A****e 发帖数: 310 | 1 比如有2组零均值的样本,x_i,y_i,i从1到n,然后算出来样本的相关系数\pho是很小
的一个数字,比如说0.0001,那么怎么判断这个数字是否统计意义上显著的大于0呢?
谢谢!~~~
--------
自己的思路是,这个是不是需要用一个什么hypothesis test来做?但是如果x,y的分
布不知道的情况下,相关系数\pho的分布还是不知道的,对吧?
-----
或者当n很大的时候,比如n=10^4,可以看成样本是近似normal分布?然后呢?
----
谢谢大家! |
m********9 发帖数: 208 | 2 You can perform the hypothesis test. Let rho be the population correlation
coefficient.You are interested in testing
H0 rho = 0 vs Ha rho neq 0
then check the absolute value of the sample correlation coefficient (for
short, |r|). If |r| > r_critical, then reject the null, which implies the
linear relation exists between x and y. Here the r_critical can be found via
http://www.gifted.uconn.edu/siegle/research/correlation/corrchrt.htm.
If your sample size is really large, then you can use the normal
approximation, or do regression analysis y = alpha+beta x, then use t-test
for beta.
Hope the information above is helpful for you. |
g********r 发帖数: 8017 | 3 permute y生成null?
【在 A****e 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 比如有2组零均值的样本,x_i,y_i,i从1到n,然后算出来样本的相关系数\pho是很小 : 的一个数字,比如说0.0001,那么怎么判断这个数字是否统计意义上显著的大于0呢? : 谢谢!~~~ : -------- : 自己的思路是,这个是不是需要用一个什么hypothesis test来做?但是如果x,y的分 : 布不知道的情况下,相关系数\pho的分布还是不知道的,对吧? : ----- : 或者当n很大的时候,比如n=10^4,可以看成样本是近似normal分布?然后呢? : ---- : 谢谢大家!
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A****e 发帖数: 310 | 4 many thanks!
就是说如果没有normal approx,r_critical的求值就比较复杂了
如果有normal approx,就是t-test for beta,恩,这个时候没什么不直接test rho呢
?:)
via
【在 m********9 的大作中提到】![](/moin_static193/solenoid/img/up.png) : You can perform the hypothesis test. Let rho be the population correlation : coefficient.You are interested in testing : H0 rho = 0 vs Ha rho neq 0 : then check the absolute value of the sample correlation coefficient (for : short, |r|). If |r| > r_critical, then reject the null, which implies the : linear relation exists between x and y. Here the r_critical can be found via : http://www.gifted.uconn.edu/siegle/research/correlation/corrchrt.htm. : If your sample size is really large, then you can use the normal : approximation, or do regression analysis y = alpha+beta x, then use t-test : for beta.
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P****D 发帖数: 11146 | 5 这个有若干种方法,wikipedia给了三种。
http://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coef
Determining significance
One approach to testing whether an observed value of ρ is significantly
different from zero (r will always maintain −1 ≤ r ≤ 1) is to
calculate the probability that it would be greater than or equal to the
observed r, given the null hypothesis, by using a permutation test.
Another approach parallels the use of the Fisher transformation in the case
of the Pearson product-moment correlation coefficient.
One can also test for significance using t
SAS用的是第三种。
http://support.sas.com/documentation/cdl/en/procstat/63104/HTML
【在 A****e 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 比如有2组零均值的样本,x_i,y_i,i从1到n,然后算出来样本的相关系数\pho是很小 : 的一个数字,比如说0.0001,那么怎么判断这个数字是否统计意义上显著的大于0呢? : 谢谢!~~~ : -------- : 自己的思路是,这个是不是需要用一个什么hypothesis test来做?但是如果x,y的分 : 布不知道的情况下,相关系数\pho的分布还是不知道的,对吧? : ----- : 或者当n很大的时候,比如n=10^4,可以看成样本是近似normal分布?然后呢? : ---- : 谢谢大家!
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A****e 发帖数: 310 | 6 谢谢谢谢!~~~仔细看看这三种方法
btw,想问下,如果rho很小,比如0.001,然后n较大,比如10^4,是不是不用怎么计算
,或者手算下,就能够confident的说rho比0没有显著的大?
case
【在 P****D 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 这个有若干种方法,wikipedia给了三种。 : http://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coef : Determining significance : One approach to testing whether an observed value of ρ is significantly : different from zero (r will always maintain −1 ≤ r ≤ 1) is to : calculate the probability that it would be greater than or equal to the : observed r, given the null hypothesis, by using a permutation test. : Another approach parallels the use of the Fisher transformation in the case : of the Pearson product-moment correlation coefficient. : One can also test for significance using t
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