I think some of my comment was ambiguous. When I wrote, “what happened between most measurements” I was referring to missing measurements, not the time within an interval during which there are no measurements.

Agreed, balance is the key. For any continuous variable, you have to ask if smaller intervals would change the signal or just introduce noise. You’re completely right, the trade-off is required for any chart of continuous data.

You got me thinking though. Is Nasdaq value at close really continuous? Nasdaq value during market hours is continuous. With unequal interval observations you would definitely have a continuous function. But if you rigidly define the interval, does that change the problem? If so, does that add more importance for Stephen’s argument in favor of equal intervals?

Maybe the Nasdaq example is confusing. Is there a difference (of problem attributes, not actual values) between the questions of, “How many people are in an office building at any one time today?” and, “How many people showed up to work today?”

John’s x-axis (1st chart) does have equal intervals: 22 months. It’s a strange interval, but it is equal. The data are plotted correctly – the date at which the price change occurred.

Stephen’s criticism is connecting the measurements with a line. The truth is, you don’t know what happened between most measurements. Implying that the movement from one point to the next is gradual is misleading.

John recognizes this and his solution is the Step Chart (2nd chart). In the case of the stamp prices, you do know what happened to price between the dates: nothing. I think the step chart is completely appropriate.

Very misleading are time series charts where the x-axis is categorical but is implied as being continuous, like the second chart in Stephen’s newsletter article (x-axis of 1997, 1998, 2000). But this is not what John did.

Not related to this post, but I’m pretty sure you could find some use for this dilbert cartoon http://dilbert.com/strips/comic/2009-03-07/

In business: taking measurements is usually much more arbitrary and the context and purpose is crucial though typically obscure (I work in a LARGE corporation). Attempting to investigate and assess the sources of error is often difficult, time consuming, and may be opposed by those who own the “measurement” systems/data sources (among others!).

Worse, the people who ask for a report may want it in the morning but have gone home, so it can be difficult to be sure what they want to know. (I have found that a big source of error is simply the meaning of words commonly used. I once tried to make a list of all the ways the term “cost” was used in my area, and quickly gave up. The implications for people creating and marketing dashboards in their organizations are significant. )

In my job, a major source of time uncertainty is that, of necessity, systems produce data that is consumed by other systems that in turn feed others. Some of it may be entered by hand, and people can be inconsistent in getting that bit of their job done. So there can be many different (and inconsistent) lags involved in piecing together a report. In such circumstances, getting equal time intervals, much less an accurate picture of even simple data, is sometimes a bit of a struggle!

As far as “inconsistently manipulating the sizes of intervals”, that is simply fraud, and sounds like Few is addressing a somewhat different topic, yes?

How could we trust graphical representations of time series or frequency distributions if their shapes could have been altered by inconsistently manipulating the sizes of intervals along the scale, either arbitrarily or intentionally to deceive?

The above question is what the issue really is about: trust in the truthfulness of a chart. If you have a good reason to use irregular intervals then use them only if you also make perfectly clear what you do in creating your chart and why. Without such kind of ‘full disclosure’ your readers simply can’t trust your chart. Also, you could also give thought to rearranging your irregular data to fit regular intervals (for example by interpolating where necessary and clearly marking which data points are real and which are derived).