Assembly
Block D esign
= .553
* -. 3 0 2
Digit
Symbol
= .332
Thi s f a c t o r can be i d e n t i f i e d b r o a d l y as a p e r f o r ma n c e f a c t o r .
The ve r y h i g h l o a d i n g s i n t h e Ob j e c t Assembly and Fl ock F e s i g n T e s t s
may l e a d one t o b e l i e v e t h a t t h e f a c t o r i s t h a t o f v i s u a l i z a t i o n , i n ­
v o l v i n g p e r c e p t i o n o f form and space r e l a t i o n s .
That t h e F i g i t Symbol
Te s t c o n t a i n s such a f a c t o r i s a u i t e p o s s i b l e .
Tabl e ?1 (p. ?Pl g i v e s t h e r o t a t e d f a c t o r l e a d i n g s f o r age f i f t e e n .
£t t h i s age a s i g n i f i c a n t f a c t o r l o a d i n g exceeds . F l l .
The f i r s t f a c t o r
has s i g n i f i c a n t lo ad in gs in the following t e s t s :
P i c t u r e Arrangement
P ic tu r e Completion
O bjeot Assembly
= .497
= .503
= .357
Block
Digit
Design
Symbol
= .357
= .353
T h i s may b e s t be i d e n t i f i e d as a n o n - v e r b a l or p e r f o r ma n c e f a c t o r .
The second f a c t o r has s i g n i f i c a n t l o a d i n g s i n t h e f o l l o w i n g t e s t s :
Comprehension
Inform ation
* .473
= .499
A rithm etioal Seasoning
P i c t u r e Arrangement
= .729
= .424
Thi s may be b e s t d e s c r i b e d as
a verbal or v e r b a l i z a t i o n f a c t o r .
F i g i t Ppan has a r a t h e r hi gh l o a d i n g h e r e t o o , b e i n g eoual t o . ?8F.
That t h e P i c t u r e Arrangement Te s t f a l l s i n t h i s group i s n o t s u r p r i s i n g ,
s i n c e v e r b a l i z i n g t h e s equence i s q u i t e common.
The t h i r d f a c t o r has t h e f o l l o w i n g s i g n i f i c a n t t e s t l o a d i n g s :
Inform ation
O b . i e o t A3 3 9 m b l y
= .395
= .557
Block
Design
= .507
What t h e t e s t o f I n f o r m a t i o n has i n common with t h e e t h e r two t e s t s
i s not v e r y c l e a r , e x c e p t p e r h a p s t h a t t h e y a l l i n v o l v e some form of
r e s t r i c t i o n accompanying t h e i r s o l u t i o n .
Put t h i s i s n e t l i k e l y t o be
s c , s i n c e t h e t e s t o f A r i t h m e t i c a l Reasoni ng has a n e g a t i v e l e a d i n g i n
th is factor.
I t i s ver y d i f f i c u l t t o d e s c r i b e t h i s f a c t o r , e x c e p t t o
say t h a t t h e t e s t s a l l r e q u i r e an awareness t o t h e envi r onme nt .
In a g e s t w e n t y - f i v e t o t w e n t y - n i n e a s i g n i f i c a n t l o a d i n g exceeds
. ?fp.
Py r e f e r e n c e t o Tabl e ?? (p. ?7^ i t w i l l be seen t h a t t h e f i r s t
f a c t o r ha s s i g n i f i c a n t l o a d i n g s in t h e f o l l o w i n g t e s t s :
C o m p r 9 h9Q3±' on
Inform ation
Thi s
the Digit
= . 5 0
= .534
Digit
Symbol
= .395
i s b e s t d e s c r i b e d as a v e r b a l or v e r b a l i z a t i o n f a c t o r .
Pymbol T e s t i s grouped along with t h e e t h e r two a t t h i s
That
age
l e v e l i n d i c a t e s t h a t t h i s p a r t i c u l a r t y p e o f work i s q u i t e c l e r i c a l in
n a t u r e and has devel oped al ong with v e r b a l a b i l i t y .
I t i s t o be not ed
t h a t , a t t h i s age, t h e t e s t s of A r i t h m e t i c a l Reasoning and F i g i t Fpan
have al mo s t zer o l o a d i n g s in t h i s f a c t o r , gi v i n g e v i d e n c e o f s p e c i a l i z a ­
t i o n in t h e s e a b i l i t i e s .
The second f a c t o r has s i g n i f i c a n t l o a d i n g s in t h e s e t e s t s :
D igit
Thi s
Span
= .493
Digit
appfears t o be a memory f a c t o r ,
Symbol
= .334
s i n c e each t e s t c e r t a i n l y i n ­
volves th a t function.
