# Is Pearson Coefficient applicable to my data (mixed variable types)?

TL:DR is Pearson correlation acceptable for a binary variable?

For my study I have measured and determined a "change in anxiety" in a group of students (the change has been found significant with large effect size using paired t-test [same group of students: test/re-test]). I have 4 variables that I want to to see if there is any correlation between them and the change in anxiety. I have been at this for 6+ hours reading Dornyei's book on Research Methods and Green and Salkind's SPSS Handbook and posts on ResearchGate, etc, etc, etc. No clear answers.

My variables are

1. (Binary) Gender
2. Age
3. Field of study (11 categories)
4. (Binary) whether the instructor is a native English speaker or a non-native English speaker

For gender, in SPSS, I used 1 for male and 2 for female.

For #4 I did similar. 1 for native, 2 for non-native speaker of English.

I ran bivariate correlation analysis (in SPSS). I got no significant correlation for #1, #2, or #3.

For number #4 my Pearson output data indicated a significant (but weak) correlation and effect size: r(397) = .109, p .05 (sig = .030).

Is this data okay? If I try to publish a paper saying I used Pearson's correlation are they going to say "okay" or "what the hell are you thinking" because I see no clear answer out there on the forums or in my reference books. Some say binary data is perfectly acceptable for Pearson correlation.

Just for kicks

Kendall tau b: r(397) = .086, p .05 (sig = .037).

Spearman's rho: r(397) = .105, p .05 (sig = .037).

Maybe I am just tired and the answer is right in front of me, but how can I see the relationship between native and non-native English speaking teachers and change in anxiety. I don't just mean "there is/is not a correlation". The above data is showing there is a SMALL but significant correlation, but how do I show (with data or graphs) the effect of native English speaking teachers on the change in anxiety and the effect of non-native English speaking teachers on the change in anxiety.

• I'm commenting instead of leaving an answer because I don't have time to create a nice long technical answer for you. But briefly: to correlate a binary variable with a continuous one, it is technically recommended to use a point-biserial correlation. If I remember correctly, though, the point-biserial formula is just a shortcut for the more complicated Pearson formula that works when one variable is binary. If you have software, you might as well just run the Pearson correlation. Just be careful to note how the coding scheme so you know how to interpret a positive vs. negative correlation. – psychometriko Dec 9 '15 at 13:29
• Thank you for the comment! My SPSS reference book states that SPSS "automatically adjusts the calculations accordingly" for "variables [that] are dichotomous (like gender)". This is listed under the "point-biserial correlations" sub heading. So with your comment, and if the above is true, then my Pearson correlation should be valid data. – Robert Dykes Dec 9 '15 at 13:53