鐃緒申鐃峻ワ申鐃殉ワ申僚鐃緒申鐃緒申愀鐃緒申鐃�

鐃緒申鐃峻ワ申鐃殉ワ申僚鐃緒申鐃緒申愀鐃緒申鐃�鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申Last modified: Sep 02, 2003

鐃緒申鐃緒申鐃緒申

鐃緒申鐃緒申表 1 鐃祝わ申鐃緒申鐃銃￥申鐃術随申 $X$鐃緒申鐃術随申 $Y$鐃塾間のワ申鐃峻ワ申鐃殉ワ申僚鐃緒申鐃緒申愀鐃緒申鐃緒申鐃緒申鐃淑わ申鐃緒申鐃緒申鐃緒申

表 1鐃緒申鐃緒申鐃術随申鐃叔￥申鐃緒申
$i$	鐃緒申1	鐃緒申2	鐃緒申3	鐃緒申4	鐃緒申5	鐃緒申6	鐃緒申7	鐃緒申8	鐃緒申9	鐃緒申10
鐃術随申 $X_{i}$	2.8	3.4	3.6	5.8	7.0	9.5	10.2	12.3	13.2	13.4
鐃術随申 $Y_{i}$	0.6	3.0	0.4	1.5	15.0	13.4	7.6	19.8	18.3	18.9

鐃竣誌申鐃緒申鐃�鐃緒申

鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申 $n$ 鐃夙わ申鐃暑。
鐃術随申 $X$鐃緒申鐃術随申 $Y$鐃祝つわ申鐃銃￥申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃縮わ申弔鐃緒申襦Ｆ縁申鐃縮わ申鐃緒申鐃緒申鐃緒申砲鐃淑随申兔鐃縮わ申弔鐃緒申襦�
両鐃峻の緒申未虜鐃緒申鐃夙り，$d_{i}$ 鐃夙わ申鐃緒申鐃�$\displaystyle \sum_{i=1}^n d_{i} = 0$鐃祝￥申
$\displaystyle \sum_{i=1}^n d_{i}^{2}$ 鐃緒申 2 鐃術随申鐃塾緒申鐃緒申琉鐃緒申鐃緒申鐃緒申了鐃宿醐申任鐃緒申襦�
- 2 鐃術随申鐃塾緒申鐃緒申鐃緒申鐃緒申鐃緒申飽鐃緒申廚鐃緒申鐃夙わ申鐃祝は￥申$\displaystyle \sum_{i=1}^n d_{i}^{2} = 0$ 鐃叔わ申鐃暑。
- 2 鐃術随申鐃塾緒申鐃緒申鐃緒申媾鐃祝器申鐃緒申鐃祝逸申鐃竣わ申鐃緒申箸鐃緒申砲蓮鐃�$\displaystyle \sum_{i=1}^n d_{i}^{2} = \frac{n^{3} - n }{3}$ 鐃叔わ申鐃暑。
鐃緒申鐃塾よう鐃淑わ申鐃夙わ申鐃初，鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃出￥申 $- 1 \leqq r_{s} \leqq 1$ 鐃夙なる。鐃緒申鐃曙が鐃緒申鐃峻ワ申鐃殉ワ申僚鐃緒申鐃緒申愀鐃緒申鐃緒申任鐃緒申襦� \[ r_s = 1-\frac{\displaystyle 6 \sum_{i=1}^n d_{i}^{2}}{n^3-n} \] 鐃緒申鐃緒申任蓮鐃�$\displaystyle \sum_{i=1}^n d_{i}^{2} = 24$ 鐃叔わ申鐃暑か鐃初，$r_{s} = 1 - \displaystyle \frac{6\times 24}{ 1000 - 10 } = 0.85455$ 鐃夙なる。
- 鐃緒申愀鐃緒申鐃緒申鐃緒申鐃緒申両鐃緒申鐃緒申鐃緒申竸鐃緒申砲鐃緒申鐃緒申鐃緒申鐃舜関件申鐃緒申鐃緒申鐃緒申廚箸鐃緒申鐃緒申鐃緒申鐃緒申鐃舜￥申
- 鐃緒申愀鐃緒申鐃緒申鐃緒申鐃塾常申鐃緒申鐃緒申鐃術随申鐃祝わ申鐃緒申鐃緒申鐃舜関件申鐃緒申鐃緒申鐃緒申廚箸鐃緒申鐃緒申鐃緒申鐃緒申鐃舜￥申
- 鐃緒申愀鐃緒申鐃緒申鐃緒申鐃緒申剖瓩わ申箸鐃緒申鐃緒申鐃緒申竸鐃緒申鐃縮居申鐃舜でわ申鐃緒申廚箸鐃緒申鐃�

