I am facing a situation where the correlation changes from .7 to .5 from time 1 to time 2 for data A and the corr changes from .3 to .1 from time 1 to time 2 for data B. The absolute magnitude of the change from time 1 to time 2 is the same (decline by .2) for both data sets, but the percentage change is different. For data A, correlation declines by 29% (=(.5-.7)/.7). For data B, corr declines by 67% (=(.1-.3)/.3). My gut feeling is that it does not make sense to measure correlation change in relative or percentage terms, as it seems to be heavily affected by the denominator. But I am not sure. Does anyone have a clue? Thanks!
7
-
1$\begingroup$ Isn't percent change always heavily affected by the denominator? $\endgroup$– DaveCommented Jul 2 at 14:55
-
$\begingroup$ @Dave thanks. So what is your answer to my question? $\endgroup$– dlqcCommented Jul 2 at 14:56
-
1$\begingroup$ It’s just math. The particular calculation might not give the most useful information, but the math is whatever it is. Now what’s your answer to my question? $\endgroup$– DaveCommented Jul 2 at 14:59
-
1$\begingroup$ How does that George Box line apply to this discussion? $\endgroup$– DaveCommented Jul 2 at 15:15
-
1$\begingroup$ Again, how does that apply here? I will disengage from non-sequiturs if your comments are not related to the topic. $\endgroup$– DaveCommented Jul 3 at 15:02
|
Show 2 more comments
1 Answer
$\begingroup$
$\endgroup$
1
It's not helpful or even always valid to talk about percentage change in correlations.
Let's note that in principle a correlation could be exactly zero, in which case percentage change from zero isn't even defined.
There are plenty of situations otherwise in which percentage change isn't helpful. So, an increase of $0.01$ from $0.01$ to $0.02$ is a $100$% increase, but any increase from $0.51$ could never be as much as that? So, a percent change from $-0.2$ to $-0.4$ is ... not helpful.
Sometimes the difference between correlations is worthy of focus, although showing what the correlations are is more informative.
If there is an alternative scale on which correlations $r$ might be well compared, it is that given by Fisher's transformation $z = \ \text{atanh}\ r$.