The t h i r d f a c t o r has t h e f o l l o w i n g s i g n i f i c a n t t e s t l o a d i n g s :
Comprehension
Inform ation
A rithm etical Seasoning
This
striction
fact that
more t h a n
=
=
.551 P i o t u r s
.415 P ic tu re
=. 5 5 1
Arrangement = .351
Completion = .403
p a r t i c u l a r g r o u p i n g seems b e s t e x p l a i n a b l e i n t er ms o f a r e ­
in solution.
All t h e t e s t s seem t o i n v o l v e t h a t f a c t o r .
The
A r i t h m e t i c a l Reasoni ng and I n f o r m a t i o n i n v o l v e t h i s f a c t o r ,
do t h e o t h e r t e s t s , a f f o r d s r e a s o n a b l y good e v i d e n c e t h a t i t
i s t h e f a c t o r c a l l e d r e s t r i c t i o n by Thur s t one .
The f o u r t h f a c t o r o f t h e age group t w e n t y - f i v e t o t w e n t y - n i n e
contains s i g n i f i c a n t loadings in these t e s t s :
P io tu re Completion
O bjeot Assembly
= .379
= .729
P lo o l? D e s i g n
= .743
Thi s can be d e s c r i b e d a s a per f or mance f a c t o r , or one t h a t d e a l s
wi t h s p a t i a l r r a t e r i a l .
The t e s t s o f Di c t u r e Compl et i on and D i g i t
Fymbol, wi t h t h e a l mo s t s i g n i f i c a n t f a c t o r l o a d i n g s o f .
and . ?0 8
r e s p e c t i v e l y , tend to bear t h i s out.
All t h e r e ma i n i n g t e s t s , con­
s i d e r e d t o be v e r b a l i n n a t u r e , have e i t h e r a p p r o x i m a t e l y zer o o r low
n e g a t i v e l o a d i n g s in t h i s f a c t o r .
In t h e age group t h i r t y - f i v e t o f o r t y - f o u r a s i g n i f i c a n t l o a d i n g
ex c e e ds . ? 7 F . On r e f e r r i n g t c Table
(p. ?7) i t w i l l be seen t h a t
t h e f i r s t f a c t o r co n tai n s s i g n i f i c a n t loadings in the following t e s t s :
Inform ation
A rithm etioal
Seasoning
= .397
=. 4 4 1
D igit
D igit
Span
Symbol
=
=
.493
.519
Thi s f a c t o r e v i d e n t l y c a l l s upon memory, s i n c e a l l t e s t s a r e known
t o involve i t .
That I n f o r m a t i o n has a s i g n i f i c a n t l o a d i n g i n memory a t
t h i s age i s a u i t e u n d e r s t a n d a b l e .
That A r i t h m e t i c a l Reasoni ng a t t h i s
age i n v o l v e s so much o f memory i s s u i t e not ewor t hy.
The second f a c t o r has s i g n i f i c a n t l e a d i n g s in t h e f o l l o w i n g t e s t s :
A rithm etioal Seasoning
P io tu r e Arrangement
P io tu re Completion
=. 3 3 3
=. 5 9 0
=. 5 3 0
Object
Assembly
Plook. D e s i g n
= .342
= .707
D i g i t Symbol, wi t h a l o a d i n g of . ? ? ? , i s r a t h e r s i g n i f i c a n t .
It
i s e v i d e n t t h a t a l l f i v e t e s t s c o n s i d e r e d t o be o f a pe r f or ma nc e n a t u r e
a r e , t h e n , i n c l u d e d i n t h i s one f a c t o r .
Thy A r i t h m e t i c a l Reasoni ng i s
a l s o p a r t o f t h i s group i s n e t c l e a r , e xcept t h a t t h i s t e s t has a s i g n i f ­
ic a n t loading in a l l t h r e e of the f a c t o r s .
It is rather likely that all
t e s t s i n v o l v e r e a s o n i n g o f some ki n d.
I t i s known t h a t t h e s o - c a l l e d
p e r f o r ma n c e t e s t s become more d i f f i c u l t f o r t h e o l d e r age gr oups, as
shown by an i n v e s t i g a t i o n o f t h e norms f o r t he v a r i o u s t e s t s s u p p l i e d
by F e c h s l e r i n t h e t e x t on h i s Ccal e.
The t h i r d f a c t o r h a s s i g n i f i c a n t l o a d i n g s i n t h e s e t e s t s :
Comprehension
Inform ation
A rith m etio al Reasoning
*
-
.805
.501
=. 3 8 9
D i g i t Span
P io tu re Completion
- .299
= .347
Thi s f a c t o r i s p r o b a b l y b e s t d e s c r i b e d as d e a l i n g wi t h v e r b a l r e ­
lations.
The two h i g h e s t l o a d i n g s a r e i n t h e t e s t s of Comprehension
and I n f o r m a t i o n , and t h i s f a c t d e f i n i t e l y p o i n t s t o such an i n t e r p r e t a t i o n .
