This might be a very basic question, but I've failed in finding an explanation on the web ...
How is it possible that a variable (Var1) that significantly correlates with two different variables (Var2 and Var3), would not correlated also with a fourth variable (Var4) which is the result of dividing the later two variables (Var4 = Var2/Var3)?
For example: I have an image in which one of the properties is "Quality". I use this image to obtain two measurements: $M_1$ and $M_2$. From $M_1$ and $M_2$ I calculate $F_1$ (which is my endpoint) by dividing $M_1$ by $M_2$ ($F_1 = M_1/M_2$).
Although I get a significant correlation between "Quality" to both $M_1$ and $M_2$ (Spearman's -0.625, P<0.0001 and -0.636, P<0.0001 respectively), the correlation between $F_1$ and "Quality" is non-significant (-0.095, p=0.565). It should also be noted that $M_1$ and $M_2$ strongly correlate with each other (0.692, P<0.0001).