Commenting results in a ratio scale

Question

Consider the following plot:

Is it mathematically correct if I say blue is 50% lower than red. Because from the plot it appears so, but what confuses me here is the scale in the y axis. So there blue appears to be ~10% lower than red.

In a plot where a metric is given as a ratio in the y axis. Can you use ratios again to explain the difference between observed variables. If so, should you comply to the values shown in the y axis, or can one explain the difference with relative ratios for the variables?

EDIT: to avoid confusion -- x axis shows just categorical variables. lets say method1, and method2.

Answer 1

There is always some confusion when talking about these things, I always get annoyed how the press seem to always make a mess.

If I sell 20 cars yesterday and 10 cars today, then the sale today is $50\%$ lower than the sale yesterday. I also sold $10$ fewer cars than yesterday. Therefore:

• The absolute difference is $10$ cars
• The relative difference is $50$ percent

Similarly, if, for example, the air humidity today is $10\%$ and it was $20\%$ yesterday, the humidity level is $50\%$ lower, than yesterday, and it is lower by $10\%$ (of humidity) compared to yesterday.

• The absolute difference is $10$ humidity percentages
• The relative difference is $50$ percent

Answer 2

The absolute difference by which the blue is lower is $\approx$ 10%

The % difference by which the blue is lower is $\approx$ 50%

Please note that we can compute a % difference only for a ratio scale.

To summarize, for this ratio scale, taking the base figures to be red,

Absolute difference = blue - red

% difference = $\dfrac{blue - red}{red}\times 100$