秩系数与卡尔皮尔逊相关系数之间的差异

相关系数秩是确定相关系数的方法。它也被命名为Spearman 的相关系数。它根据属性测量分配给各个项目的等级之间的线性关联。属性是那些无法用数值衡量的变量，例如人的智力、外貌、诚实等。

它是由英国心理学家查尔斯·爱德华·斯皮尔曼开发的。当变量无法有意义地测量时使用它，例如价格，收入，体重等定量变量的情况。基本上，它用于定性表达值时。

公式：

Rank Coefficient of Correlation (rs)= 1 – 6ΣD2  / (N3–N)

例子：

Rank in Computers (X)	Rank in English(Y)
1	2
2	4
3	1
4	5
5	3
6	8
7	7
8	6

解决方案：

Rank in Computers (X)	Rank in Computers (Y)	Differences Between Ranks D = (X-Y)	D2
1	2	-1	1
2	4	-2	4
3	1	2	4
4	5	-1	1
5	3	2	4
6	8	-2	4
7	7	0	0
8	6	2	4
			6ΣD2 = 22

这里，n = 8

(rs)= 1 – 6ΣD2  / (N3–N)
     = 1- 6 * 22 / 504 
     = 1- 132/504
     = 0.74

秩相关系数 (r _s )= 0.74

Karl Pearson 的相关系数：

Karl Pearson 的相关系数（或乘积矩相关或简单相关系数或协方差方法）基于算术平均值和标准偏差。

根据卡尔·皮尔森的说法，两个变量的相关系数是通过将两个系列的各个项目的相应偏差与各自平均值的乘积之和除以它们的标准偏差和观察对数的乘积而得到的。基本上，它是基于相关变量 s 的协方差。

公式为：

Karl Pearson's Coefficient of Correlation  (r) = NΣXY−ΣX.ΣY / √NΣX2 - (Σx)2 √NΣY2 - (ΣY)2

例子：

从下表中找出 Karl Pearson 相关系数的值：

SUBJECT	X	Y
1	43	99
2	21	65
3	25	79
4	42	75
5	57	87
6	59	81

解决方案：

SUBJECT	X	Y	XY	X2	Y2
1	43	99	4257	1849	9801
2	21	65	1365	441	4225
3	25	79	1975	625	6241
4	42	75	3150	1764	5625
5	57	87	4959	3249	7569
6	59	81	4779	3481	6561
Σ	247	486	20485	11409	40022

(r) = NΣXY−ΣX.ΣY / √NΣX2 - (Σx)2 √NΣY2 - (ΣY)2
 (r) = 6(20,485) – (247 × 486) / [√[[6(11,409) – (2472)] × [6(40,022) – 4862]]]

Karl Pearson 的相关系数 (r) = 0.5298

秩系数和卡尔皮尔逊相关系数之间的差异

Rank Coefficient 和 Karl Pearson's Coefficient of Correlation 的区别如下：

Sr. No.	Rank Coefficient	Karl Pearson’s Coefficient
1.	It is suitable when data is given in the qualitative form.	It is a suitable method when data is given in the quantitative form.
2.	It cannot be applied in the case of bivariate frequency distribution.	It is an effective method to determine the correlation in the case of grouped series.
3.	It is not possible to determine the combined coefficient of correlation.	If coefficients of correlation and number of items of each subgroup os given then one can determine the combined coefficient of correlation items.
4.	Changing the actual values in the series does not result in a change in the coefficient of correlation.	Changing the actual values in the series results in a change in the coefficient of correlation.
5.	The coefficient of correlation is perfectly positive if both the series have equal corresponding ranks i.e. D = 0 for each.	The coefficient of correlation is perfectly positive if both the series change uniformly i.e. X and Y series are related linearly correlation.
6.	It is difficult to use and understand.	It is easier to use and understand.