In another post, I created a bar graph that allows for quick visual comparison of Milwaukee cordless drill specs, with respect to maximum torque and no-load speed.
The two types of important technical specifications are not directly related, but it can be helpful to see how the values compare for different models in tandem.
For example, let’s say one drill delivers higher maximum torque but has a considerably lower top speed than another model. Seeing the torque and speed specs together can help convey and compare performance potential more clearly than simply looking at a bunch of numbers in a list.
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If we’re going to include more of these bar graphs in other posts, it made sense to have a separate primer as to how to interpret them.
Bar graphs are usually fairly easy to understand, but two-axes bar graphs can be tricky. Hopefully this helps ensure everyone is on the same page. I’ll link to this post when using double axes graphs in the future.
| Apples | Oranges | |
|---|---|---|
| John’s Farm | 20 | 45 |
| Jane’s Farm | 15 | 35 |
| Amy’s Farm | 30 | 15 |
| Adam’s Farm | 25 | 50 |
For example purposes, let’s say there are 4 farmers, with each one growing apples and oranges. The two types of fruit are not directly related, but it can be helpful to see the data visualized together.
In the bar graph shown here, we have the number of applies on the primary y-axis to the left, and the number of oranges on the secondary y-axis to the right.
In this chart, the two y-axes are identical. The second axis here, to the right, is redundant.
In this chart, the scale corresponding to the number of apples has been adjusted to the count of apples.
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We still have the number of apples to the left and number of oranges to the right.
Both of these charts show the same data, only in a different manner, depending on what’s important.
The chart with a common reference scale makes it easier to compare apples and oranges together, and the chart with two separate scales is for comparing apples to apples and oranges to oranges.
The axes will rarely be scaled similarly, and the units can also change.
In this example, we have the number of pizzas served and the number of olives used for 4 different pizzerias.
This chart has the numbers different on the primary (left) and secondary (right) axes. Couldn’t the data be shown with just one axes used as the reference scale?
Yes, and this is what it would look like. Which chart provides clearer or more helpful information with respect to pizzas served?
We could use two bar graphs instead. Combining them isn’t necessary, but can make it easier to see the relationship between two or more variables at the same time.
Let’s say we have a set of data with three variables, similar to how the chart at the top of the post shows maximum torque, and maximum no-load speeds for low and high gearbox settings.
| Apples | Small Oranges | Large Oranges | |
|---|---|---|---|
| John’s Farm | 20 | 35 | 10 |
| Jane’s Farm | 15 | 30 | 5 |
| Amy’s Farm | 30 | 10 | 5 |
| Adam’s Farm | 25 | 25 | 25 |
Consider the same 4 apple and orange farmers as above, but this time we are also interested in seeing how their total orange harvest is comprised of small and large oranges.
In this chart, we have the farmers and their farms on the x-axis, and the number of fruit on the y-axes.
The breakdown of oranges by size might not be important to everyone reading the chart, but nothing is lost by including it in this manner.
The chart makes it easier to compare apples to apples and oranges to oranges, and the ratio of small to large oranges for each farmer.
We can also compare small oranges to small oranges between different farmers, and large oranges to large oranges, although it’s not as efficient. If such comparisons were a higher priority, a modified or separate chart would needed.
Finally, here’s the graph comparing max torque and speed ranges for Milwaukee’s M18 cordless drills.
The units for max torque and speed are completely different – inch-pounds for torque and rotations per minute for speed. This requires that two axes be used, or for the data to be shown on two separate charts.
Having the data grouped together in a single chart is better than using two graphs that would have to be referred to separately.
What can you see from this chart? A lot, but we can save that discussion for another time.
I color-coded the left and right axes labels to help guide readers who might be less familiar with this type of chart, and will try to do the same in the future.
Having the different sets of data in one chart makes it easier to get into more complex comparisons.
Questions?
If there’s something I can do a better job explaining, please let me know!
Steve L
A picture is worth a thousand words.
Graphs were well done. Can you arrange delivery of the pizzas?
