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I'm taking a research class for Social Work and this is not my strong suit, so please be kind. :) The system that I have to do my statistical testing includes only the following tests: (ANOVA, Chi Square, Pearson's correlation, Spearman's correlation, Kruskal-Wallis H, Mann-Whitney U, Indpendent t-test, Paired t-test, Wilcoxxon Signed Ranks)

My problem is that I am working with a VERY small sample (currently only 9). I am trying to determine if there is a correlation between 2 ordinal variables. When I enter my data the scatterplot shows that it is non-monotonic. I believe this is due to 2 of my respondents' data being serious outliers. I'm hoping once I get my full results that the outliers will have less of an effect. However, I have to submit a preliminary analysis with the data I currently have. Can I use Spearman, or would one of the other tests be more appropriate?

Thank you so much!!

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  • $\begingroup$ When the variables are ordinal, what other options for measuring correlation do you have? $\endgroup$
    – whuber ♦
    Commented May 7, 2019 at 18:58

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Welcome to the site, and don't assume you cannot get good at statistics even if it seems daunting, just keep on trying to learn.

When choosing a statistical test, I think there are two important things to keep in mind: 1. Does it test the thing/question that you are trying to ask? (in this case whether there is a correlation between your two variables). 2. Does your data meet all of the assumptions of the test?

If the answer to either question is no, then you should probably not be using that test (or consider what you can do so you are no longer violating the assumptions, e.g. data transformation where possible).

If the answer to both questions is yes, a third question I might then consider is whether it is the most powerful test that can fulfil 1. and 2. (i.e. would another test have a greater probability of detecting a real difference or correlation, if it truly exists).

From what you have described of 1. what you are trying to test and 2. your data, I would say that the Spearman's rank test is appropriate, but you should read up on the assumptions of the test and check for yourself that you're happy your data meets the assumptions.

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