# Homework Help: Distinguish between sign test and Wilcoxon signed rank test

1. Dec 24, 2017

### tzx9633

1. The problem statement, all variables and given/known data
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 ?

2. Relevant equations

3. The attempt at a solution
Sorry , i am not sure whether i am posted in the correct section or not .

2. Dec 24, 2017

### 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.

3. Dec 24, 2017

### tzx9633

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 ?

4. Dec 24, 2017

### 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.

5. Dec 24, 2017

### tzx9633

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

6. Dec 24, 2017

### FactChecker

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.

Last edited: Dec 24, 2017
7. Dec 25, 2017

### tzx9633

why ? Can you explain further ?

8. Dec 25, 2017

### FactChecker

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.