Tt i s not c l e a r why P i c t u r e C o m p l e t i o n • a l s o has a s i g n i f i c a n t l o a d i n g
i n t h i s f a c t o r , b u t i t may be not ed t h a t t h i s t e s t and t h a t o f P i c t u r e
Arrangement seem t o s l i p e a s i l y i n t o t h e v e r b a l gr o up s .
Tn t h e age group f i f t y t o f i f t y - n i n e a s i g n i f i c a n t l o a d i n g exceeds
. ?«1. P e f e r e n c e t o Table ?4 (p. ?7) shows t h a t t h e f i r s t f a c t o r has
s i g n i f i c a n t lo ad in g s in the following t e s t s :
Inform ation
A rithm etioal
D ig it Span
Seasoning
= .474
= .59?
= .414
P i o t u r e Arrangement
"P icture Completion
P lo o ls D e s i g n
= .415
= .479
= .579
Thi s i s a p e c u l i a r a d m i x t u r e o f v e r b a l and n o n - v e r b a l t e s t s , i n d i ­
c a t i n g a breakdown i n t h i s t y p e o f c a t e g o r i z a t i o n f o r t h e c i d e r age
grouD.
i l l t h a t one can say about such a g r c u o i n g of t e s t s i s t h a t t hey
a l l c o n t a i n seme form of r e a s o n i n g .
Tt i s t c be not ed t h a t T i g i t Fpan
i s i n c l u d e d i n t h i s f a c t o r , and a t t h i s age may r e a u i r e t h e a p p l i c a t i o n
o f some s o r t o f r e a s o n i n g .
The second f a c t o r h a s s i g n i f i c a n t l o a d i n g s in t h e f o l l o w i n g t e s t s :
Compr9h9nsion
Inform ation
= .904
= .375
P ic tu r e Arrangament
D i g i t Symbol
= .391
= .427
A r i t h m e t i c a l Rea s oni ng, wit h a f a c t o r l o a d i n g of . cF9, and F l e c k
Des i gn, wi t h a l o a d i n g o f . FF7, a r e a l s o f a i r l y s i g n i f i c a n t .
Pe r e agai n
i t i s e x t r e m e l y d i f f i c u l t t o i n t e m r e t t h e gr oupi ng i n t e r ms o f a s i n g l e
factor.
All t h e t e s t s have p o s i t i v e l o a d i n g s , and t h e a v e r a g e v a r i a n c e
o f a l l t h e t e s t s i s t h e h i g h e s t of t h e t h r e e f a c t o r s e x t r a c t e d f o r t h i s
gr oup, sc t h a t t h i s f a c t o r may be s i m i l a r t o t h e 0 f a c t o r found i n t h e
n i n e - y e a r gr ouo.
The t h i r d f a c t o r of t h e age group f i f t y t o f i f t y - n i n e y e a r s has t h e
following s ig n if ic a n t t e s t
P io tu r a Arrangement
P ic tu r e Com pletion
O b je c t Assembly
loadings:
= .531
= .492
= .389
Plook
D igit
Design = .429
Symbol = . 9 4 3
Thi s i s a p p a r e n t l y a o e r f o r ma n c e f a c t o r .
Tt i s t c b e not ed t h a t
t h e A r i t h m e t i c a l Re a s o ni n g Te s t has a f a i r l y s i g n i f i c a n t l o a d i n g i n
t h i s group, as a l s o i n t h e age group t h i r t y - f i v e t o f o r t y - f o u r y e a r s .
On l o o k i n g o v e r T a b l e s 19-?4 of Ro t a t e d F a c t o r Lo a di ng s , i t may
b e o b s e r v e d t h a t a s i n g l e s u b t e s t may have s i g n i f i c a n t l o a d i n g s i n one
o r more f a c t o r s .
Thi s i n d i c a t e s t h a t t h e s u b t e s t s a r e complex r a t h e r
t h a n s i mp l e .
T h i s c o m p l e x i t y i s c h a r a c t e r i s t i c of most t e s t s t h a t go
t o make up an i n t e l l i g e n c e s c a l e , and i s obs er ved i n t h e f a c t o r a n a l y s e s
o f o t h e r t e s t s and s c a l e s .
Th i s makes t h e i n t e r p r e t a t i o n o f t h e s e t e s t s
r a t h e r d i f f i c u l t , and h e l p s t o acco un t f o r t h e a p p a r e n t l y oppos i ng,
o r a t l e a s t d i f f e r e n t , i n t e r p r e t a t i o n s o f t h e e x a c t D u a l i t i e s measured
by any s p e c i f i c t e s t .
Although c e r t a i n f a c t o r s , such a s t h e v e r b a l , p e r f or ma nc e , r e s t r i c ­
t i o n , and some s o r t o f r e a s o n i n g f a c t o r s , oc c ur as i ndeDendent and may
be i s o l a t e d s e v e r a l t i me s t h r o u g h o u t t h e v a r i o u s ages , t h e same s u b t e s t s
do not al ways compose them.
