Fixing a Dual Y-axis Chart from a Real Industry Report: Two Alternatives

The “Dual Y-Axis” Chart

Dual Y-axis charts are common in business reporting, and most of them do more harm than good. As Exhibit A, I present…

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I’ve anonymized this chart to not offend the organization who published it, but this chart is based on a real industry report. Unfortunately, it’s not an uncommon choice and arises when anyone is challenged with presenting two pieces of (supposedly) related data on a single chart or slide. I have several issues with the chart:

  • The bar chart is correctly scaled to a lower value of zero but the large values make it difficult to see year to year changes which only occur within the upper 15% of the range.
  • The trend line has been “smoothed”. This obscures the data and implies movement between quarters that doesn’t exist.
  • The quarterly results are from Q2 of one year to Q3 of the next—six quarters. This seems like an odd choice and I would argue starting at Q1 and continuing through the latest quarter (or quarter of interest).
  • The year-over-year percent change implies past values are important, but the reader needs to back-out the prior year values if they want to make a direct comparison to the prior year. If we’re looking at changes over the past, in this case, three years, let’s show that data for each year.

To address these issues, I want to apply the following ideas to make the charts more accessible to the reader: don’t use two y-axes (make this a rule, not a guideline), trends should be captured with a line chart, the time frame of interest should be clearly stated in the title or subtitle (preferably the subtitle), the x-axis dates should be legible (the chart above does this well, but it’s often a challenge with time-series data), and finally, any chart created should stand on its own without needing a table—if a table is needed for reference, it should be a standalone item.

Can this data be presented on a single panel without two y-axes? Here are two ways.

Alternative A

First, I decided that the period of interest is from 2023 to 2025 with the main message being captured in the title and the period clearly defined in the chart subtitle. Most importantly, I’ve changed the bar chart to a line chart as I want to focus on trends in the data; this immediately frees me to narrow the y-axis scale making the year-to-year variations visible. For this chart, I decided that I want the reader to have access to all the data, so each point is labeled with both the number of units (shipped) and the year-over-year percent change positioned above and below each marker, respectively. This chart pushes the upper limit of values placed on a chart—I see 10 to 12 labeled points being an upper limit. There’s a real argument that I’ve just moved the data table into the chart rather than eliminating it, but I’d rather have annotations the reader can immediately follow than a separate table they have to cross-reference. Units use a bold font to ensure a dominant position. Overall, I would argue this chart captures elements from the original while reducing the cognitive load required by the reader.

One thing I’d consider changing is my display of each period (quarters). While the major grid lines are sufficient for the calendar year, the minor grid lines are subtle and may not provide sufficient differentiation for some viewers. Adding a light shading to the panel with white grid lines would be an option worth exploring.

Alternative B

Since the dual y-axis chart is really two charts, it makes sense to create two charts. The question is then, how do I place these charts on the page to help the reader digest the content quickly. Not only do we have the obvious options of side-by-side versus stacked, but we also have to consider the relative size of each chart and how that conveys the message we want to deliver.

In the second example above, I’ve kept my basic line chart, but decided to only include the minimum and latest value in the chart. Because of this choice, I’ve reintroduced the y-axis which allows the reader to approximate the other values as needed. I could have used a second line chart for the year-over-year percent changes; however, the bar chart clearly differentiates the two sets of data. The ability to color negative values as red is a further visual cue that the period from 2023 to early 2024 was difficult, but that since Q3 2024, the trend has been positive.

I also made a choice to move the y-axis titles to a horizontal position at the top of the panel of each chart. No need for the reader to tilt their head as they scan down the page. I’m aware of at least one plot tool that implements this style as the default placement.

That said, the size of each panel is used to convey importance, with the top chart (Units) dominating the bottom chart (YoY%).

Again, to aid the reader, I’d like to find a way to incorporate quarterly labels to the chart; however, my fear is that additional labels would add visual clutter. The quarterly bars do an adequate job providing this differentiation. If my plan is to use this chart in a presentation, I’d take time to ensure the fonts are appropriate—they may need to be increased.

My Conclusion

The visual clutter and cognitive load associated with dual y-axis charts can be avoided by using annotations on a single chart, or by creating two separate charts. This can be a time-consuming task in Excel; however, modern data analytic packages in python (Plotnine) or R (ggplot2) enable a repeatable framework that can streamline the process.

There are some great books available to help you create impactful charts and presentations. Three resources I continually reference are: Storytelling with Data by Cole Nussbaumer Knaflic which provides a solid framework to build effective data visualizations; Strategic Storytelling by Dave McKinsey, an overlooked gem demonstrating how top consulting firms incorporate visualizations into effective presentations; and Slide:ology by Nancy Duarte, which pushes the reader to think like a designer. While each has their own terminology, the goal is always the same, create visualizations (presentations) that inform the reader or audience.

