# Nonparametric test choice for skewed data

#### n_knight

##### New Member
Hello,

My first thread on the board... I posted this to the SPSS-X list , but thought this forum may be more appropriate.

I was wondering if you could help me with a data analysis problem. Here is a description of the data and of the issue -- sorry about the length of the post but I wanted to be as clear as possible;

Two age groups:

1. Young

Two conditions (each participant was assigned to one of the two groups):

3. Prime A
4. Prime B

Two sets of responses for each condition (each participant gave answered both sets):

5. Set A
6. Set B

Responses to sets A and B are ordinal and range from zero to seven (integers only). Now, the problem is that most of these eight (2x2x2) distributions are non-normal -- in particular, they are mostly strongly J-shaped, which is to be expected given the experimental question. Here are the frequencies:

[1,3,5]

0 1
1 0
2 0
3 2
4 1
5 7
6 12
7 5

[2,3,5]

0 0
1 0
2 1
3 0
4 2
5 2
6 3
7 15

[1,3,6]

0 1
1 1
2 4
3 7
4 1
5 3
6 6
7 5

[2,3,6]

0 0
1 1
2 7
3 3
4 3
5 3
6 2
7 4

[1,4,5]

0 0
1 0
2 0
3 0
4 0
5 2
6 4
7 22

[2,4,5]

0 0
1 0
2 0
3 0
4 1
5 0
6 7
7 15

[1,4,6]

0 0
1 0
2 1
3 1
4 0
5 6
6 4
7 16

[2,4,6]

0 1
1 2
2 3
3 1
4 4
5 1
6 1
7 10

I want to test differences in the shape of the distribution; more precisely, I am interested in developmental effects, to be assessed by the following tests:

A. [1,3,5] vs [2,3,5]
B. [1,3,6] vs [2,3,6]
C. [1,4,5] vs [2,4,5]
D. [1,4,6] vs [2,4,6]

I believe such distributions call for nonparametric testing; in particular, I would like a test that is sensitive to changes in the lengthening of the tail of the distribution, which is the clearest observable effect. The Moses test is supposed to be able to do just that. I've run it on the data, and the results are as follows (all with outliers automatically trimmed as recommended by SPSS):

Test A: (N = 39, p <.009)
Test B: (N = 46, n.s.)
Test C: (N = 32, p <.001)
Test D: (N = 31, p < .001)

The Mann-Whitney U and Kolmogorov-Smirnov results are similar, except that test A comes out non-significant.

And in priming effects, to be assessed by the following tests:

E. [1,3,5] vs [1,4,5]
F. [1,3,6] vs [1,4,6]
G. [2,3,5] vs [2,4,5]
H. [2,3,6] vs [2,4,6]

Here are the (automatically trimmed) Moses results for the above:

Test E: (N = 35, p <.001)
Test F: (N = 42, p <.001)
Test G: (N = 30, p <.001)
Test H: (N = 40, n.s.)

Again, the M-W and K-S tests are similar, except that for both test G comes out non-significant.

I am not wedded to the Moses test but it seemed the most appropriate for my purposes. I am also not too worried about the difference in results, given the small sample size. I just want to give a truthful statistical picture of the data that does not involve looking at histograms and guessing whether the distributions are different.

Now, my questions are:

-- Is the Moses test adequate for these data, or is there another test that is both powerful and more appropriate?

-- If I end up using Moses, should I change the trimming technique (for example, should I only trim at one end given the shape of the distribution), or not trim at all, given the small sample size? Are these variations justifiable?

-- Whatever test I end up using, should I worry about ties in the data, since SPSS does not adjust for them?

Many thanks for your help, it is very much appreciated.

Nicola Knight

#### n_knight

##### New Member
Let me just add: chi-square gives same results as K-S and M-W (but not Moses), but I can't use it given the low cell frequencies.

#### JohnM

##### TS Contributor
Until I read your post, I had never heard of the Moses test, but then I found a link that describes it as a test of "polarization" or "extreme reactions:"
http://www2.chass.ncsu.edu/garson/PA765/mann.htm

For each of the tests / contrasts you are examining, the K-S, M-W, and Moses tests are each looking for different things, each one more specific:

K-S --> general change of shape
M-W --> change in central tendency / median
Moses --> change in tails

I would make a table that shows each contrast you are examining in a row and each test on them in a column, and whether or not it's significant - that should reveal overall patterns in the effects.

