# Nonparametric methods

##### New Member
If I have a sample with the size of the right and left arms of each of these people.So I have two dependent groups, since these are the same person, right? I I can apply a Wilcoxon test to see if the two groups are equal, or if there is a difference between these?

#### hlsmith

##### Omega Contributor
askazy, you driving me crazy with the Wilcoxon. Try to add which test in particular, since his name is associated with many tests.

Yes, you could subtract the two paired values and use the Wilcoxon sign rank test (on the differences). What is your sample size and data distribution. Many programs will conduct an exact test when the sample sizes are small (e.g., in SAS, n-value < 20), also some people feel the central limit theorem comes into play as the sample size increases.

This is a better dataset idea than the previous proposed sets!

##### New Member
askazy, you driving me crazy with the Wilcoxon. Try to add which test in particular, since his name is associated with many tests.

Yes, you could subtract the two paired values and use the Wilcoxon sign rank test (on the differences). What is your sample size and data distribution. Many programs will conduct an exact test when the sample sizes are small (e.g., in SAS, n-value < 20), also some people feel the central limit theorem comes into play as the sample size increases.

This is a better dataset idea than the previous proposed sets!

So the question is do I have to prepare a study where I use this test. Data can not have normal distribution. How have to collect the data I think of using a sample of size 15 or 20.
The ideas that I had to apply this test following these standards are:

These are the ideas that I had, but I'm sure if they fit in this test. Because exercise says to compare two groups, and do not know if these ideas fit together like two groups.

Last edited:

#### hlsmith

##### Omega Contributor
So you will have a dataset with difference values. Now you want to stratify the data set and test additional hypotheses. I am guessing using Wilcoxon rank sum.

Not sure if your Wilcoxon sign rank test is not significant if that will indirectly lower the potential power for subsequent tests, unless all of the -'s and +'s signs get group together in your subsequent stratifications.

##### New Member
So you will have a dataset with difference values. Now you want to stratify the data set and test additional hypotheses. I am guessing using Wilcoxon rank sum.

Not sure if your Wilcoxon sign rank test is not significant if that will indirectly lower the potential power for subsequent tests, unless all of the -'s and +'s signs get group together in your subsequent stratifications.
Look realizing that third option that I presented obtained the following result

Last edited:

#### noetsi

##### Fortran must die
A minor point. SAS will run an exact test with any sample size. It just takes longer. I think you could run an exact test in a reasonable time with a lot more than 20 cases.

##### New Member
I have doubts about the state the hypotheses of my test. If my test is about the size difference between the arms of a person, then the chances should be

$$H_0$$: There is no difference between the sizes of arms
$$H_1$$: There is a difference between the sizes of arms

I am confused by this because in some references I read, the assumptions are set based on the median.

What is the test statistic should I use for a population of size 20?
I think not give to approach the normal, then I use the Wilcoxon table to determine the critical region of the right sided test?

#### hlsmith

##### Omega Contributor
I typically run the non-parametrics based on median since extreme outliers can provide an off measure of central tendancy.

$$H_0:m_0=m$$
$$H_1:m_0=m$$
$$H_0$$:There is no difference between the size of the arms
$$H_1$$:There is difference between the size of the arms.