Tips To Help You When Starting Graduate School

It’s all about understanding their process.

A little over five years ago, I took a university administrator (staff) position after 15 years working at public and private companies. This change was somewhat of a homecoming as I had left a faculty position before moving into my industry work, but that is another story.

My goal here is to help guide folks on how to be successful in graduate school. 

First, I recognize there are significant differences between STEM fields and non-STEM fields—I come from the former. STEM fields include engineering, life sciences, physical sciences, and mathematics; non-STEM areas include social sciences and the humanities. A Council of Graduate Schools presentation from 2007 showed Ph.D. completion rates for STEM fields between 48% and 57% after seven years, with graduate students completing non-STEM degrees at 29% for Humanities and 41% for Social Sciences. At the 10-year mark, approximately 64% of engineering and life sciences graduate students completed the Ph.D.; social sciences and physical sciences topped out at 55%; the humanities failed to break 50%—showing only a 49% Ph.D. completion rate after ten years. (https://nanopdf.com/download/phd-completion-project-nsf-agep_pdf#)

A summary of the STEM master’s completion rates after four years was 66%. (https://cgsnet.org/masters-completion-project)

This article isn’t a research paper, so I didn’t dig further, but I would wager these numbers haven’t improved. 

How do you make sure you’re in the group that makes it?

Do the math.

If you’re applying for a Ph.D. program, you should expect a stipend and a tuition waiver, and you should look at this as a full-time job. For first-year graduate students in STEM fields, the department will likely tie compensation to being a teaching assistant (TA). In other words, you’re working for the money. Ideally, your faculty sponsor will be able to fund your work after the first year with a continued tuition waiver. Even if you’re getting paid and receive a tuition waiver, there is still the lost opportunity cost of what you could be earning by starting your career. That lost opportunity cost only gets more significant as the time to degree grows. Few people get rich after earning a Ph.D., and fewer doctoral graduates are finding tenure-line positions that offer lifetime job security. So do the math and figure out if the financial commitments and personal rewards are balanced.

If you’re applying to a master’s or professional program (e.g., health, MBA, professional science master’s), you will most likely be paying tuition—just like an undergraduate program. Unfortunately, unlike undergraduate studies, there are fewer opportunities for financial aid. One bright spot is that some employers have tuition reimbursement programs as part of their often underused benefits. I recognize that this assumes you are working in a closely related field, but this is an option to consider if the stars align in your favor.

Does it ever make sense to pay for a master’s or professional degree? If the total debt is manageable and the salary increases authentic, there should be a reasonable return on investment, but you have to do the math.

Before you apply, find out if you need a faculty sponsor (Ph.D. programs).

I’ll admit, this is not a requirement I’m familiar with as it’s not common in my field; however, I understand it is becoming more prevalent for smaller STEM programs and non-STEM areas. It’s frustrating to have a stellar GPA, excellent GRE scores, and solid letters of recommendation only to find out you weren’t accepted into a program because you didn’t nail down a sponsor during the application process. If the program you’re interested in doesn’t clearly state this requirement on their website, send an email to the program advisor and ask the question. 

Before you commit to a program, find out what their graduates are doing.

If you’re starting down the Ph.D. path, you probably have visions of being a professor. Unfortunately, the number of tenure-line faculty positions has collapsed as colleges and universities have decided to follow the cost-saving practice of hiring non-tenure line (aka, adjunct) faculty. Perhaps you’re doing better work than graduates from the nation’s top research institutions, but don’t ignore the inherent bias towards prestigious universities built into the system. Understanding what graduates do after completing their degree is a reasonable way to gauge your possible paths after graduation. Tracking graduate outcomes is hard, and most departments are just learning how to do this, so you might want to do this on your own. Successful faculty mentors will often advertise where their alumni go; however, some diligent work using LinkedIn might provide enough insights to guide your decision. 

Choose your advisor carefully.

If you’re looking at a traditional, research-based graduate program, you will spend most of that time working with a single faculty advisor. Yes, you may be required to rotate through several groups during your first year or “interview” multiple faculty as potential advisors, but this can be a ceremonial dance for many. Regardless, at the end of the courtship, it will come down to choosing one person to be your boss for the next four-plus years. If everything goes great, they will be a mentor and eventually a colleague, but at the beginning, they’re your boss. If you can’t identify who you’ll work for before starting a program, you should determine several faculty with whom you’d be willing to work—make sure you have options.

Focus on the process.

Each program should document the expected milestones for its program. Are placement exams required? How many courses do you need to complete, and by when? How are qualifying exams managed? When will you choose an advisor (if you weren’t required to do so before starting the program)? When will you form an advisory committee and present your dissertation proposal? What resources are available to students. And finally, when do you get to defend your work and graduate?

Be wary if a program hasn’t documented its process.

When you start your research, begin with the end in mind. 