I t has been not e d t h a t t h e t e s t s of P i c t u r e
Arrangement, Di c t u r e Compl et i on and D i g i t Rymbol f a l l i n t o gr oups t h a t
a r e known t o be v e r b a l t e s t s .
There a r e t i me s when not a l l t h e s o - c a l l e d
per f o r man ce t e s t s f a l l t o g e t h e r t c g i v e s i g n i f i c a n t l o a d i n g s i n t h e p e r ­
formance f a c t o r ,
^he f a c t o r s t h e m s e l v e s change i n t h e a v e r a ge p e r c e n t a g e
o f v a r i a n c e a t t r i b u t a b l e t o them from age t c age.
^or i n s t a n c e , t h e
v e r b a l f a c t o r a t age n i n e has an a v e r a g e v a r i a n c e of 11 p e r c e n t ; a t
age t wel ve i t i s
p e r c e n t ; a t age f i f t e e n , IF p e r c e n t ; a t age t w e n t y f i v e t o t w e n t y - n i n e , P p e r c e n t ; a t age t h i r t y - f i v e t c f o r t y - f o u r , 1?
p er c e n t ; and a t age f i f t y t o f i f t y - n i n e t h e r e i s no c l e a r l y d e f i n e d
verbal factor.
Tt i s t o be no t e d t h a t t h e t e s t o f D i g i t Span i s i n t h e group c a l l e d
v e r b a l a t ages n i n e , t we l v e , and t h i r t y - f i v e t c f o r t y - f o u r , b u t i s n ot
i n t h e v e r b a l group a t age f i f t e e n , and comes out as a s e p a r a t e f a c t o r
a t age t w e n t y - f i v e t o t w e n t y - n i n e .
The same phenomenon may be not ed
wi t h r e g a r d t o t h e t e s t o f A r i t h m e t i c a l Reasoni ng. The p er f or mance
f a c t o r does not a p p e a r u n t i l age t we l v e , where i t does not c o n t a i n t h e
t e s t s of P i c t u r e Arrangement and Di c t u r e Compl et i on.
At age f i f t e e n
t h i s f a c t o r c o n t a i n s a l l p e r f o r ma n c e t e s t s ; a t age t w e n t y - f i v e t o t w e n t y n i n e i t c o n t a i n s a l l p e r f o r ma n c e t e s t s , b u t wi t h two h avi ng on l y f a i r l y
sig n ifican t loadings.
At age t h i r t y - f i v e t o f o r t y - f o u r t h e per f or mance
f a c t o r c o n t a i n s t h e t e s t of A r i t h m e t i c a l Reasoni ng b e s i d e s t h e p e r f o r m ­
ance t e s t s , and a t age f i f t y t o f i f t y - n i n e t h e per f o r man ce f a c t o r a l s o
has a f a i r l y s i g n i f i c a n t A r i t h m e t i c a l Reasoni ng Te st l o a d i n g .
All t h e s e
d a t a t e n d t o i n d i c a t e t h a t t h e f a c t o r s , a l t h o u g h r e c u r r e n t , t a k e on
d i f f e r e n t meaning i n t e r ms o f t h e v a r i o u s s u b t e s t s as t h e y go from age
t c age.
Any g e n e r a l i z e d s t a t e m e n t about t e s t r e s u l t s must, t h e n , t a k e
i n t o account t h e f a c t o r o f age.
A c a r e f u l s t u d y o f b o t h t h e u n r c t a t e d f a c t o r l o a d i n g s and t h e
r o t a t e d , p s y c h o l o g i c a l l y meani ngf ul f a c t o r s w i l l a l s o r e v e a l much p e r ­
tinent material.
I t w i l l be n e c e s s a r y t o examine t h e f i r s t f a c t o r of
u n r o t a t e d l o a d i n g s f o r each age l e v e l .
Th i s f i r s t f a c t o r n e c e s s a r i l y
a c c o u n t s f o r most o f t h e v a r i a n c e o f t h e s u b t e s t s , b e c a u s e t h e f a c t o r
method i s such t h a t t h e f i r s t e x t r a c t i o n t a k e s c u t most of t h e v a r i a n c e
NEW YORK U N I V E R S IT Y
S C H O O L O F E D U C A T IO N
•
LIBRARY
o
of the t e s t s .
For age n i n e i t a c c o u n t s f o r FF p e r c e n t o f t h e t o t a l
v a r i a n c e ; f o r age t w e l v e ,
p e r c e n t ; f o r age f i f t e e n , f4 Der c e n t ;
f o r ages t w e n t y - f i v e t o t w e n t y - n i n e , onl y ?0 per c e n t ; f o r ages t h i r t y f i v e t o f o r t y - f o u r , f ? p e r c e n t ; and f o r age f i f t y t o f i f t y - n i n e , 4F
per cent.
The magni t ude of t h e s e f i r s t u n r o t a t e d l o a d i n g s i s u n a f f e c t e d
by f u r t h e r e x t r a c t i o n s , and may t h u s be compared i n t s r se.
