# Log scale not enough

I want to show faster runtimes of a technique compared to another technique. On the x-axis, I have different scenarios and on the y-axis the runtime for each technique in each scenario.

The problem is that the runtimes of the newer technique are magnitudes shorter and are not visible (on the x-axis) even when using a log-scale.

Is there another kind of scale that would help and that's appropriate? Or does it make more sense putting the values in different plots with different y-axis scales?

• Is there a problem with setting the range of the y-axis to include all the log values? – whuber Feb 2 '17 at 15:34
• The reciprocal of a time is a (kind of) speed. Reaction times in psychology and other times are often transformed in this way. (In the latter case, lab rats or students who never solved the problem can be coded as infinite time => zero speed.) – Nick Cox Feb 2 '17 at 15:45
• I think the suggestion of considering speed is a good one. It might perhaps make more sense to consider "never solved" as censored (left censored for a speed variable), since presumably they might have solved it in finite time if observed for longer; a different symbol, might suit (if uncensored observations were a solid point, then perhaps an open circle at the censoring speed with a line segment down to zero might suffice). However, it's not clear if there are any such cases here. – Glen_b Feb 3 '17 at 1:55
• I think the consideration of speed is a little uncommen in computer science, but I will think about it. All scenarios were solved in finite time, so I don't have to worry about that. I'm thinking about just comparing the values in a table rather then plotting them. – CGFoX Feb 3 '17 at 9:33

## 1 Answer

I think considering reciprocal of time (speed) - as Nick suggested in comments - is worth a try; it's something I've done on a number of occasions with time variables.

Another option might be to consider scale breaks (Which I think is best done by dividing the entire plot with a little whitespace between two enclosed plot regions).

If there are any cases that are never solved (it sounds like this is not the case but it's worth mentioning anyway), it might perhaps make more sense to consider the never solved cases as censored (left censored for a speed variable), since presumably they might have solved it in finite time if observed for longer; a different symbol, might suit (if uncensored observations were a solid point, then perhaps an open circle at the censoring speed with a line segment down to zero might suffice).