(With apologies to the late Steven Covey)

When I started graduate school and joined a research group, several members were finishing—each was kind enough to give me a “comb” bound copy of their thesis. I didn’t realize this at the time, but this gave me a clear vision of what I needed to do to graduate. 

Go to the library (or open up a web browser) and download several recent dissertations from previous students in your group or department. Don’t look at how long it took the authors to complete the work—ask yourself, “can I complete a similar project in under five years?” Better yet, ask the question, “what do I need to complete a similar project in under five years?”

Don’t rely on luck.

I lucked into a good graduate experience; unfortunately, I’ve known people who struggled. Many don’t have a mentor with whom they can work as they contemplate graduate school, so I hope the thoughts above are helpful.

Planning for the long term

When do we make long term plans? 

As winter moves towards spring, my main job is to help potential students apply to graduate school—for programs that won’t start until Fall. And while most people assume a master’s degree takes two years to complete, that quickly goes to three when attending part-time. 

So, I’m asking people to envision their life three-plus years down the road when most of us can barely figure out what we’re going to do this week.

When I talk to people contemplating graduate school and the time commitments needed to be successful, I tell them it will go by quickly if they can fully commit to the program—planning for interruptions and distractions that will undoubtedly come. For working professionals, particularly in STEM disciplines, the goal of higher education usually isn’t learning for the sake of learning but to develop new knowledge and skills that will create value for themselves and their future employers. (Although I don’t think you can be successful without finding pleasure in learning itself.)

So what’s the plan?

Most people overestimate what they can do in one year and undersetimate what they can do in ten years.

Bill Gates

Opportunities to make change

I was listening to Freakonomics Radio podcast interview with Rahm Emanuel, who pointed out his somewhat famous quote is often shortened. Here is the full quote:

“You never want a serious crisis to go to waste. And what I mean by that is an opportunity to do things that you think you could not do before.”

Rahm Emanuel

I have taken this to heart in making changes at work, which means taking some professional risks. These are not substantial personal risks—they are trivial in the grand scheme of things, but meaningful to a small group of people where we can make work better. I am grateful that others have supported these changes.

We should not need a crisis to initiate change, and many managers have more authority to make changes than they think. We should want to make things better—always.

Applied Statistics

In some circles, “Statistics” has a bad reputation—primarily because most of us had limited training though the techniques are applied in numerous fields. The pharmaceutical industry uses statistical tests to determine if new drugs are effective (or harmful), manufacturing industries implement statistical process control to maintain ever higher quality standards, politicians have increased the use of polling to drive policy decisions, and the list could go on.

But in the current discussions on STEM education, I have yet to see an argument where statistics is elevated in the curriculum the way “computer programming” has been promoted.

Is it the way we teach math in general—heavy on theory and light on applications? For many, the applications are what makes the work interesting.

The $100,000 master’s degree?

The discussion on college debt seems to focus on extreme cases, and Six Figures in Debt for a Master’s Degree from Inside HigherEd pointed out several of these. While they did break down the averages by degree. It’s helpful to look at the type of institutions students attend and the programs of study. I’m personally interested in this analysis and started to explore the dataset and thought I’d share some of the first impressions.

Looking at the data from 2016–2017, the mean debt is following a log-normal distribution, so some care will need to be taken in making comparisons between the groups. Including proprietary schools may not be useful given the low number of programs, but the spread is similar to private institutions.

mastersMeanDebt1617

For all master’s degrees with reported data, the mean debt values are $52k, $44k, and $39k for private, proprietary, and public institutions, respectively. Looking at various programs, the number with student debt over $100,000 is low.

I am particularly interested in STEM fields associated with the Professional Science Master’s movement; however, a quick survey shows that many schools’ data is suppressed to maintain privacy. As a first pass, CIP descriptions aligned with keywords from the PSM programs of study were used to narrow the scope of the analysis, including:

  • Agricultural Science, Food Science, Nutrition
  • Biotechnology
  • Computational Science, Analytics, Big Data, Statistics
  • Environmental Science, Ocean Science, Sustainability, GIS
  • Physical Sciences, Chemical Sciences

Business Administration, Management and Operations shows a wide range and is included for comparison. Dietetics and Clinical Nutrition Services also shows a wide range of mean debt, but the remaining programs have more modest ranges.

professional_masters

These are preliminary numbers but would indicate most students are managing their graduate education debt responsibly.

Exploring​ the “data” before EDA

Whiteboard space is at a premium in my office, but I’m always willing to erase a section to brainstorm a potential solution to new problems—afterall if we can visually create a “product” that provides insight, we can work backward and determine what data we need to produce that work.

I read Steven Covey’s book The 7-Habits of Highly Effective People well over a decade ago; however, “Begin with the End in Mind” has stuck with me as I’ve worked on various projects since that first reading. Currently, I’m working on several data-driven activities that remind me why this habit is so important.