Tt i s im­
m e d i a t e l y e v i d e n t , t h e n , t h a t l e s s and l e s s of t h e v a r i a n c e can be a c ­
c ount ed f o r by a s i n g l e f a c t o r t hr o u g h t h e age group t w e n t y - f i v e t o
t w e n t y - n i n e , whi l e more and more o f t h e v a r i a n c e can be so a c c o un t e d
f o r as t h e h i g h e r age g r ou ps a r e r e a c h e d .
Thi s f i n d i n g f i t s i n p e r ­
f e c t l y well with t h e f a l l and r i s e of t h e aver age i n t e r c o r r e l a t i o n s as
n ot e d above, and l e n d s s t r e n g t h t c t h e i n t e r p r e t a t i o n t h a t t h e r e i s a
g r e a t e r s p e c i a l i z a t i o n u p t c a c e r t a i n p o i n t , f o l l owe d by a l a t e r r e ­
i n t e g r a t i o n of t h e v a r i o u s a b i l i t i e s i n t o a f l e x i b l e whole.
The o l d e r a d u l t , above t h e age of about t w e n t y - s e v e n and c n e - h a l f
y e a r s , becomes mere a b l e t c u t i l i z e h i s v a r i o u s a b i l i t i e s f o r d i f f e r e n t
tasks.
Tt i s as t hough t h e v a r i o u s s p e c i a l i z a t i o n s became p a r t o f t h e
i n d i v i d u a l , and he w3s new a b l e t c use them r e a d i l y and f l e x i b l y t h r o u g h ­
out more t h a n one t a s k .
As t h e immature pe r s on makes use of s e v e r a l
a b i l i t i e s i n o r d e r t c s o l v e a p a r t i c u l a r problem f o r which he as y e t
h as no s p e c i a l method of o r g a n i z a t i o n , sc does t h e o l d e r , c o m p l e t e l y
mat ur e a d u l t .
Fut t h e vcung p e r s o n was f o r c e d t o use s e v e r a l a b i l i t i e s
b e c a u s e he had no s p e c i a l i z e d method f o r a t t a c k i n g t h e problem, whi l e
t h e o l d e r per s on made use o f a v a r i e t y o f a b i l i t i e s , b e c a u s e a l l h i s
a b i l i t i e s were i n t e g r a t e d i n t o such an o r g a n i z a t i o n t h a t he c o u l d use
them e a s i l y and f l e x i b l y .
The g e n e r a l i n t e l l i g e n c e f a c t o r , 3, d e s c r i b e d by fpearman as p e r ­
vadi ng a l l mental t a s k s , can be s a i d t o a p pear , a f t e r r o t a t i o n , i n t h e
age groups n i n e and f i f t y t o f i f t y - n i n e .
I n s p e c t i o n of Ta b l e s 1F-F4,
c o n t a i n i n g t h e r o t a t e d l o a d i n g s , shows t h a t t he h i g h e s t s i n g l e a v e r a ge
p e r c e n t a g e of t h e f a c t o r l o a d i n g s v a r i e s from ahi gh of F? p er c e n t at
age n i n e , t c a low of IF p e r c e n t a t ages f i f t e e n and t w e n t y - f i v e t c
t w e n t y - n i n e , and u p a g a i n t o FO p e r c e nt a t f i f t y t o f i f t y - n i n e .
Al­
though t h e age gr oups t we l v e and t h i r t y - f i v e t c f o r t y - f o u r a l s o have
hi gh av er age p e r c e n t a g e s ,
per c e n t and n p e r c e n t r e s p e c t i v e l y ,
th e indi vid ual l o ad in g s for the various s u b t e s t s i n d i c a t e d e s c r i p t i o n s
on l e s s ge ner a l t e r ms .
Thus t h e ages t we l ve and t h i r t y - f i v e t o t h i r t y n i n e have more d e f i n i t e l y i n s i g n i f i c a n t s u b t e s t l o a d i n g s i n t h e f a c t o r
a c c o u n t i n g f o r t h e h i g h e s t a v e r a g e p e r c e n t a g e of v a r i a n c e t h a n do t h e
ages n i n e and f i f t y t o f i f t y - n i n e .
Cn l o o k i n g a t t h e f i g u r e s headed
i n t h e Tabl es 1P-T4 o f Ro t a t e d
Lo a d i ng s , one can once more n o t e t h e t r e n d toward g r e a t e r s p e c i a l i z a t i o n
up t h r o u g h t h e age t w e n t y - f i v e t o t w e n t y - n i n e , and t h e n , f o r t h e l a t e r
ag es , l e s s s p e c i a l i z a t i o n i n d i c a t i n g g r e a t e r compl exi t y.
The f i g u r e s
(TjT?) show t h e amount o f v a r i a n c e , a c t u a l l y d e s c r i b e d in p e r c e n t a g e s ,
which i s a t t r i b u t a b l e , on t h e a v e r a g e , t o t h e v a r i o u s f a c t o r s .
