This blog series is devoted to the question of how statistics and errors in the geospatial sciences are connected, applied, worked with, and generally how you get along with and live with errors.
Starting from first principles, and first causes, we will attempt to build a picture of statistics and errors that may make a bit more sense than more theory-based discussions. Ultimately, the purpose is to provide the reader with a deep understanding of the nature of errors and their impact on everything that happens with spatial, data, information, knowledge, processing, and what happens after that.
Understanding errors in geospatial endeavors, be they measurement, computation, analysis or representation, is a weak area in the wider geospatial sciences. This blog will attempt to fill in a few gaps in that understanding.
What Are We Really Measuring?
The last few posts have focused on things we need to think about, or bear in mind, before we begin making measurements. In this post, the issue of what is the raw measurement being made will be considered. In many cases, what is being measured in not what you thought! The value you get is unlikely to be a raw measurement, but a derived value based on something very different being measured.
Conceptually, the simplest measurement is perhaps measuring a distance with a tape. The value on the tape may seem to be the ‘measurement,’ but it really starts with two measurements on the tape: one where the numbers are read, and the other at the zero point. Both points need to be positioned and measured to get the correct raw distance along the tape between the two points. If the ‘zero’ point isn’t actually zero, then the difference between the two readings must be calculated.
To make life easier, we usually try to align the tape’s zero point with one end of the measurement, so that the subtraction is not required. But if the zero point is not clear, as was the case with some old surveyors bands, then reading to some other point is required.
That may seem a little pedantic, but the point to note is that even the simplest measurements may not be as simple as they seem. Even with the distance along the tape known, there remains a group of ‘corrections’ that need to be made to get the corrected distance. These allow for the calibrated length of the tape to be used, and allowances can be made for changes in the tape length for temperature, tension and sag, followed by corrections to allow for the distance above the ellipsoid or sea level, and the slope of the tape.