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Rows of dots

Visualizing the asymmetry between hospital arrivals and departures


It's not just that we don’t draw enough scatterplots. Although it’s true: we don’t draw enough scatterplots. It’s also this: scatterplots are a useful springboard for other visualizations. You can start with scatterplots even though it's not actually a scatterplot you want to end up with. Two parallel rows of dots, for example:


23 admissions toand 22 discharges fromthe Acute Medical Unit (AMU) : Friday 8th January 2010

Rows of dots are useful whenever you want to represent the way thingspatients, attendances, admissions, tests, eventsare distributed through time. They are particularly well-suited to showing how events are spaced and clustered differently from one another. Like admissions and discharges, for example.

The chart above is an attempt to visualize one of the most intractable problems faced by Acute Medical Units (AMUs). Discharges tend to be concentrated in the late afternoon and early evening whilst admissions are more evenly spread throughout the day. In fact, admissions usually start happening long before discharges start happening. Which means that AMUs will fill up in the morning and often be full by early afternoon. Which means that if there weren't enough empty beds at the start of the day, it will be a big struggle to match demand and capacity as the day develops, and the likely result will be long waits for the patients in the Emergency Department.

One way of expressing this mismatch would have been to look at the day's data and then to simply compare two numbers. The average time of admission, for example, was 14:15; the average time of discharge was 17:28. And we could compare those two times and wonder if that meant there was a three-hour period in the afternoon between 2:15pm and 5:30pm when things were out of balance..? No, that wouldn’t be right. The discomfort was being felt long before 14:15. By 9:00am, for example, there had already been five admissions compared with only two discharges.

So although we've visualized the asymmetry between arrivals and departures, we're still left with the problem that we haven't visualized the effect of this asymmetry. So let’s try another visualization method. And—as before—let's start with a scatterplot even though we don't want to end up with a scatterplot

Let’s take the number of beds occupied throughout the day and plot that.

This means using a different dataset, so a bit of number-crunching needs to go on in the background if we want to end up with a graph like this:


Changes in the number of beds occupied in the Acute Medical Unit (AMU) : Friday 8th January 2010

And now we can see how the bed occupancy in the AMU changed as the day progressed, and we’ve used a scatterplot to draw this graph because there's an x-value (the time of each AMU “transaction”and by "transaction" we mean admission or discharge) and a y-value (the number of occupied beds at the time each transaction took place). That gave us 45 transactions, so we have 45 dots on the chart. Except that you can't see the dots because we’ve joined the dots together using x-error bars (the horizontal joins) and y-error bars (the vertical joins). And once we've done that (to create the stepped effect), we've deleted the dots.

But anyway, to sum up, the two points I'm making here are that (a) rows of dots and dots joined together often work well as visualizations that have resonance for NHS managers and clinicians; and (b) the best way to generate rows of dots is usually to start with Excel's X-Y chart.

One last thing. Going back to the first chart we drew, the one at the top of the page. If you want to know what the two rows of dots looked like on Christmas Eve, they looked like this:


16 admissions toand 21 discharges fromthe Acute Medical Unit (AMU) : Friday 24th December 2010

Five more discharges than admissions. Average time of admission: 17:21; Average time of discharge: 15:01. How many AMU charge nurses wish it could be Christmas every day?

[17 January 2014]

Comments on this article

17 January 2014:

Interesting stuff. It's strange that the bread-and-butter important data—or the front line data that matters—is still not given the focus it needs by managers. We still spend lots of effort looking at the data at the end of the process (e.g. 4-hour wait or RTT) and not the causes of lack of capacity. Have you looked at the data against staffing levels on wards ... What does that tell us?

Dylan Williams

Assistant Director of Informatics, Betsi Cadwaladr University Health Board

18 January 2014:

I like this simple way of visualising inflow and outflow and it is so easy to do in Excel - if you have the event data. It is a nice way to ease into drawing Gantt charts ... as Henry L Gantt drew them -- with pencil and paper. Thanks for this.

Simon Dodds

Improvementologist, SAASoft Ltd

18 January 2014:

This is very intuitive once you've seen it explained as clearly as this. It would be really helpful to see the X-Y data that you use for this please..?

Ian Reeves

Consultant Geriatrician, NHS Greater Glasgow & Clyde

22 January 2014:

Helpful. Thanks, Neil. Too often we jump to aggregating data without understanding the distribution. I've tried tricking Excel into doing something similar in the past but got stuck discriminating between data points that are bunched together. Your demo data shows something of this in the period 18:00 to 21:00. I think I can see all the dots but I'm really not sure how they are clustered. Any thoughts..?

Mark Lambert

Consultant in Public Health Medicine, Sunderland City Council




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