Pmal l er
p e r c e n t a g e s a r e n o t e d up t o t h e age t w e n t y - f i v e t o t w e n t y - n i n e , and then
l a r g e r ones a p p e a r a g a i n .
Thus f o r age n i n e the p e r c e n t a g e s a r e , r e ­
s p e c t i v e l y , ?? p e r c e n t and 11 per c e n t f o r f a c t o r s one and two; and f o r
age t we l v e , ? p p e r c e n t , 14 p e r c e n t and 11 per cent f o r f a c t o r s one,
two and t h r e e .
At age f i f t e e n , t h e p e r c e n t a g e s a r e l ower , b e i n g 1?
p e r c e n t , 1 F p e r c e n t and 10 p e r c e n t r e s p e c t i v e l y f o r f a c t o r s one, two
and t h r e e .
They a r e s t i l l l ower f or age t w e n t v - f i v e t c t w e n t y - n i n e :
h e r e t h e p e r c e n t a g e s a r e r e s p e c t i v e l y R per c e n t , F p e r c e n t , 10 p e r
c e n t and 1 F per c e n t f o r f a c t o r s one, two, t h r e e and f o u r .
At age
t h i r t y - f i v e t o f o r t y - f o u r t h e y r i s e once mere t o 11 p e r c e n t , 00 p e r
c e n t and 1? p e r c e n t f o r f a c t o r s one, two and t h r e e , and a t age f i f t y
t o f i f t y - n i n e t h e y a r e as h i g h as 17 p e r c e n t , ?D per cent and 00 p e r
cent r e s p e c t i v e l y for the t h r e e f a c t o r s .
CHA°TER V
F umvi ary
and
Co n c l u s i o n s
In o r d e r t o s t u d y t h e ment al f a c t o r s and t o n o t e any changes i n
t h e s e f a c t o r s and t h e i r o r g a n i z a t i o n , v a r i o u s age sampl i ngs s p r e a d i n g
over t h e y e a r s from n i n e t o s i x t y were s e l e c t e d .
The r e s p e c t i v e age
s ampl i ngs ar e n i n e y e a r s , t w e l v e y e a r s , f i f t e e n y e a r s , t w e n t y - f i v e t c
t w e n t y - n i n e y e a r s , t h i r t y - f i v e t o f o r t y - f o u r y e a r s , and f i f t y t c f i f t y nine years.
M l of t h e s e age gr oups had been gi ven t h e satre t e s t ,
namely t h e We c h s l e r - F e l l e v u e I n t e l l i g e n c e F c a l e .
The s u b t e s t s t h a t compose t h e F c a l e were each c o r r e l a t e d with t h e
o t h e r a t every age l e v e l , t h e sex f a c t o r c o m p l e t e l y removed from t h e
i n t e r c c r r e l a t i c n s b.v p a r t i a l l i n g i t o u t , and t h e new i n t e r e c r r e l a t i c n s
of t h e s u b t e s t s f a c t o r e d by T h u r s t o n e ’ s c e n t r o i d method. These f a c t o r
l o a d i n g s were t hen r o t a t e d u n t i l t h e y gave p s y c h o l o g i c a l l y meani ngful
f a c t o r s or a b i l i t i e s , each i n d e p e n d e n t of t h e e t h e r .
The naming c f t h e f a c t o r s , of c o u r s e , r e a u i r e d t hor ough s t u d y of
t h e t e s t s t h a t had s i g n i f i c a n t l o a d i n g s i n them. The f a c t o r s coul d
on l y be named a f t e r much s p e c u l a t i o n , and a t t i me s coul d n e t be d e f i n ­
i t i v e l y described.
I t i s , n e v e r t h e l e s s , i m p o r t a n t t o not e t h a t t h e
names gi ve n t o t h e f a c t o r s by a l l t h e i n v e s t i g a t o r s employing t h e f a c t o r
a n a l y s i s t e c h n i a u e a r e s i m i l a r , and a l l t h e f a c t o r s found i n t h i s s t udy
have been named by e t h e r r e s e a r c h wor k e r s , u s i n g d i f f e r e n t sampl i ngs
and d i f f e r e n t t e s t s . 1
The i n de pe n d e n t ment al f a c t o r s found i n t h i s s t u d y a r e t he f ol l owi ng :
(1) For age n i n e , a G f a c t o r and a v e r b a l f a c t o r .
( ?) For age t we l v e , a v e r b a l f a c t o r , a per f o r man ce f a c t o r , and one
c a l l e d seeing r e l a t i o n s h i p s in s o c ia l s i t u a t i o n s .
(c) For age f i f t e e n , a v e r b a l f a c t o r , a p e r f o r ma n c e f a c t o r , and one
t h a t coul d not be c l e a r l y i n d i c a t e d .