表 2鐃緒申鐃緒申鐃峻ワ申鐃殉ワ申僚鐃緒申鐃緒申愀鐃緒申鐃緒申侶彁鐃緒申鐃�
$i$	鐃緒申1	鐃緒申2	鐃緒申3	鐃緒申4	鐃緒申5	鐃緒申6	鐃緒申7	鐃緒申8	鐃緒申9	鐃緒申10
鐃術随申 $X_{i}$ 鐃塾緒申鐃�	1	2	3	4	5	6	7	8	9	10
鐃術随申 $Y_{i}$ 鐃塾緒申鐃�	2	4	1	3	7	6	5	10	8	9
鐃緒申未虜鐃� $d_{i}$	$-$1	$-$2	2	1	$-$2	0	2	$-$2	1	1	鐃緒申$\displaystyle \sum_{i=1}^n d_{i} = 0$
鐃緒申未虜鐃緒申鐃緒申鐃緒申 $d_{i}^{2}$	1	4	4	1	4	0	4	4	1	1	鐃緒申$\displaystyle \sum_{i=1}^n d_{i}^{2} = 24$

鐃緒申鐃緒申

鐃宿わ申鐃初か鐃緒申鐃緒申鐃淑まわ申鐃緒申両鐃緒申鐃祝わ申鐃術随申鐃祝わ申鐃緒申鐃緒申鐃緒申鐃銃のワ申鐃緒申鐃緒申鐃緒申同鐃緒申鐃緒申佑鐃夙わ申鐃緒申砲蓮鐃緒申鐃緒申團鐃緒申泪鐃塾緒申鐃緒申鐃舜件申鐃緒申鐃緒申鐃緒申鐃緒申任鐃緒申覆鐃緒申鐃�
同鐃緒申未鐃緒申鐃緒申鐃緒申鐃祝は￥申鐃術随申 $X$鐃緒申鐃術随申 $Y$鐃祝わ申鐃緒申鐃緒申同鐃緒申未慮朕鐃緒申鐃� $n_x$ 鐃緒申$n_y$ 鐃緒申同鐃緒申未鐃緒申腓㍼申鐃緒申鐃� $t_{i}$ 鐃緒申$t_{j}$ $(i = 1, 2, \dots , n_x$鐃緒申$j = 1, 2, \dots , n_y)$ 鐃夙わ申鐃緒申鐃夙わ申鐃緒申鐃緒申鐃緒申鐃叔計誌申鐃緒申鐃緒申襦Ｆ縁申鐃縮わ申鐃淑わ申鐃緒申鐃祝わ申 $\displaystyle \sum_{i=1}^{n_x} \left (t_i^3-t_i \right )=0$鐃緒申$\displaystyle \sum_{j=1}^{n_y} \left (t_j^3-t_j \right )=0$ 鐃夙なり，鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃淑る。 \[ \begin{align*} & r_s = \frac{T_x+T_y-\displaystyle \sum_{i=1}^n d_i^2}{2\sqrt{T_x\ T_y}} \\ & T_x = \frac{\left (n^3-n \right )-\displaystyle \sum_{i=1}^{n_x}\ \left (t_i^3-t_i \right )}{12} \\ & T_y = \frac{\left (n^3-n \right )-\displaystyle \sum_{j=1}^{n_y}\ \left (t_j^3-t_j \right )}{12} \\ \end{align*} \]

