Comment from Bob
Time: Thursday, May 28, 2009, 5:09 am

Hi Jon,

Since the start of the new year, I’ve been incorporating small multiples of charts in reports from my department. I have found that the size of the marker needs to increase in relation to line and other elements as the overall size of chart is reduced.

The layout I use is 2 x 2 in a word document.

Any thoughts?

Cheers,

Bob

Comment from Michael
Time: Thursday, May 28, 2009, 7:24 am

Mr. Peltier:

Regarding your post on Smoothed Lines, it is incorrect to state that straight lines connecting adjacent points do not make any implicit statements about values between data points. In fact, straight lines imply a linear relationship (y = mx + b) governing whatever process is represented by the two adjacent, discrete samples. If the data were, for example, distance from (x) and intensity of (y) a point-source light, a straight line would of course be wrong.

The only honest way to represent data (observations) is to use markers for each known point, with error bounds (usually bars) indicated. Connecting the data (or indicating a best-fit trend among the data), by whatever shape of line, immediately implies an inferred relationship governing the independent and dependent variables.

All this aside, thanks for yet another thought-provoking post; your Excel blog, the local newspaper online and a decent cup of coffee are all that I require to get my day underway!

Comment from Dick Kusleika
Time: Thursday, May 28, 2009, 9:09 am

I’m not a charting guy, so ignore everything I say! I think the first question is, what are you trying to convey. If you want to know what sales in April were, then perhaps a chart, smoothed or otherwise, isn’t the right vehicle. If, however, you want to demonstrate that August and Christmas are big selling months and March stinks, then a chart, smoothed or otherwise, seems fine.

I guess my question is: If I want to display imprecise information, like general trends, is it OK to use a chart with a low level of precision?

Comment from Thom Mitchell
Time: Thursday, May 28, 2009, 12:59 pm

Great title for the post, Jon!
(with apologies to the Chiffons?)

Comment from derek
Time: Thursday, May 28, 2009, 2:07 pm

Regarding the shape of markers with low screen resolution: that’s why I mostly stick to the square marker. Then the shape is less vulnerable to Excel 2003 or lower’s poor symbol handling. I’m hoping 2010 will be an improvement (psst.. Microsoft! there’s this technology called Truetype, you may have heard of it?)

Speaking of which, I sometimes abandon crude markers altogether, in favour of Wingdings or other text symbols. But that has its own hazards, because they don’t always match up nicely with the lines. You can use error bars as crosshairs to check whether any drift is small enough to tolerate.

Or you can use the error bars themselves. A zero-length error bar with no crossbar and a thick line width makes a surprisingly neat small circular dot, just as precisely placed as, but less pixellated than, the circle marker.

Comment from Mike Woodhouse
Time: Thursday, May 28, 2009, 2:49 pm

Plotting data like this (these?) as line charts just begs for someone to add smoothing (almost always a guarantee of lost information) or some inappropriate trend or curve-fit. In pre-computer days we’d join the dots on our paper charts to save ourselves the tedium of hand-colouring the bars; these days we can just change to a column chart and be done with it. Discrete points should be plotted discretely. Something like that.

Comment from Lori Miller
Time: Monday, June 1, 2009, 7:10 pm

Joining points with straight lines makes more sense than smoothed lines for financial series as the relationships are often not inherently smooth, instead they are modeled on random walks or fractals.

If the underlying relationship is smooth however, smoothed lines will generally be closer to the truth than straight lines (i.e. the error term is smaller) and these kinds of curve are used widely in situations when no particular functional form is assumed. Applications include engineering design, computer animation, typography, non-parametric statistics, fixed-income finance, etc.

The Excel curve is a type of spline with tension applied in parts of the curve where points are relatively close to each other, details can be found in a few threads in excel.charting. For a non-technical description, see:
http://msdn.microsoft.com/en-us/library/ms536358(VS.85).aspx

Comment from Lori Miller
Time: Monday, June 1, 2009, 9:43 pm

Jon – i agree that measured data should generally be handled using regression techniques particularly for making forecasts. But the simple trends often inserted into Excel charts can be quite misleading particularly for financial or time series data where other factors are in play such as serial correlation and hidden variable bias.

When mesurement errors are small compared to the chart scale or data is quoted at a fixed level it can make sense to use splines for estimation and there is a large literature on the subject. For example they are used to construct yield curves from bond yields of varying maturities and for modeling empirical distribution functions. Coming from a stats/finance background, i don’t know much about how it works in engineering or other areas.

The conclusions about Excel curves actually followed from Brian’s analysis and i’ve been in contact with him to discuss this. Cardinal splines can be viewed as just a particular type of Bezier curve, restricted to one parameter and using a different set of reference points.