(4) For age t w e n t y - f i v e t o t w e n t y - n i n e , a v e r b a l f a c t o r , a per f or m­
ance f a c t o r , a memory f a c t o r , and a f a c t o r c a l l e d r e s t r i c t i o n i n s o l u t i o n .
(?) For age t h i r t y - f i v e t o f o r t y - f o u r , a v e r b a l f a c t o r , a per for mance
f a c t o r , and a memory f a c t o r .
( a ) For age f i f t y t o f i f t y - n i n e a G f a c t o r ,
a pe r f or mance f a c t o r ,
and a f a c t o r i n v o l v i n g some s o r t of r e a s o n i n g .
I t should be emphasized a t t h i s t i me t h a t t h e f a c t o r s i s o l a t e d in
t h i s s t ud y a r e dependent on t h e s u b t e s t s us ed.
I f one were t o use
1 . Thus T h u r s to n e h a s i i e n t i f i e a su c h f a c t o r s a s V e r b a l , Memory, I n d u c t i o n , and Re­
s t r i c t i o n , amon? o t h e r s . A le x a n d e r h a s i d e n t i f i e d such f a c t o r s as
v e r b a l , and p e r ­
fo rm a n c e .
-39-
d i f f e r e n t t e s t s , one would n a t u r a l l y e x p e c t d i f f e r e n t f a c t o r s .
£gain,
i f o t h e r t e s t s were added t o t h e b a t t e r y o f t e s t s used i n t h i s s c a l e ,
o t h e r g r ou pi ng s might become e v i d e n t .
I t can be s a i d , however, t h a t
t h e above f a c t o r s a r e t h e ones e x i s t e n t i n t h e We c h s l e r - P e l l e v u e Fcal e,
and a r e s u f f i c i e n t t o d e s c r i b e a l l t h e t e s t v a r i a b l e s at each l e v e l .
Put t h i s s t u d y was u n d e r t a k e n wi t h t h e i n t e n t i o n o f doi ng more
t h a n merely d i s c o v e r i n g and i s o l a t i n g t h e ment al f a c t o r s .
The pur pos e
o f t h e i n v e s t i g a t o r was t c n o t e t h e s t a b i l i t y o f t h e s e f a c t o r s from age
t o age, t o s t udy t h e t e s t s t h a t e n t e r e d i n t o t h e f a c t o r s a t each age
l e v e l , and t o o b t a i n f u r t h e r f a c t s r e g a r d i n g mental o r g a n i z a t i o n .
Concerning t h e s t a b i l i t y of t h e f a c t o r s from age t o age, t h e f o l ­
l owi ng c o n c l u s i o n s have been r e a c h e d :
( l ) That t h e same f a c t o r s do not al ways a p p e a r a t each age l e v e l .
(?) That t h e v e r b a l and pe r f o r ma n c e f a c t o r s a r e most c o n s i s t e n t .
(?) That t h e memory f a c t o r a p p e a r s onl y i n ages t w e n t y - f i v e t o
t w e n t y - n i n e and t h i r t y - f i v e t o f o r t y - f o u r .
(4) That a 3 f a c t o r i s found f o r t h e n i n e - y e a r age group, t hen i s
a p p a r e n t l y submerged and a p p e a r s a g a i n , b u t not as d e f i n i t e l y , a t age
f i f t y to f i f t y - n i n e .
On l o o k i n g over t h a t p a r t of Ch a p t e r IV where t he f a c t o r s were
named, i t w i l l be seen t h a t t h e same t e s t s di d n o t al ways e n t e r i n t o
t h e same f a c t o r a t each age l e v e l .
I t can a l s o be seen t h a t where t h e
same t e s t s did e n t e r i n t o t h e same f a c t o r s , t h e y di d not always do so
t o a s i m i l a r d e gr e e .
The s t udy has y i e l d e d s i g n i f i c a n t f a c t s about mental o r g a n i z a t i o n .
Thi s m a t t e r has been more t h o r o u g h l y d i s c u s s e d i n t h e p r e c e d i n g c h a p t e r .
The aver a ge o f t h e s u b t e s t i n t e r c o r r e l a t i o n s r a n ge d from a high of . F?
f o r age n i n e t o a low of . 1 ° at age t w e n t y - f i v e t c t w e n t y - n i n e , and
t h e n back t o a hi gh o f . *F f o r age f i f t y t c f i f t y - n i n e .
The f i r s t
f a c t o r l o a d i n g s e x t r a c t e d a t each age l e v e l a l s o i n d i c a t e d a s i m i l a r
trend.
Thus, f o r age n i n e , t h e f i r s t f a c t o r a c c o u n t s f o r FP p e r c e n t
o f t h e t o t a l v a r i a n c e o f t h e s u b t e s t s ; f o r age t we l v e , FP p e r c e n t ;
f o r age f i f t e e n , ?4 p e r c e n t ; f o r age t w e n t y - f i v e t o t w e n t y - n i n e , onl y
?C p e r c e n t ; f o r age t h i r t y - f i v e t o f o r t y - f o u r , as much as FF p er c e n t ;
and f o r age f i f t y t o f i f t y - n i n e , al most h a l f , o r 4F Der c e n t .
