l*********s
发帖数: 5409 | 1 both procedures are for testing if median is a certain value.
however, under null hypothesis the test stat of signed rank has a variance
of n(n+1)(2n+1)/24, much bigger than the variance for sign procedure.
My question is, signed rank procedure utilize more information about
distribution (property of symmetry), why it is not more efficient? |
w**********r
发帖数: 986 | 2 If my remember is correct, sign test is applied on paired data, while signed
rank test is not. The information provided by the data itself is different.
It is like comparing paired t-test with t-test, the paired t-test is more
powerful because of the paired data.
【在 l*********s 的大作中提到】
: both procedures are for testing if median is a certain value.
: however, under null hypothesis the test stat of signed rank has a variance
: of n(n+1)(2n+1)/24, much bigger than the variance for sign procedure.
: My question is, signed rank procedure utilize more information about
: distribution (property of symmetry), why it is not more efficient?
|
l*********s
发帖数: 5409 | 3 Sorry about my misleading description. Both procedures are used for testing
if population median is a certain value.
Sign test is not applied on paired data in this setting.
signed
different.
【在 w**********r 的大作中提到】
: If my remember is correct, sign test is applied on paired data, while signed
: rank test is not. The information provided by the data itself is different.
: It is like comparing paired t-test with t-test, the paired t-test is more
: powerful because of the paired data.
|
b*******r
发帖数: 152 | 4 my thoughts to your point:
1. the signed test uses binomial distribution (the test stat follows a binml
(), so the var=np(1-p), here p=0.5, so var=n/4?) and only tests/cares if the
delta is > or < 0, essentially only cares about the direction.
2. the signed-rank test uses normal dist, it uses more info than only the
direction in case 1. so it should be more precise and powerful.
3. what do u mean by 'efficient'? |
l*********s
发帖数: 5409 | 5 Let B denote test statistics
For signed test,
(1) no presumption on underlying distribution
(2) under H_0, B follows Binomial(n,0.5), Expected value is n/2 and variance
is n/4
For signed rank test,
(1) requires that random variable follow symmetrical distributions
(2) under H_0, expected value is n(n+1)/4, and variance is n(n+1)(2n+1)/24 |
P*******9
发帖数: 9700 | 6 i feel like you mixed the concepts of estimation and testing
for estimation you can talk about the efficiency/compare variance, but for t
est, you should compare power.
I think larger variance of test statistic doesn't mean anything
variance
it
【在 l*********s 的大作中提到】
: Let B denote test statistics
: For signed test,
: (1) no presumption on underlying distribution
: (2) under H_0, B follows Binomial(n,0.5), Expected value is n/2 and variance
: is n/4
: For signed rank test,
: (1) requires that random variable follow symmetrical distributions
: (2) under H_0, expected value is n(n+1)/4, and variance is n(n+1)(2n+1)/24
|
l*********s
发帖数: 5409 | 7 Many times inference are derived from test statistics. Aren't they closely
related?
t
【在 P*******9 的大作中提到】
: i feel like you mixed the concepts of estimation and testing
: for estimation you can talk about the efficiency/compare variance, but for t
: est, you should compare power.
: I think larger variance of test statistic doesn't mean anything
:
: variance
: it
|
P*******9
发帖数: 9700 | 8 you can standardize test statistics to take away the effect of large varianc
e, and of cause you need to adjust the critical value.
estimation is quite different from testing.
【在 l*********s 的大作中提到】
: Many times inference are derived from test statistics. Aren't they closely
: related?
:
: t
|
l*********s
发帖数: 5409 | 9 let us apply central limit theorem and use z test for both test.
You still think large variance is non consequential?
varianc
【在 P*******9 的大作中提到】
: you can standardize test statistics to take away the effect of large varianc
: e, and of cause you need to adjust the critical value.
: estimation is quite different from testing.
|
c******n
发帖数: 380 | 10 Why do you say signed rank test utilize more information about distribution?
Both tests are nonparametric and free of underlying distribution.
And what do you mean by 'efficient'? Powerful?
I've only heard of the efficiency of a statistics,not of a test. |
o***o
发帖数: 43 | 11 Efficiency一般是比较对于同一个parameter的两个不同的estimator。现在你这个例子
，两个test
statistics并不是对同一个东西的估计，怎么可以比较efficiency?
如果说两个test本身的relative efficiency,我想正确的意思应该是，在达到相同
power的情况
下，哪个需要的sample少。那么，比较test statistic在H_0下的variance能有什么意
义呢？
variance
it
【在 l*********s 的大作中提到】
: Let B denote test statistics
: For signed test,
: (1) no presumption on underlying distribution
: (2) under H_0, B follows Binomial(n,0.5), Expected value is n/2 and variance
: is n/4
: For signed rank test,
: (1) requires that random variable follow symmetrical distributions
: (2) under H_0, expected value is n(n+1)/4, and variance is n(n+1)(2n+1)/24
|
l*********s
发帖数: 5409 | 12 aren't they both for testing median?
【在 o***o 的大作中提到】
: Efficiency一般是比较对于同一个parameter的两个不同的estimator。现在你这个例子
: ，两个test
: statistics并不是对同一个东西的估计，怎么可以比较efficiency?
: 如果说两个test本身的relative efficiency,我想正确的意思应该是，在达到相同
: power的情况
: 下，哪个需要的sample少。那么，比较test statistic在H_0下的variance能有什么意
: 义呢？
:
: variance
: it
|
