0

I have a dataset where I test for correlation and then if the correlation is significant. And basically my results are A correlates with B significantly and B correlates with C significantly, but A doesnt correlate significantly with C.

It is kind of unintuitive for me, I would have thought that A would also significantly correlate with C. Can anyone explain me why this is perfectly reasonable? I read about this question: If A and B are correlated with C, why are A and B not necessarily correlated?

But I dont think thats the exact same scenario here.

Baran Calisci
  • 35

2 Answers2

2

Happens all the time. Imagine a model:

  • $A \sim N(0,1)$,
  • $C \sim N(0,1)$,
  • $E \sim N(0,1)$,
  • $A$, $C$ and $E$ are independent (and, therefore, uncorrelated),
  • $B = 0.1 * A + 0.2 * C + \sqrt{1 - 0.1^2 - 0.2^2} * E$.

By construction,

  • $B \sim N(0,1)$,
  • ${\rm corr}(A,B) = 0.1$,
  • ${\rm corr}(B,C) = 0.2$.
stans
  • 1,746
2

Let $U, V$ denote uncorrelated random variables with variance one. Suppose that \begin{align*} B &= U + V \\ A & = U \\ C &= V \end{align*} $A$ and $C$ are uncorrelated by definition. However, \begin{align*} cov(A, B) = var(U) = 1 = var(V) = cov(B, C). \end{align*} This shows that $A, B$ and $B,C$ are pairwise correlated.

Andreas Dzemski
  • 822