Mann-whitney U test: All values are tied values - Is that ok?

[mantrak88]

The following link provides great help for analysing agreement between two groups (say male & female) on a statement ranked on Likerts 5 point scale (e.g. Outdoor games is the best pass time). I am sure it is a useful one. Assume 45 Male and 55 Female respond giving their agreement on the scale: 1- Strongly Agree, 2-Agree, 3- Neutral, 4- Disagree, 5- Strongly disagree.
To test the Null Hypothesis that Both Male and Female like playing outdoor games equally in their pass time; the following link gives the methodology.

http://www.joe.org/joe/2011october/pdf/JOE_v49_5tt7.pdf


The author advocates Mann-Whitney U-test. Obviously, for the likert scale of 1 to 5, the data when ranked will ultimately consist of only 5 ranks repeated for the 100 responses. Unfortunately, the author does not mention the formula. I have the same apprehension as you do as there will note be a single non-repeated rank.
The following link gives the formula for tied ranks:
http://www.brightstat.com/index.php?...ask=view&id=35
However, I am not confident whether it is applicable in such a case. Please suggest if ok to use or indicate an alternative methodology.!

[badibad]

but what if i do not want to comprare men and women in the same group but
one group (men and women together) but in different time points?

[gianmarco]

Hi!

I am not going to fully answer your question.

Just to stress that Sheskin "Handbook of non-parametri statistics" (Googlebook), speaks about some modifications available to "correct" the U test statistic formula when ties are present ("Some sources recommend that when an excessive number of ties are present in the data, a tie correction should be introduced"; enphasis is mine).
Giving a quick look at the book, I do not see any warning about the use of the test when values are all tied.

May be that other members can provide further insight on the issue.

Regards
Gm

[mantrak88]

Thank you for the reference. Yup!! No warning seems to be present when all values are tied. However, in our daily life, if we understand the term "correction" means repairing/compensating something that has gone wrong which in other words implies that "rank being tied" is considered an error. On this philosophy, one or two errors are tolerable. But can all readings be erroneous (which here means tied)? Looking for more opinions on the subject. Guys, it is interesting how far "correction" factor can "correct" things.I hope I am making the problem clear. Statisticians, please understand that the such correction term does not mention how many maximum tied values can be present whereas the literal meaning of the term "correction" implies there has to be a limit. Please help.

[CulturalAnthro]

In your case with two samples and one variable,

Mann-Whitney U test is for independent samples which have the same size and spread, but different central tendency.
Wald-Wolfowitz is for independent samples which have the same size and central tendency, but different spread.
Fligner-Policello is for independent samples with vast differences in size or spread.
Kolmogorov-Smirnov is for independent samples with many ties.

Wilcoxon signed rank test is used for matched/dependent or before-and-after samples.

edit: Whoops, forgot to add... the W value you get from running Mann-Whitney in SPSS for example, that's a different Wilcoxon variable. That however is a value which is corrected for many ties, and you can find critical values tables easily via Google.