Richard
> The vertical y-axis labels are also color-coded to help guide you.
I’m color blind. The orange and red are very similar. I can distinguish them but it takes a split second longer. Colors on the text are basically not noticeable on any of them. I had to scroll back to realize they were color coded the first time.
An explicit legend would help or some differentiation (like stripes versus solid) in addition to the colors.
One positive bit: thanks for labeling your axis. That’s a huge gripe with a lot of charts.
Stuart
Sorry; I was conscious of that for the actual Milwaukee charts, with red for torque and dark blue for speed.
I can try solid and striped patterns, but that will make it harder to match to the left and right axes.
I will look into better color combinations. Are you able to differentiate the colors in the cordless drill spec charts?
John Blair
This is a nice article that helps visualize what color blind people see.
https://www.datylon.com/blog/data-visualization-for-colorblind-readers#:~:text=Color%20blind%20palette,-The%20picture%20below&text=The%20first%20rule%20of%20making,out%20of%20these%20two%20hues.
Ross
When I read your explanation about the need for two y-axes, my immediate thought/explanation was “put an M18 Hole Hawg into the mix.” If the graphs were separate, the Hole Hawg would comparatively look like a hero on the torque graph and like trash on the RPM graph. With the combined graph, you could visually see that it’s just a totally class of tool.
Stuart
We can do that too.
I’m working on a chart to show M18 Fuel progression to satisfy a reader question, and can certainly put together cross-brand or cross-category comparisons.
jake
Thank you for the thoughtful and informative discussion. Two-axis bar charts could be very helpful in understanding some datasets. Do you favor using spreadsheet(s) or other apps for data analysis and graphing?
Stuart
I feel that spreadsheets are easier to use for something like this – once you work out how to do what you want to do – and more versatile with respect to customizing the presentation.
In general, I prefer data analysis and graphing software for use with measurement data. However, I’ve looked into getting a new license, and found the packages to be bloated and prohibitively expensive.
I also used a spreadsheet to assemble the data tables.
So, I used a spreadsheet for this, but to answer your question, I would prefer to use other apps for data analysis and graphing. I consider what I did in the other post to be more data visualization than analysis.
If say I wanted to plot torque and max speed measurements, rather than taking values from a specs table, I might use spreadsheets for casual use, but would switch to analysis and graphing software for regular use.
TonyT
I just did some research into open source statistics programs, and ended up using Blue Sky Statistics, partly because it was the only one with Six Sigma/SPC charts.
I like it do far, although the latest version (newly cross platform, so a huge change) isn’t polished yet. There’s also a commercial version available with extra features and support that’s much cheaper than Minitab (we plan on getting a permanent license)
I also found some programs that are more focused on interactive graphing but haven’t tried any out yet.
Stuart
Thanks, will take a look! I never had good luck with free graphing software, but am open to new ones.
Regarding paid software I had access to:
Kaleidagraph was my favorite – I liked that it was functional and quick. It might have gained some bloat in the years since I’ve used it.
I have used Origin a little and believe I tried SigmaPlot at one point. They were more sophisticated and polished than Kaleidagraph, but I always went back.
I used Mathematica, mainly for classwork, and then Matlab for a bit.
I’ve been meaning to try Labview’s free “Community Edition” software.
TonyT
BlueSky is really statistics, so it’s a bit different in orientation than Kaleidagraph. It uses R under the hood and is supposedly similar to SPSS.
Graphing is quick but not interactive and not flexible. But it handles 30,000 data points with ease.
Kaleidagraph is $250. Commercial statistics programs are at another level, e.g. MiniTab wants almost $2k per year for a subscription.
There is a lot of interesting
free software such as Octave and SMath. And programs without a commercial equivalent such as Jupyter, but I haven’t used these (yet).
alex
Python w/ matplotlib is excellent and very flexible, though (of course) you have to know/learn python (useful in itself!)
Also, Free!