The tests you are running are all "adequate." What may be working against you is a small sample size, but it's really not that small - some of the effects you are looking for just may not be there....

I really don't have an opinion on trimming and adjustments for ties - try it with and without, and see if it makes any difference. Bottom line - any trimming you do must be justifiable from a data perspective (the data point is a bona-fide outlier), not significance.

#### n_knight

##### New Member
Thanks so much for the help, JohnM!

JohnM said:
Until I read your post, I had never heard of the Moses test, but then I found a link that describes it as a test of "polarization" or "extreme reactions:"
http://www2.chass.ncsu.edu/garson/PA765/mann.htm

For each of the tests / contrasts you are examining, the K-S, M-W, and Moses tests are each looking for different things, each one more specific:

K-S --> general change of shape
M-W --> change in central tendency / median
Moses --> change in tails

I would make a table that shows each contrast you are examining in a row and each test on them in a column, and whether or not it's significant - that should reveal overall patterns in the effects.
Good idea -- I'll probably use the K-S and Moses as they seem most appropriate for my purposes.

JohnM said:
I really don't have an opinion on trimming and adjustments for ties - try it with and without, and see if it makes any difference. Bottom line - any trimming you do must be justifiable from a data perspective (the data point is a bona-fide outlier), not significance.
Right -- but I was just wondering if, having a theoretical reason for doing so, trimming at one end only (for example) would be permissible. I think I'll go with the standard SPSS 5% trim rule.

Again, many thanks for the help. I'll post to let you know what the referees thought...

Best,

N Knight

#### Anna

##### New Member
Moses or Mann-Whitney?

Hi guys,

I thought I'd ask for your advice because no one I know seems to have heard of the Moses Extreme test. I am looking at the effects of depression upon memory in an experimental grp compared to a control grp. So far I have performed a Mann-whitney on my (non-normal, unequal variances) data. This has come out insignificant (not what I was hoping for) but when I perform a Moses test it came out significant. Since I am expecting the grps to score highly on opposite ends of the measure, I expect a Moses test to be most suitable.

However when I carry out both tests on another aspect of memory that I have measured the results are reversed (Moses = ns, U = sig) this seems strange because I was expecting both grps to score highly on opposite ends of both measures.

So basically is it better to use a Moses or Mann-Whiteney?

Also, I've read that Mann-Whitney's are not appropriate for data unequal in variance (Siegel & Castellan, 1988). So does that force me into using the Moses test?? I'm so confused!

#### JohnM

##### TS Contributor
Anna said:
However when I carry out both tests on another aspect of memory that I have measured the results are reversed (Moses = ns, U = sig) this seems strange because I was expecting both grps to score highly on opposite ends of both measures.

So basically is it better to use a Moses or Mann-Whiteney?
If the Moses test is insignificant, then maybe that aspect of memory doesn't have the same response as the other aspect of memory.

It's OK to use either test, or both of them - the fact that you are getting inconsistent results tells you that different aspects of memory are affected in different ways by depression.....

#### Anna

##### New Member
wow! thanks for the quick reply! I have got reasons to use both tests, so I'll prob put both in. Thanks for the advice, really helped me see the bigger picture

#### kalbright36

##### New Member
Anna,
What's SPSS - X? I sure would like help figuring out how to use it!
Thanks!
Karen

#### statstats

##### New Member
Nonparametric Test (Moses)

Hi,

I have a similar question regarding a nonparametric test for dispersion applied to n shaped data (right-skewed or positive skewed) for comparing 2 groups.

There are several tests available for this and the Moses Test seems the best for my data. However, there are two different tests suggested by Moses:

- Moses test of extreme reactions (1952) --> available in SPSS
- Moses rank-like test for scale differences (1963) --> available ???

Do these 2 tests answer the same question ? If not, what is the difference ?

SAS provide the user with others tests like Ansari-Bradley, Klotz and Mood.

I am a bit lost and have difficulty finding relevant literature for taking a good decision. I made a search on PsycInfo and Scirus.com, but there seems to be few (accessible) papers on the question.