Is it a good idea to connect data points on a plot to increase readability in slides?

Question

I have a graph of points from a set of experiments, that I want to present on a slide.

The important information in the graph is both the values of the points, and more significantly, that the green points are above the blue points.

It is quick and easy to get my plotting framework (matplotlib) to connect each point to the next:

It should be fairly clear to anyone that the relationship between points is not expected to be linear.

I thought I could want to put the line in to make it clear that one is below the other. It can be hard to see the point markers on the projector screen.

Is this a good idea? Does showing plots this way enhance the visibility of the them for presenting, or does the fact the that lines themselves are fairly meaningless distract too much?

Audience concerns:

The whole presentation is for graduating engineering students and must be simple. While they would normally have the capacity to deal with complicated plots, the content of the presentation is complicated enough that I don’t want to distract them with anything that might waste thought time. I have already rejected the box-and-whiskers plot as too complicated; this is a plot of the mean values of that data.

Answer 1

Concerning the general question

Yes, it is acceptable to connect points, even if only discrete data points exist in theory and there is no continuum. If there is reason to expect that somebody misinterpretes your visualisation due to this or if you can expect the audience to be picky about this, add the sentence (on the slide or spoken):

Lines are for eye guidance only.

Concerning your special diagram

• As already remarked, the colours are not well chosen (and will probably look even worse when projected). I recommend to use colours with a strong contrast, for example a white or almost white background and for the data 1) black or almost black, 2) pure red. (Be careful about pure green though, since most projectors will screw it up – dark green is better.)
• Depending on how important you consider certain things:
  • Use a logarithmic scale (or similar) for the abscissa (x-axis). This way points do not cluster that much for small x and will be easier to read.
  • Use a logarithmic scale for the ordinate (y-axis). This way, the exponential relationship you mentioned becomes apparent immediately. However, the points for small x will get even closer to each other.

Answer 2

Drawing the lines implies a continuous relationship between the parameters. So if you can expect continuity, then connecting the points is fine. A second point to make is to avoid colours that are as similar as the green and blue you have chosen. One reason the difference is hard to see in the first scatter plot is due to colour. Try to experiment with colours that contrast better and your problem may be solved by just altering colours for one or both of the data sets.

Answer 3

You say you want to compare your data sets qualitatively, that is make clear which is "better". Since they seem to follow similar functions and are close together, normalisation can be a good tool.

Consider, for instance, this plot:

^{Note how the defaults of Mathematica 10 end up creating a far clearer plot.}

Knowing both functions are basically 1/√n you can multiply the value by, say, n:

Now the "winner" is more clear.

Similar effects can be achieved by (other) axis transformations, cut-offs, zooms, etc. You have to be transparent about what transformations you apply, though, because you can easily end up with a plot that says "A is thrice as good as B!" even though the real difference was miniscule.

Answer 4

I'm going to bring particle physics practice to the table and say never connect-the-dots. Nor should you run splines through data. Run meaningful fits through the data or nothing.

These rules reflect the understanding in that discipline that individual points can have significant error or uncertainty associated with them, and the reader needs to see the data in toto without focusing on individual anomalies. If you know the data can't have these issues then relaxing these rules probably doesn't cause a lot of harm.

So what can you do.

1. Use more visually distinguished markers. A combination of shape, fill and color (with as color-blind friendly a palette as you can of course) gives the reader several ways to hook into the difference.

2. Use a different plotting (normalized, anomaly from theory, linearization of power-laws, etc). This is what Raphael suggested. Finding these can be a bit of an art.

3. If you have a well justified theory (or even a good seat of the pants model), draw fit lines: those automatically reflect the whole data set (good!).

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Some points on the basic drawing of your figure.

1. Ditch the gray background. It only makes the data harder to read and makes Tufte cry.

2. Using filled circles for both series is a way to cause maximum visual confusion.

Answer 5

For display purposes, a smooth curve is the most logical thing to use. There are some nice spline fitting routines that allow you to create a fit that can be constrained to minimize curvature (in the process missing points that don't quite lie on the smooth curve), or you can simply eyeball the data and come up with a reasonable fit (for display - not for analysis).

I spent just a couple of minutes on this, but came up with the following:

This is basically an overlay of an Excel plot that I created (making the axes invisible) - using a simple 4 parameter model:

For the blue and green curves, I found parameters

    blue  green
A    0.8    0.8
B    1.0    1.0 
C    1.0    0.5
D    .05    .03

Obviously since you have the raw data and matplotlib, you must know how to do a better fit, but this works well.

In general, I like to show only as much information as is needed on a plot. If the point is "this is a rapidly decaying curve and green is above blue", then I would definitely leave off the grid, and maybe even most of the numbers (run the X axis from 0 to 100, with just two labels, and the Y axis from 0 to 1).

I think that your data probably doesn't go negative - so I would definitely want to fix that X axis.

If you want to further make the point "we measured this data", then leaving the points on the graph as well as the smooth fit is an OK thing to do. I would consider adding error bars to show that the fit is good - and that the points are bad.

Again - you want to make it so that the information is "only what you need". My personal preference would be like this:

So fewer ticks on the axes, but do add a legend (I call them "blue" and "green", but you should use a more meaningful name) and do label the axes - numbers alone are not enough.

Answer 6

Grids are an obsolete fossil that should no longer be used. Back in the days, they helped to make the plots, and also made easier to manually retrieve the data from the graph. Nowadays, it is no longer necessary, as tables with the data are available elsewhere.

And if and when they are necessary, they should be as little intrusive as possible. Your grey-blue background is just too heavy.

Once that is out of the way, you can try a log scale for the x axis, as many points are accumulated near 0:

I think here is pretty clear that blue is always greater than green. Whether adding a line or not is good, is a matter of taste:

In my opinion, and as a general rule, I would say that the lines are acceptable as long as the "wiggling" is due to the actual shape of the function, and not due to noise. That is, when adding more points (taking more measurements) will not change significantly the shape of said curve (or we don't expect it to).

Answer 7

An alternate approach to connecting the dots: insert a line between the datasets to illustrate that one set of points is above the line and the other below. If it is not inappropriate to the data, use a log scale for X to gain some space between the packed points at the left to improve visibility. Use of higher contrast colors and marker shapes was previously suggested.

Answer 8

Normally it is better to use some kind of curve fitting (splines, etc), as we are not assuming that the measurements are absolutely accurate and the connecting lines should go from point to point.

However measurement points must also be present and very clearly visible, as they are our results and the line is our hypothesis, interpretation. Ideally showing error bars (confidence intervals) would be a good idea.