The
magni t ude of t h e s e f i r s t f a c t o r l o a d i n g s i s u n a f f e c t e d by f u r t h e r ex­
t r a c t i o n s , and t h e s e a r e c o mpar abl e among t h e m s e l v e s .
Summarizing t h e t r e n d s i n d i c a t e d i n t h e d a t a , i t can be s a i d t h a t
t h e r e was not ed a t endency toward g r e a t e r s p e c i a l i z a t i o n from age ni ne
t o age t w e n t y - f i v e t o t w e n t y - n i n e , and t h e r e a f t e r an a p p a r e n t r e o r g a n ­
i z a t i o n t o a comp l e x i t y which c o ul d be d e s c r i b e d as f l e x i b l e .
g e n e r a l c o n c l u s i o n s g l e a n e d from a l l t h e d a t a , i n c l u d i n g t h e ma­
t r i c e s o f i n t e r c o r r e l a t i o n s , t h e u n r c t a t e d f a c t o r l o a d i n g s , and t h e
r o t a t e d f a c t o r l o a d i n g s , a r e as f o l l o w s :
(1) The s u b t e s t i n t e r c o r r e l a t i o n s were a l l p o s i t i v e , e x c e p t f o r a
few a t ages t wel ve, f i f t e e n , and t we n t . v - f i v e t o t w e n t y - n i n e , which were
ver y lew n e g a t i v e .
(?) The a v e r a g e of t h e s u b t e s t i n t e r c o r r e l a t i o n s d e c r e a s e d from age
n i n e t o t w e n t y - f i v e t c t w e n t y - n i n e , and t hen i n c r e a s e d up t o age f i f t y
to fifty - n in e .
(F) The p e r c e n t a g e o f v a r i a n c e due t c t h e f i r s t o f t h e c e n t r o i d
f a c t o r l o a d i n g s showed a s i m i l a r t r e n d from an o r i g i n a l h i gh o f FP p er
c e n t a t age ni n e t o a low of ?0 p e r c e n t a t age t w e n t y - f i v e t c t we n t y n i n e , and t hen back t o a n o t h e r s t i l l g r e a t e r h i g h o f a? p e r c e n t 3 t age
f i f t y tc fifty-nine.
(4) C e r t a i n d e s c r i p t i v e f a c t o r s c o u l d be i s o l a t e d a t t he v a r i o u s
a g e s , b u t di d n ot al ways have t h e same t e s t s gr ouped w i t h i n them.
(?) I n d i v i d u a l s u b t e s t s changed t h e i r f a c t o r i a l comp o s i t i o n from
age t o age.
(P) The a ve r a g e v a r i a n c e s due t o t h e v a r i o u s r o t a t e d f a c t o r l e a d ­
i n g s were g r e a t e r f o r ages n i n e , t we l v e , t h i r t y - f i v e t o f o r t y - f o u r ,
and f i f t y t o f i f t y - n i n e t han t h e y were f o r ages f i f t e e n and t went . v- f i ve
to twenty-nine.
(*7) A 3 f a c t o r seemed t o be p r e s e n t a t ages n i n e and f i f t y t c f i f t y n i n e , b u t was not d i s c l o s e d f o r t h e e t h e r age gr ou p s .
(P) Tt was e v i d e n t from an i n s p e c t i o n of t h e c c mmu n a l i t i e s o f t h e
v a r i o u s s u b t e s t s t h a t each s u b t e s t had a u n i c u e c h a r a c t e r i n a d d i t i o n
t o t h e group c h a r a c t e r s , s i n c e none of t h e c c m m u n a l i t i e s approached
unity.
(9) As a r e s u l t o f t h e above f i n d i n g s , i t coul d be s t a t e d t h a t t he
ment al t r a i t s change and under go r e o r g a n i z a t i o n e v e r a span o f y e a r s .
T h e r e f o r e , when i n t e r p r e t i n g t e s t s o f i n t e l l i g e n c e , i t i s o f i mport ance
t o t a k e i n t o c o n s i d e r a t i o n t h e age o f t h e i n d i v i d u a l .
The same t e s t ,
gi ven t o a per s on o f a c e r t a i n age, may not be meas ur i ng t h e same a b i l ­
i t i e s i n him t h a t i t would measure when g i v e n t o an o l d e r or younger
person.
Fven though t h e whole i n t e l l i g e n c e s c a l e may y i e l d t h e same
f a c t o r s f o r a wide span of y e a r s , t h e s e p a r a t e t e s t s t h a t compose t he
s c a l e may not n e c e s s a r i l y be d e s c r i b e d i n t e r ms o f t h e same f a c t o r s
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