Distinguish between sign test and Wilcoxon signed rank test

[tzx9633]

Homework Statement

I know that for both method are used to test the 2 group sample for a non-normally distributed population ... But , i am not sure the difference between them . Can someone explain the difference between them ? When to use sign test and wilcoxon signed rank test ?

Homework Equations

The Attempt at a Solution

Sorry , i am not sure whether i am posted in the correct section or not .

 

[FactChecker]

The sign test only requires that you know which of the paired tests are larger. The signed rank test requires that you can put all the results in increasing order. So the signed-rank test has a lot more information to work with. If you can put all the results in order, use the signed-rank test.

PS. For a general statistics question like this, where you are not asking about a specific homework problem, there is a section for Statistics under Math that might be a better place to post.

 

[tzx9633]

The sign test only requires that you know which of the paired tests are larger. The signed rank test requires that you can put all the results in increasing order. So the signed-rank test has a lot more information to work with. If you can put all the results in order, use the signed-rank test.

PS. For a general statistics question like this, where you are not asking about a specific homework problem, there is a section for Statistics under Math that might be a better place to post.

So , if the college statistics question didn't ask for whether we should put the results in increasing order or not , both can be used ? Am i right ?

 

[FactChecker]

If you can put them in order, it is probably better to do that. The signed-rank test may be a stronger test. But often there is no such thing as order -- you just have a (greater-than, less-than) boolean paired-data sample. Then you can not use the signed-rank test.

 

[tzx9633]

If you can put them in order, it is probably better to do that. The signed-rank test may be a stronger test. But often there is no such thing as order -- you just have a (greater-than, less-than) boolean paired-data sample. Then you can not use the signed-rank test.

Do you mean If I can put them in order , then it's recommended to use signed-rank test over sign test ?

 

[FactChecker]

Do you mean If I can put them in order , then it's recommended to use signed-rank test over sign test ?

There is a trade-off. By putting them in ranks, you are gaining the ranking information but giving up the pairing information. I believe that there are examples where each is stronger. Certainly, pairs of data like (1,2) (3,4) (5,6) (7,8) are very clear, whereas the rank ordering of 1, 2, 3, 4, 5, 6, 7, 8 hides the important information and is weak. On the other hand, (1, 7), (3, 2) (5,8) (4,6) looks much stronger in the form of 1, 2, 3, 4, 5, 6, 7, 8 because when the second entries of the pairs are larger, they are not just larger than the first entry of that pair -- they tend to be larger than all first entries of all pairs.

 

[tzx9633]

whereas the rank ordering of 1, 2, 3, 4, 5, 6, 7, 8 hides the important information and is weak.

why ? Can you explain further ?

 

[FactChecker]

why ? Can you explain further ?

The ordering of the two sets is entirely swapped if the lowest ranked element is deleted. So it is my assumption that the statistical result will be weak and insignificant. In the paired results, (1,2) (3,4) (5,6) (7,8), it is very clear, and I assume statistically significant, that the second set ranks above the first set.