I'm trying to find out if a nominal variable A (2 values: x and y) and a numerical variable B (integer) are somehow related. E.g., does A=x mean that B will be lower than when A=y. I'm working with SPSS, and I have to admit that I'm not a very skilled statistician. Can anyone explain to me how to approach this?


1 Answer 1


There are many options. You could code the values of A as 0 and 1 (doesn't matter which, so long as you keep track) and calculate a point-biserial correlation with B, or Spearman's $\rho$, Kendall's $\tau$, or a Goodman–Kruskal $\gamma$ for that matter (good comparison questions to be found here and here). There are hypothesis tests for the difference of these effect sizes from zero.

You could also compare central tendencies of the two independent samples using A as a grouping variable, as by a t-test, Mann–Whitney U, or bootstrap test (you could also bootstrap the aforementioned effect sizes AFAIK). You can then calculate effect sizes from these statistics, including Cohen's d, Hedges' g, a few others, or even the r you'd get from the point-biserial correlation.

Some of these effect sizes differ in scale and need to be interpreted a little differently, but otherwise their differences are subtle. You'd probably do just about as well with any of them unless your situation is more peculiar than you've described it to be. If you're looking to test hypotheses, mind your test's assumptions, and consider differences in statistical power if you're short on data.

  • $\begingroup$ +1, good, comprehensive answer. Note also that from the OP's description, it sounds like they may just want a t-test rather than an actual correlation. $\endgroup$ Jun 8, 2014 at 1:04
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    $\begingroup$ @gung: I read it the opposite way because of the question of a relationship, but the "e.g." section seems to ask for a test of group differences. The difference between these approaches is part of what I meant to refer to as subtle. I wonder if we have any good questions yet about when to prefer one or the other... $\endgroup$ Jun 8, 2014 at 1:10
  • $\begingroup$ Good point, @NickStauner, you may be right. It's ambiguous. $\endgroup$ Jun 8, 2014 at 1:15
  • $\begingroup$ Apologies for the very late accept. :) I went with point-biserial correlation which worked out great for me, although I had to explain to my professors what it was... $\endgroup$
    – Korijn
    Apr 22, 2015 at 7:04

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