独立性の検定・ピボットテーブル
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1 II L04( Thu) : Time-stamp: Thu 12:48 JST hig 2, χ 2, V Excel ( ) L04 II(2016) 1 / 20
2 L03-Q1 Quiz : 1 { 0.95 (y = 10) P (Y = y X = 1) = 0.05 (y = 20) { (y = 10) P (Y = y X = 2) = (y = 20) ( ) L04 II(2016) 2 / 20
3 2 y\x P (Y = 10 X = 1)P (X = 1) P (X = 1 Y = 10) = x P (Y = 10 X = x)p (X = x) = = P (Y = 20 X = 2)P (X = 2) P (X = 2 Y = 20) = x P (Y = 20 X = x)p (X = x) = = ( ) L04 II(2016) 3 / 20
4 L03-Q2 Quiz : Y, X, P (X = Y = ) P (Y = X = )P (X = ) = P (Y = X = )P (X = ) + P (Y = X = )P (X = ) = = Y \X L03-Q3 Quiz : χ 2 ( ) L04 II(2016) 4 / 20
5 1 χ 2 = ( ) = k = C 1 = 4 1. α = 0.05, χ α (4 1) = > 16 3.,. L03-Q4 Quiz : χ 2 1. χ 2 = 1 ( ) = ( ) L04 II(2016) 5 / 20
6 2 α = 0.05, 1 6,., χ 2 k = C 1 = 6 1..,, χ 2 = , χ 0.05 (6 1) = > 4.2,. ( ) L04 II(2016) 6 / 20
7 2 : : V ( ) L04 II(2016) 7 / 20
8 2 : 2 Y \ X A A P( =A, = ) P( =A, = ) P( =A, = ) P( =A, = ) 1 A 2 A N = A, A A n 11 = 1 n 12 = 2 n 21 = 4 n 22 = 5 n ij, 1 i c, 1 j r. r, c. Excel ( ) L04 II(2016) 8 / 20
9 2 :?.., P ( =A, = ) =P ( =A ) P ( = ) f XY (x, y) =f X (x) f Y (y). ( ) L04 II(2016) 9 / 20
10 2 :, y \ x A A P ( = ) p 1 = 3 12 P ( =A ) q 1 = 5 12, (= ). A = N p 1 q 1 = = 1.25 ( ) L04 II(2016) 10 / 20
11 2 : : χ 2 A A Np 1 q 1 Np 1 q 2 Np 1 Np 2 q 1 Np 2 q 2 Np 2 Nq 1 Nq 2 N ( ) 2 = ( ) 2 : χ 2 ( ) p i (i = 1,..., r), q j (j = 1,..., c):. χ 2 = ( )2 = 1 i r,1 j c (n ij Np i q j ) 2 Np i q j ( ) L04 II(2016) 11 / 20
12 2 : χ 2 = (1 1.25) (2 1.75) (4 3.75) (5 5.25) = χ 2 ( ) 0 χ 2., (r 1)(c 1). Example Excel χ 2 Excel RaMMoodle >. ( ) L04 II(2016) 12 / 20
13 1 2 2 : V ( ) L04 II(2016) 13 / 20
14 1 α =..., 2 3, X,Y 4 χ 2 (c 1)(r 1). 5 χ 2 =... 6 χ 2 p,, α / / (X Y / ) ( ) L04 II(2016) 14 / 20
15 L04-Q1 Quiz( χ 2 ), 6,,, ( ) χ α = 0.05,. ( ), /. X Y /. ( ) L04 II(2016) 15 / 20
16 V : V ( ) L04 II(2016) 16 / 20
17 V V V χ 2 : χ 2, N:. V = = V = χ 2 N V χ 2, r 0 V 1 V = 0 V = 1 ( ) L04 II(2016) 17 / 20
18 B V : A = 1, A = 0. A B = 1, A B = 0.? A A A r.? 0 100? 0 1? 2 2 r V r = V ( ) L04 II(2016) 18 / 20
19 V I. RaMMoodle II(2016) /Math ryukoku.ac.jp manaba ( ) L04 II(2016) 19 / 20
20 V α, k, α = P (Y > χ 2 α(k)) χ 2 α(k). k\α ( ) L04 II(2016) 20 / 20
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More informationax 2 + bx + c = n 8 (n ) a n x n + a n 1 x n a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 4
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More information09 II 09/12/ (3D ) f(, y) = 2 + y 2 3D- 1 f(0, 0) = 2 f(1, 0) = 3 f(0, 1) = 4 f(1, 1) = 5 f( 1, 2) = 6 f(0, 1) = z y (3D ) f(, y) = 2 + y
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L06(2014-10-29 Wed), A/D..... http://hig3.net ( ) L06 A/D (2014) 1 / 24 : L05-S1 Quiz :int 16 2 15 x 2 15 1, 16 0 x 2 16 1. L05-S5 Quiz : 2 17 < 200000 2 18, 18. 2 10 = 1024, 2 16 = 65536. log 10 2, log
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