5.8 PROC UNIVARIATE (hitogram, tem and leaf plot, box-whiker plot), (p- ). Univariate( ).. NORMAL (Shapiro- Wilk Kolmogorov-Smirno D- OUTPUT( SAS ). PROC MEANS PROC MEANS. (moment) E( X ). k Sehyug Kwon, Dept. of Statitic, HANNAM Univerity http://wolfpack.hannam.ac.kr Spring, 004 copy right all right reerved. 9
N= ( ) (weight) xi (mean) x = (um) x i n (td) = (kewne) ( xi x) n n xi x ( ) ( n )( n ) 3 (variance) ( xi x) = n (kurtoi) n( n + ) x ( ( n )( n )( n 3) i x ) 4 3( n ) ( n )( n 3) ( 0 0. 3 ) (um of quare) x i (adjuted) ( x i x) (CV) CV = 00 (STDERR) x n,. (mode) ( ). ( ~. µ 0 = 00 ). MU0. Sehyug Kwon, Dept. of Statitic, HANNAM Univerity http://wolfpack.hannam.ac.kr Spring, 004 copy right all right reerved. 30
t-. 0.4095. 4. ( 4 ) 0.048. (nonparametric, ditribution-free tet) (ign tet). Shapiro Wilk. 0.0945 ( ). AL.. 75% (Q3), 50%, 5% Q( ).. Sehyug Kwon, Dept. of Statitic, HANNAM Univerity http://wolfpack.hannam.ac.kr Spring, 004 copy right all right reerved. 3
PLOT. Graphic.. +. AL.?.. Q3 Q ( : 9 ) HISTOGRAM.. Sehyug Kwon, Dept. of Statitic, HANNAM Univerity http://wolfpack.hannam.ac.kr Spring, 004 copy right all right reerved. 3
.. AL... Shapiro-Wilk. Q-Q plot( ). Sehyug Kwon, Dept. of Statitic, HANNAM Univerity http://wolfpack.hannam.ac.kr Spring, 004 copy right all right reerved. 33
A:\JUNE\UNIVAR.doc x ± t( n ; α / ) n 5.9 PROC TTEST (, ), t-,. 5.9. µ σ /.. n Sehyug Kwon, Dept. of Statitic, HANNAM Univerity http://wolfpack.hannam.ac.kr Spring, 004 copy right all right reerved. 34
5.9. PROC TTEST t-.. σ,σ,..... Sehyug Kwon, Dept. of Statitic, HANNAM Univerity http://wolfpack.hannam.ac.kr Spring, 004 copy right all right reerved. 35
: H µ µ 0 (.) 0 : = : ( ) H a : µ µ 0 ( ) H a : µ > µ H a : µ < µ : ( x, x,..., x n ) x, ( x, x,..., x ) x, n = σ σ ) ( σ =,. σ (pooled x variance). x ( µ µ ) = 0 T = ~ t( df = n + n ), p + n n p ( n = ) + ( n ) n + n ( µ µ 00(-α)% : ) (( x x ) t n + n ) *,( x x) t( / ; ) * p + + α n n n + n p + n ( α / ; n ) A, B 8. x = 9, =. 39, x = 93, =. 98... ( =0.05).. (adjuted) t-. T = x x ( µ µ ) = 0 ~ t( df p + n n * = ( / n ) n + ( + n n ) ( / n) + n + ) Sehyug Kwon, Dept. of Statitic, HANNAM Univerity http://wolfpack.hannam.ac.kr Spring, 004 copy right all right reerved. 36
CLASS.txt.. 90%. : H µ µ 0 ( ) 0 : = : H µ µ 0. a :. Sehyug Kwon, Dept. of Statitic, HANNAM Univerity http://wolfpack.hannam.ac.kr Spring, 004 copy right all right reerved. 37
( µ µ ) 90%(Alpha=0. ) 5.9.3 t- t-. EXAMPLE A, B. 8... ( =0.05) A B 3 4 5 6 7 8 74 76 74 69 58 7 66 65 78 79 75 66 63 70 66 67-4 -3-3 -5 0 - : H : µ µ µ 0 (A, B ) 0 a = b d = : H : µ µ µ 0 (A, B ) 0 a b d d µ d 0.375 0 : T = d = = =. 46, / n.67 / 8 d d t( α / ;7) =.365. Sehyug Kwon, Dept. of Statitic, HANNAM Univerity http://wolfpack.hannam.ac.kr Spring, 004 copy right all right reerved. 38
A:\JUNE\TTEST.doc.. : 45 50 53 48 4 5 46 54 39 48 : 5 50 47 55 40 46 58 5 5 43 0.05 95%. A:\JUNE\TTEST.doc A, B 0.. ( : ) A:9.5.3.34 0.4.9 3.7.7.4 3.63.44 B:.99 4.88 5. 7.0 6.89 6.6 5.38 4.40 3.9.87 0.05 95%. 004. Sehyug Kwon, Dept. of Statitic, HANNAM Univerity http://wolfpack.hannam.ac.kr Spring, 004 copy right all right reerved. 39