鐃初習鐃緒申鐃緒申鐃緒申

鐃緒申鐃緒申表 3 鐃祝わ申鐃緒申鐃銃￥申鐃術随申 $X$ 鐃緒申鐃術随申 $Y$ 鐃塾間のワ申鐃峻ワ申鐃殉ワ申僚鐃緒申鐃緒申愀鐃緒申鐃緒申鐃緒申鐃淑わ申鐃緒申鐃緒申鐃緒申

表 3鐃緒申鐃緒申鐃術随申鐃叔￥申鐃緒申
$i$	鐃緒申1	鐃緒申2	鐃緒申3	鐃緒申4	鐃緒申5	鐃緒申6	鐃緒申7	鐃緒申8	鐃緒申9	鐃緒申10
鐃術随申 $X_{i}$	2	3	3	5	7	9	10	12	13	13
鐃術随申 $Y_{i}$	0	3	0	1	15	13	7	19	18	18

鐃緒申鐃緒申1鐃緒申$T_{x}$ 鐃緒申鐃緒申鐃緒申鐃緒申鐃祝居申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃旬ワ申鐃緒申鬟�鐃獣ワ申鐃緒申鐃淑わ申鐃緒申鐃緒申

鐃緒申鐃緒申2鐃緒申$\displaystyle \sum_{i=1}^{10} d^{2}$ 鐃緒申鐃緒申鐃緒申鐃緒申鐃祝居申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃旬ワ申鐃緒申鬟�鐃獣ワ申鐃緒申鐃淑わ申鐃緒申鐃緒申

鐃緒申鐃緒申3鐃緒申$r_{s}$ 鐃緒申鐃緒申覆鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申肋鐃緒申鐃緒申鐃緒申焚鐃� 5 鐃緒申鐃旬で四捨醐申鐃緒申鐃緒申鐃緒申鐃粛わ申鐃緒申鐃緒申鐃祝居申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃旬ワ申鐃緒申鬟�鐃獣ワ申鐃緒申鐃淑わ申鐃緒申鐃緒申

鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申

鐃緒申鐃緒申表 2 鐃祝わ申鐃緒申鐃緒申鐃術随申 $X$鐃緒申$Y$ 鐃塾緒申未鐃叔￥申鐃緒申鐃夙みなわ申鐃緒申鐃峻ワ申鐃緒申鐃緒申鐃緒申鐃塾�申鐃舜件申鐃緒申鐃緒申鐃緒申董鐃緒申鐃緒申團鐃緒申泪鐃塾緒申鐃緒申鐃舜件申鐃緒申鐃緒申 $r_{s} = 0.85455$ 鐃祝わ申鐃緒申咾鐃緒申覆鐃緒申鐃緒申鐃緒申鐃�

表 4鐃緒申鐃緒申未鐃叔￥申鐃緒申鐃夙みなわ申鐃銃ピワ申鐃緒申鐃緒申鐃緒申鐃塾�申鐃舜件申鐃緒申鐃緒申彁鐃緒申鐃緒申鐃�
$i$	鐃緒申1	鐃緒申2	鐃緒申3	鐃緒申4	鐃緒申5	鐃緒申6	鐃緒申7	鐃緒申8	鐃緒申9	鐃緒申10
鐃術随申 $X_{i}$ 鐃塾緒申鐃�	1	2	3	4	5	6	7	8	9	10
鐃術随申 $Y_{i}$ 鐃塾緒申鐃�	2	4	1	3	7	6	5	10	8	9

鐃緒申鐃緒申1鐃緒申鐃宿のよう鐃祝なっわ申鐃緒申鐃緒申a鐃緒申b 鐃塾わ申鐃緒申鐃曙か鐃緒申鐃緒申鐃緒申鐃祝居申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃旬ワ申鐃緒申鬟�鐃獣ワ申鐃緒申鐃淑わ申鐃緒申鐃緒申

直鐃緒申鐃塾ペ￥申鐃緒申鐃緒申鐃緒申鐃�鐃緒申鐃緒申

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