Data Analysis (and Data Science) are hot topics, but too often folks want to jump right in and start crunching numbers—”Let’s run an X test on the Y samples and calculate the Z results.” It is easy to create large datasets that miss the mark and become wasted effort. While it may be hard, we need to get everyone to step back and ask the simple questions: “What problem are we trying to solve?” “What will this look like when we are ‘done’?”

Selfishness and unintended consequences

The 5 Whys is a simple technique for looking at problems—if you participate in community discussion groups, the issue of property taxes will undoubtedly come up. Here is my take on the problem applying a 5 Whys analysis:

Why are property taxes increasing?
Because home values are going up.

Why are home values going up?
Because more people are willing to pay more money to buy a home in our community.

Why are people willing to pay more money to by a home in our community?
Because the demand for homes in our community exceeds the supply.

Why is the demand for homes exceeding the supply?
Because we won’t allow new homes to be built.

Why won’t we allow new homes to be built?
Because people won’t support policies that allow for new development.

I’ve seen this play out in California, and the unintended consequences for the community will be devastating. Maybe not next week or next year, but eventually, the market price will force people rooted to the community out, and it’s not the “transplant” from the Bay Area or Los Angeles or Portland or Seattle or “name a major metropolitan area here” who will be at fault, it will be us. Our children will pay the price.

One of the main reasons I returned to Utah was simple economics. From a family point-of-view, I could not see my children being able to enjoy the same, high quality of life I had experienced if they chose to stay in California. The cost of living was too high, and this was driven primarily by the cost of housing. Why were housing prices so high? (See above)

The residents of Holliday, Utah unanimously rejected a new development on a vacant mall site that would have added a 775-unit high rise apartment tower and 210 single-family homes which would have included higher density townhomes. These would have been new places to live for young families and first homes for others. The development would have added office space for businesses as well as dining and entertainment options for the local community. But the residents didn’t want to change; they didn’t want something different in their city; they didn’t want to open up their community to others who can’t afford a $700,000 home.

I only hope that my city of Millcreek is less selfish and works to find solutions that allow our children (and newcomers) to live next to us along the Wasatch front.

No, but . . .

Did my degree get me a job?
No, but it got me noticed.

Did I learn everything needed to do the job in school?
No, but I learned how to learn new things.

Did I know what I would be doing five, ten, fifteen years after graduating?
No, but there were always new problems to solve or a need to simply get stuff done.

Did every new job come with a raise?
No, but each new job allowed me to grow professionally.

Did I do it alone?
No, I had—and still have—support from others every step of the way.

Don’t let my timeline limit your path forward

Applying the mantra of “what can I do now” is an effective way to move forward on long, complex projects that may be stuck or delayed. So, before becoming fixated on the finish, focus on how to keep moving so you can get started.

Following that . . . Academic calendars are not very flexible.
K-12 education has been on a fall/spring schedule for over 100 years and, surprising to me, an agricultural calendar was not the driving factor. (https://www.pbs.org/newshour/education/debunking-myth-summer-vacation)

For better-or-worse, higher education follows a similar calendar although most public colleges and universities now allow undergraduate students to start a program during fall or spring or summer (i.e., they have rolling enrollment) but this is not the case for most graduate and professional programs where a new cohort is formed each year. If someone wants to start a professional program and they miss the application deadline, they will look at the calendar and think there is nothing they can do until next year—don’t let the institution’s schedule prevent you from moving forward.

In the fall, I get emails asking if it’s too late to enroll—and at this point, it is for our program. However, for those wanting to start a graduate degree or certificate program, and it is past the official application deadline, I’ve recommended that they take the opportunity to identify possible gaps in their education or training that may come up during the application review when they do apply. Admission committee’s look at many factors (GPA, letters of recommendation, statement’s of purpose, etc.); however, most are trying to answer a simple question—will this person be successful in our program. Here a few items I’ve recommended to potential students as they navigated the application process.

Enroll in undergraduate courses (for credit) as a non-matriculated student to address gaps between your undergraduate degree and the graduate program. (A non-matriculated has permission to register but is not formally working toward a degree.) Earning a “B or better” can demonstrate readiness for more advanced work in the field and can effectively offset concerns that admission committees may have if a transcript shows underperformance as an undergraduate. If your undergraduate work was sufficient and you meet the pre-requisites then . . .

Ask for permission to enroll in a graduate course (for credit) as a non-matriculated student. If you are able to take a class associated with the program of study, it may be counted towards the graduate degree. But be warned, Colleges and Universities have strict rules for if this may be done and, if it is allowed, how many credits earned as a non-matriculated student can be applied to the degree or certificate.

My advice is pretty simple, even though you can’t start a program now, you can move forward and what looked like a one-year delay may become less than six months.