Champs
The graphs already made sense to me, but then again, I believe in the line Ronald Reagan made famous: “if you’re explaining, you’re losing.”
No matter, I suspect that this is content mostly written for backreference. Hello future reader! We made it!
Stuart
Simple bar graphs shouldn’t need explaining, but double axes charts might.
What if say a theater club student is shopping for stage building tools and lands on the Milwaukee drill comparison post? Or someone who hasn’t seen any bar graph in years?
After creating the first chart with drill torque and speed specs, it hit me that dual axes charts are a great way to visualize indirectly related but cross-relevant specs.
Consider, for instance, reciprocating saw stroke length and strokes per minute, or circular saw blade size and rotational speed.
Rather than explain how to read dual axes charts in every use, I can add a line or two and link to this primer.
Rx9
Having cobbled together many, many of these things in Excel and PowerBI, I liked the clarity and appearance.
Dave
I disagree. It’s about what’s really important or what you stress. You don’t have to waste time highlighting least important numbers and creating presentations of many many graphs is a waste of time. You loose the audience quickly by overloading. Use graphs ONLY for the most important bits to give a picture to remember. Limit graphs only to what you want to stress and what the user finds important and limit the number of graphs to three or so. Put worthless data (like what is on this) in a table for the adhd affected to study.
If I have to suffer through presentations or explanations with many multi-axes graphs over inconsequential data, the presenter either provides bagels or doughnuts or I deny funding.
MM
I think this is dependent on the target audience. I suspect Stuart is used to academic presentations. In an academic presentation there’s rarely such a thing as inconsequential data. As a former academic and a current engineer the data is the only thing I want to see. I don’t care about someone’s opinions or useless stock photos, I want to see numbers. And I want to see all of them because if the presenter is leaving something out I’m wondering if the omission was deliberate, either to hide unfavorable information or to cover up a half-ass job where certain data was never studied at all. What the presenter doesn’t talk about can be just as meaningful as what they do. For example, in this context if a new power tool brand talks about how their new drill competes versus brands A, B, D, E, and F: I’m instantly wondering why Brand C is omitted from the comparison. Is it because Brand C outperforms this new tool? Or is it because the new company failed to include all the competition in the test matrix from the get-go and the work was never done? Or, if the hypothetical new brand hypes up torque, RPM, and tool weight in their presentation…that’s nice, but why aren’t we hearing about runtime or charging speed? Even if the data is not all that important it is included because it demonstrates that it was considered. If nothing else it’s due diligence, and an experimental control.
A presentation to a non-technical audience is a whole different ballgame, as you just described. But the hardest is when you have a mixed audience, which I suspect is the case here on Toolguyd. If you leave out too much data the technically minded think you’re a windbag–or worse, a marketer–with nothing to back up your claims, and if you include too much you lose the attention of management and whatever point you were trying to make gets lost in a sea of confusion. It’s not easy to please everybody.
Stuart
Numbers are important, but so are trends and the relationship between numbers.
Let’s say one tool weighs 2.2 lbs and the other 3.2 lbs. That 1 lb difference means one is more than 45% heavier than the other. We can compare two values in a sentence or two just as I did here. But for 4 or more tools? Graphs make sense, and *show* the difference.
3 is 50% more than 2. 2 is 33% less than 3. 50% more or 33% less can be used to different effect, depending on the goal. A graph shows the raw relationship.
Graphs can be used to make a point. I also think they can be used so that readers can take what they need. If it’s not helpful, scroll past it.
In academic presentations – which I haven’t done many of, and not for well over a decade now – there can be too much data and graphics.
I came across a torque and speed chart and found it helpful, and exactly at a time when I came across a couple of truly terrible Milwaukee cordless drill buying guides on my phone’s news feed.
In the past I compared different tools with sequential specs lists. It can be a hassle to scroll up and down to compare values.
So I worked on a way to visualize co-dependent specs, and more easily build multi-product spec tables.
These will be tools I can use. If I can use them, I figure readers can too. And if not, no biggie, they’re be clearly marked. It’s easier to scroll past a chart than several paragraphs filled with numerical comparisons.
