2
data:  conflict$Livestock_density and conflict$Forest_density
S = 1e+08, p-value = 0.04
alternative hypothesis: true rho is not equal to 0
sample estimates:
rho 
-0.0694

Does $\hat{\rho} = -0.0694$ mean I should interpret test as not providing evidence of association, even though I have a low p-value?

Alexis
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  • A classic problem of either large sample size or scaled effects. Consider that sometimes our $x$ is measured on finite scales and the purpose of a regression is to be extrapolated slightly to understand the scale of an impact. Consider, for instance, associative studies of lead exposure. – AdamO Nov 28 '22 at 18:37
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    Yep, though scale on the variables won't impact a correlation -- nor indeed would it impact the precision of ranks $-$ so for this specific case only sample size will explain it. In any case its clear from the S value ($S=\sum_i d_i^2$) in the output that the sample size must be very large, looks like roughly in the ballpark of 820-920 (only having 1 significant figure on S makes it hard to be accurate; we do have three figures on the correlation ... but then only 1 significant figure on the p-value, so again hard to pin down very finely; let's say $n$ is around 870 give or take a few dozen. – Glen_b Nov 28 '22 at 23:42

2 Answers2

3

I’m guessing you have a huge sample. When this happens, your test gets very sensitive, so sensitive that it can detect tiny deviations from the null hypothesis.

Consequently, you have evidence of nonzero correlation, and that nonzero correlation seems to be quite small in magnitude.

Being slightly different from the null value is one way that the null hypothesis can be false.

Dave
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0

Your test results provide evidence of a small monotonic association at the $\alpha = 0.05$ level.

Alexis
  • 29,850