I'm calculating ratios from paired samples and there is a point I don't understand. Supposed that I measured the values of 2 paired samples: A and B, and then I calculate the ratios from those values.
Ratio 1: $\frac{A}{B} = 0.5$
Ratio 2: $\frac{A}{B} = 2.0$
Normally one would calculate the average $ratio = \frac{(Ratio 1 + Ratio 2)}{2} = 1.25$. Then the conclusion would be: the value of A is 1.25 times higher than that of B.
But, the ratios can be understood as:
Ratio 1 = 0.5 --> the value of B is double the value of A
Ratio 2 = 2 --> the value of A is double the value of B
Then, the average ratio of A and B should be equal 1.
Does that make sense to you? Where is the flaw?
Thanks all,
Your ratios imply $A=0.5B$ and $A=2.0B$.
These multiplicative relationships are compatible with geometric sequences and the geometric mean which is $\sqrt{0.5 \times 2}=1$
The 'flaw' is using the arithmetic mean $\frac{0.5+2}{2}$