Kruskal-Wallis test (which is equivalent to a Mann-Whitney test when you have just 2 groups) could be used. It can be used with ordinal data. The test automatically converts data points to ranks before calculating the test statistic.
I'm analyzing a likert questionnaire to determine if respondent's answered questions differently based on whether they compete frequently or infrequently in bodybuilding.
However, I'm having trouble determining what technique to use for efficient analysis.
I've ruled out:
Chi-Square: small sample size (N=23)
Fisher's exact test: matrix larger than 2x2
Kruskal Wallis: not rank data
Contingency table: values=0
and I'm not sure if I can use the Mann-Whitney U test either...
Anyway, two categories and five questions and I made a table with response frequency for each question and group.
If you look at the attachment, that table is in the top right corner
If anyone can point me in the right direction of a test that can handle that data, I'd greatly appreciate it!
Kruskal-Wallis test (which is equivalent to a Mann-Whitney test when you have just 2 groups) could be used. It can be used with ordinal data. The test automatically converts data points to ranks before calculating the test statistic.
StatsClue (05-21-2012)
don't mean to hijack, but only mean to clarify a small point- if the data was continuous could these tests (Kruskal-Wallis and Mann-Whitney) still be used? Asking because unless I've misunderstood, I have heard of these being used for skewed continuous data. In the question above, I guess the null would be that the frequencies do not differ by the fact of competing frequently or infrequently. If these tests are valid for continuous data, I'm not sure what the null would be.
I believe the test/s can be used in either case. Either way the original data gets converted to ranks, and then the test statistic is calculated.
As I understand it, the null hypothesis for a Mann-Whitney test is that: The probability that a randomly chosen score from population 1 is greater than a randomly chosen score from population 2 is equal to 0.5. This null would make sense for both continuous and ordinal data, I think?
StatsClue (05-21-2012)
Thank you for the fast replies!
I looked into your suggestions, but ultimately decided to do Fisher's exact test for each question, since the data set is so small. Though it's clear just eye-balling the data that there is no significant difference between the frequent and infrequent competitors I wound up with P values of:
Q1: 0.8
Q2: 0.99
Q3: 0.08
Q4: 0.41
Q5: 0.59
I was struggling to use the "R" software for the calculations, but ultimately found an online calculator that could handle a 2x4 matrix here:
http://in-silico.net/statistics/fisher_exact_test/2x4
Thanks again for the help!
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