In design or in theoretical areas (more R&D than E) you can often use some kind of smoothed lines. I mentioned wind chill; stress concentration factors is another use. As I pointed out before, if you know the shape of the phenomenon being modeled, and as you said, if the measurement errors are relatively small, then go ahead.

I still prefer to see unsmoothed lines, though, so I know clearly where the data is “known”, and I will do the smoothing in my own mind. This is for transferring information, not for making predictions.

“Cardinal splines can be viewed as just a particular type of Bezier curve”

I suspected as much.

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.

Thanks for joining the discussion. Regarding smooth lines for connecting points, I almost presented an example I made some time ago showing wind chill factors. Smoothed lines made sense in that case, as in your examples of engineering design.

When I wrote this post, I was thinking of measured data, though, not analytical output. As with financial (stochastic or random-walk exercises), measured data already has error built into the values in the chart, and there is no reason to assume the curves that Excel draws through the points will model the data any better than straight lines. If you know the shape of the relationship, go ahead and draw a best fit curve through the measured data using the known relationship.

According to Brian Murphy of Rotating Machinery Analysis, Inc. (who has analyzed the living snot out of it), Excel connects data points using beziers for the smoothed lines. Brian presents an analysis in a downloadable file, Smooth_curve_bezier_example_file.xls. I’m not sure the result is much different than for the cardinal spline you cited.

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

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.

A chart with a low level of precision conveys information better than a table with a low level of precision. Of course, if there are three numbers, then it’s not worth dusting off your seldom-used charting apparatus to make a chart. Michael’s error bars comprise one way to display imprecision, but often the degree of precision isn’t known as well as a standard deviation or range of values. Especially if the topic is financial numbers, or predictions, or predictions of financial numbers.

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?