Stuart
In the context of a cordless drill, would you say that speed is a “least important number” that’s a “waste of time” to display?
Torque and speed are interdependent. If you’re not pushing a cordless drill to max torque, its rotational speed determines its application speed.
What would you rather have, a cordless drill that delivers 650 in-lbs with a 1700 RPM max speed, or one that delivers 600 in-lbs max torque and 2000 RPM max speed?
Data tables are useful when the numbers are important. Graphs are useful when the relationship between values are important.
Koko The Talking Ape
The undeveloped yet very strict mathematician in me balks at using two different units for the Y-axis, but I can see how it makes for quick and easy comparisons. In fact, I could see adding another unit, namely cost. Then you’d have all the basic information needed to determine, roughly, which drill you’d want for which purpose.
But comparing different models is all this graph is used for. The X-axis isn’t any kind of continuous variable like time or cost. So I wonder if it shouldn’t be called a “chart” instead of a “graph.”
Stuart
Bar graphs typically have non-numerical x-axis values.
The number of apples grown at different farms would still be a bar graph, as would be the number of apples picked at different hours of the day.
When you have continuous x-axis variable with no breaks or separations, that would be a line graph.
If the x-axis in a graph can be named months of a year, why not farms or models of cordless drills?
I am deeply hesitant to include pricing in a graph or data table, as they can and often do change.
Instead of two different units, such as in-lbs and RPM, the data can be normalized with the top performer being 100%, but that would take away from its usefulness.
Ideally, graphs or charts would be side by side. But, that would make them way too small on a mobile device. It’s hard to see two relationships at the same time if charts are one after the other. So, dual y-axes seemed to be the best or least worst compromise.
David Z
I think I’m nitpicking, and i might be wrong, but I think what you’ve been focusing on isn’t 2-axis, but dual axis.
2-axis just refers to having an x and y axis, just as 3-axis adds the z-axis.
Dual axis refers to having two scales on one axis.
Stuart
I’ve seen 2-axis and dual axis used interchangeably. Is one more correct than the other? Maybe. They both seem inherently wrong to me.
Personally I think it’s better to say primary and secondary axes, but it’s too clunky.
Joe
I like this primer and I’m sure it’s helpful for people who aren’t used to looking at this kind of chart. One suggestion: When I use this type of chart, I’ll often add “(left axis)” or “(right axis)” behind the series name in the legend so it directs the reader to the right axis/scale. Just a suggestion – doesn’t always make sense depending on your available space and how cluttered the legend is, but I use it when I can.
Stuart
I didn’t think of that, will consider it – thanks!
I like to keep legends somewhat minimal, as too many additions can cause rather than avoid confusion. Part of the purpose of this primer is to make it unnecessary to add more than a couple of words whenever similar charts are used in future posts. Even with arrows directing users to the appropriate measurement scale, a separate primer should still be pointed to, to ensure everyone can be brought up to speed quickly.
I tried to write the primer for everyone, from students who might not have seen graphs like this in school, to retirees who haven’t seen any bar graph in decades, and everyone in between.
Too much text can also cause problems with resizing the charts to fit the page.
Daniel L.
All I learned from this is that guys are generally better farmers, and gals are generally better cooks. LOL.
Jokes aside, a good article on interpreting bar graphs, thanks! Also, I got a nice graph on how my M12 tools compare to my M18 tools.
Stuart
Thanks!
I included that chart and separate M12 and M18 charts in this post – https://14cyiuhvcgv.com/best-milwaukee-cordless-drills-2023/%3C/a%3E .
Craig
If you are going down this path, read one of Tufte’s books. “The Visual Display of Quantitative Data”, his first, is the best. Made all my research assistants read it.
(44 years of experience with all manor of statistical modeling software, starting with SAS 76)
Stuart
Thanks, will take a look!
TonyT
Another vote for The Visual Display of Quantitative Information. It’s a classic.