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1 < > CHAPTER 7 (FA: Factor Analysis ) Galton( ) (1888) Spearman(1904 ) . (1) ( ) (2) ( ) . , (Likert) . ( ) Cronbach . , , , , , , , . 8 ? . A 48 15 ( ) . 20 ( , , , ..) . < >Chapter 7. 152 Spearman (1904) Spearman 6.

2 ( , ) . Classic French English Math DiscoverMusic Classic 1 .83 .78 .7 .66 .63 French 1 .67 .67 .65 .57 English 1 .64 .54 .51 Math 1 .45 .51 Discover 1 .4 Music 1 ( ) (f: factor ) ( ).

3 F j . f .. (fact: ) .. 6 2 (factor1: factor2: ) . ( ) . (classic), (French), (English) (Math), (Discovery), (Music) . < > 153 1 2 3 4 5 6 (correlation coefficient) (linear relationship) 1 1 .. yyxxxyiiiiSSSyyxxyyxxr= = 22)()())(( 1 ( ) ( ) . 1 ( ) ( ) . 0 . ? , t.

4 : . 0 . 0= : . 0 )2(~)2/()1(2 = =ndftnrrt cl Difrmaen Mufactor 1 2 6 3 4 5 factor1 factor2665544332211cov +=+=+=+=+=+=fmusicferdisfmathfenglishffr enchfclassic < >Chapter 7. 154 p m (subset) .. (loading) ( subjective) . < > 155 ( ) . , , , , , , , . 8 ? A 48 15 ( ) . 20 ( , , , ..) . +=fLx + = pmpmppmmpffflllllllllxxx ..212121222211121121 x.

5 Mkfff,..,,2 ( : common factor) ijl (factor loading) i j p ,..,,21 (specific factor) . j j (R) + =LLR + ==+ =))((LPLPRLLIR L . ( . VARIMAX .) principal factoring . < >Chapter 7. 156 Principal factoring w/ or w/o iteration R eigen-value( ) eigen-vector( ) p ..21 , peee,..,,21 . pyyy,..,,21 .. ppppppppppeyeyeyxeyeyeyxeyeyeyx+++=+++=+ ++=..:..22112222211211221111 111/ yf=, 222/ yf=, .., pppyf /= pppppppppppppfefefexfefefexfefefex +++=+++=+++=..:..22211122222121212121221 1111 ijjijel = ( ) )..(2222122jmjjjjlll+++ = . (loading) ( ).

6 + = pmpmppmmpffflllllllllxxx ..212121222211121121 ( ) . (1)trivial . 1-2 . 1-2 . factor1 factor2 Error Common factors < > 157(2)Kaiser ( ): 0 ( ) R I 1 1 . 1 1 . SAS .. (3)SCREE : y- , x- SCREE . 80% ( ) . 0102030405060700246810eigen (Factor Rotate) ( ) . (1) : 2 (2) 0.

7 (rotate) QUARTIMAX rotation, OBLIQUE rotation, PROMAX rotation VARIMAX . VARIMAX Kaiser . < >Chapter 7. 158 ? (Likert) . (index) . pxxx,..,,21 . Q4-Q13 . 10 2-3 . 10 ( ) . 2 . 1 loading( ) . 2 . (1) . (2).

8 [SAS] Q4-Q12 . (Likert) (4 , 5 , 7 ) .. DATA = ~ VAR = ~ ~ . < > 159 ROTATE=VARIMAX VARIANCE . REORDER ( ) . COVARIANCE ( ) . (COVARIANCE . default) . (METHOD) default= . 1 80% 1, 2, 3, 4, 5 .(53%) . ( ) ( ) ( ) . 1(factor 1) Q5-Q8 , 2 < >Chapter 7.

9 160 Q10-Q11 . Q4, Q12 2 . ( : Q5, Q6, Q7, Q8), ( : Q10, Q11) . [SPSS] . 1 .. < > 161 . VARIMAX .. SAS . < >Chapter 7. 162 . Factor1 Factor2Q7 Q8 Q6 Q5 Q9 Q10 Q11 Q12 Q4 . 1(factor 1) Q5-Q8 2 Q10, Q11 . ( , , ) (.)

10 (1) (2) ) .. 2 55% Q8 1 Q4, Q6, Q8 .. < > ( ) 163 . ( ) .. ( ) (index) (internal consistency) Cronbach alpha( ) .. ( : observed value) (measurement error) . 0),cov( ,=+=ETETY. (reliability coefficient) . )var()var( )var()var()var( )var()var(),cov(),(222 YTTYTTYTYTY=== , ( ) Cronbach . p ),,2,1(pjETYjjjK=+= ==jjOTTYY0, . = = )var()var(11 )var(),cov(1 OjjOjijiYYppYYYpp < >Chapter 7.