# Pearson Correlation has quizzy results

I investigated experiments with SPSS and following values were out.

I have a question that in which case is possible to get Feature 1 in Group A+B as significant p<.05 while either Group A and B has low significance in Feature 1?

I hardly interpret because Group A have low correlation and Group B also, but combined group have correlation with (very) high significance.

(* p<.05)

Here you have a simple example with made-up data: there are two groups $A$ and $B$ and two variables $X$ and $Y$. In both groups alone the correlation of $X$ and $Y$ are small (r = -.17 and .23), but if you combine them you see a linear trend (r = .67).

So, as you can see, this kind of relation is possible. Local relations (or lack of them) is not the same as global relations. You can read more on atomistic fallacy and ecological fallacy - i.e. logical errors when drawing conclusions on groups based on individual level data or individuals based on group level data.

• Simpson's paradox is related. One statement is that amalgamation of subsets can result in changed magnitude and even sign of relationships. Nov 27, 2014 at 11:26
• Hi Tim, I think X and Y means random variable, it is clear, and what means group here? Like group A and group B? Sep 23, 2016 at 7:41
• And you said "combine them", what exactly you do for combine? Sep 23, 2016 at 7:42
• @LinMa X,Y are r.v. (on x- and y- axis of the plots). A,B are groups. By saying that I "combine" them I mean that I look at all of the data (third plot) ignoring the grouping.
– Tim
Sep 23, 2016 at 7:53
• @LinMa groups are groups as in the question.
– Tim
Sep 25, 2016 at 6:02