# Do I run a one-tailed or two-tailed test when running Spearman's correlation between interval and ordinal data?

I have one interval variable on a 1-25 point interval scale, i.e. placement test scores where 25 is the highest competence score (data not normally distributed), and six different ordinal variables on a 1-7 likert scale (where 7 is the highest score) in my data set. There are 12 participants (12 interval test scores) and 6 raters (each scored 6 different ordinal variables per participant).

Based on what I've read, I've decided to run the Spearman's correlation between the interval and each ordinal variable (i.e. six different correlation tests between the interval variable and each ordinal variable) in SPSS but would it be one-tailed? Or is there any other test I should run to test the level of agreement between the raters in my study?

• What hypothesis are you testing? That information is necessary for determining whether a one-tailed or two-tailed test should be run. (The data cannot tell you which one would be appropriate.) – whuber Jul 7 '14 at 19:08
• Thank you for your comment. My hypothesis is that the relationship between the two scales is unidirectional in that the higher the score on the 0-25 interval scale, the higher the score on the 1-7 ordinal Likert scale. Would that be a one-tailed Spearman's correlation test? – sb415 Jul 8 '14 at 6:03
• You can never prove a scientific hypothesis, so the way to proceed is to use your data to disprove the negation. That is, you would hope to demonstrate that the relationship is neither zero nor negative nor curvilinear. That's the null hypothesis. The alternative, which you will accept provided the null is rejected (and no other evidence emerges casting doubt on the statistical model), is what you hope to demonstrate. The curvilinearity is ruled out by assumption (which you should check). The rest can be tested using the Spearman coefficient; so yes, it's one-tailed. – whuber Jul 8 '14 at 14:09