Let’s say I want to graph a function that I think would look best like this. One axis will be linear. The other would be linear at smaller scales, let’s say from 1 to 100, but from 100 on up would work better as a logarithmic scale, going from 100 to 1,000, then 10,000 and so on. Would the be a semi-semi-logarithmic graph? Is there some other proper name for that type of graph?
I’m not sure there’s a widely accepted term but “graph with a scale break” would probably get the idea across.
Actually, “scale break” is a pretty widely accepted term, along with axis break or broken axis.
Here’s a solid discussion on graphing highly skewed data:
There’s a few basic options:
- Graph as-is;
- Graph with a second axis;
- Graph the logarithm of the data;
- Use a scale break.
- Plot the data multiple times.
I think that web page is sorely mistaken. With the data set he has there, plotting the data as-is is the one and only correct solution, because it correctly shows that essentially all of the sales are in two months, and that all of the other months have negligible sales. Sure, there’s still data in which of the other months are larger or smaller than others, but it’s utterly irrelevant data: If all of those months went completely to zero, the company that’s making those sales wouldn’t even notice the difference in their bottom line. And none of the criticisms he has of that graph actually have anything to do with the Y-axis scaling: It’s all just that the X axis is poorly labeled (which could easily be just as much of a problem with any of the other graphs, except that he quietly fixed it for them).
Chronos: That’s a nice point. I would agree if the graph is showing a seasonal effect. But if those 2 outliers are a one-off, then the reader might be interested in observing more representative observations from other months.
Here’s another approach: skip the outlying months altogether. I’ve seen Kevin Drum skip the Covid era, when plotting a long run economic trend - it is graphed as a break in the series.
You are allowed to plot the data twice, each time with different scaling, aren’t you? Assuming that is less confusing.
Back in the day, I worked at a place that tried to introduce statistical controls. One fellow wanted to show how things were (fine except for one department). But done with a linear scale,there was only one bar visible. So he simply had an even scale on the vertical - 1,2,3,50.
The big shots were not impressed. They compared the graph to manure.
If you want a discontinuous scale on a graph - you see them from time to time - the axis with the scale is usually shown with a pair of horizontal zigzags interrupting the vertical line that sort of indicate “the’re a piece missing here…”.
I would think if the scale changes type (linear to logarithmic) you would want the graph itself to to very very obviously indicate that. Otherwise, it’s misleading.
I think we have to call shenanigans on that one. The part of the axis labeled 1,2,3, if the tick marks are evenly spaced there, is fine. But there’s no way to measure the scale on the part with nothing but a “50” label. Now, if it had been 1,2,3,40,60 with some marking to indicate the location of the discontinuity, I’d be happy.
As far as big shots go, the big shots at my ex employer published several graphs with evenly spaced tick marks labeled with non-evenly spaced values, and all sorts of other nonsense, like “a decrease of -X%”. I think big shot commentary on graphs is one of those “for what it’s worth” categories.
I’m going to vote “yes” on this one. I’ve even seen a technical paper in a reviewed journal that had a “log Fahrenheit temperature” scale, in a situation where that really did allocate the viewer’s attention to heteroskedastic data quite nicely. There’s no reason to lean on scientists to make them pedestrian in their thinking.
But there aren’t two outliers on that graph. There are ten. Almost all of the sales were in those two months. The only way that the other months can be “more representative” would be if the levels stayed at a few hundred for several decades, aside from those two isolated months.
Let me try again. Say the business is plotting Christmas wrap sales. Then yes, I agree, you care a lot more about sales in December (and discounted sales in January) than the rest of the year. Because next December and January you would expect the pattern to repeat itself.
But you can also imagine that it’s a graph of a specialized part and that there was a sudden but temporary spike of demand in 2 consecutive months. You might care less about those months because this was a a one-off for the business, a one-time windfall. I admit this is less likely - I can imagine another situation where the business sells faddish items in which case they would really care about what The Next Big Thing is. If the business sells yo-yo’s, pet rocks, and Mad Libs pads, I could imagine that they would focus on riding the big sales waves, rather than the trickles at other times.
If you don’t care about those two months, you could set the vertical scale ignoring them; they will just go off-scale, indicated by a broken bar.
Wouldn’t a table make more sense?
Of course, we might not be plotting quantities. We could be plotting something like interest rates or temperature. I can imagine a situation where the underlying forces vary a lot, but you still care about the variation at the peak and trough. Temperatures on the moon might be one example: they plummet during the lunar night and skyrocket during the day. Or maybe Mars, which has a temperature-relevant atmosphere.1 Interest rates before, during, and after hyperinflation could be another example.
1 I think.
I’ve made a lot of log-linear graphs in my day (log y axis, linear x axis), but I can’t recall ever switching from one to the other at an axis break. I feel like that would be confusing more than anything…
Yeah, I was unclear - I knew “scale break” was common but I didn’t know if “graph with a scale break” was a standard term (or just an obvious use of words).
Yeah.
Agreeing with the above - “scale break” is common, but after further thought I’ve only seen it as a jump in the scale, not a transition from linear to logarithmic. Maybe it could be done somehow, but I can’t picture a non-confusing way. And that’s especially true if you plot any curves across the transition. Definitely don’t do that.
I think in most of these cases, the best choice is two graphs. Show one with a linear scale to display the detail on values from 1-100, and a second with a log scale to show the complete picture.
There’s also this. There are clearly times when a table is better than a graph.
I’ve seen a prolific but unsophisticated inventor create a graph axis that uses two different metrics which are inverses, switching between them at the value “1”. It was like, for example, switching between miles per gallon and gallons per mile, or between pounds per dollar and dollars per pound. His incentive was that a linear scale using either one of the metrics would crowd many of the points against “0” because of the large dynamic range in his data. I think he didn’t understand logarithms well enough to use them. He did accomplish avoiding crowding points together at one end or the other of his axis. But it did require a double take to realize what he was doing.