What is a 'Measurement'?
All measurements necessarily contain some level of error. So what is the point of making a measurement if we know it must be wrong? To answer this, we must look at the nature of measurement.
For an example, consider the distance between points (A and B) reasonably far apart, perhaps tens or hundreds of kilometers. If someone asks us to determine or quantity that distance, we may not even know where points A and B are, to start with. So the distance could be any value.
Actually, that isn’t quite true. If the points are on the Earth and we are measuring the separation around the surface, this distance cannot be more than 20,000 km, otherwise there will be a shorter path (the circumference of the Earth is about 40,000 km). This limits the distance to being in the range 0 to 20,000 km.
Notice how we used a little bit of common knowledge to start to narrow the range that the distance could be. It may not seem much, but it is a limit to that range, which is no longer from zero to infinity. We have reduced the amount of uncertainty associated with our knowledge of the distance, maybe not by much, but by some amount.
If points A and B are shown to us on a map, or otherwise described, we can narrow the range of the distance some more. We may be able to get it down to ±10 km, say. Again, we have achieved a narrowing of the range.
If we measure the distance using a simple compass and a vehicle odometer, we may narrow that range of possible distances down to ±1–2 km. When we use something like EDM or GNSS to measure the distance, we will get a value that has a range of, say, ±0.02 m or better.
Every time we make a reasonable estimate or measurement of that distance, we make the range of possible values smaller. Another way to look at this is to say that we are reducing the uncertainty in our knowledge of the distance. We will never remove all the uncertainty, which is to say that we cannot know the true value for the distance, but we can get it small enough that the estimate we have is good enough for the purposes for which we need the value.
A measurement, therefore, reduces the uncertainty of our estimate of the true value of the unknown we seek to know. This is the essential purpose and nature of measurements.
Once we realize this about measurements, it becomes a lot easier to talk about how much any given measurement, or set of measurements, reduces that uncertainty. The greater the quality of the measurement (or the quality of the set of measurements), the smaller is the uncertainty of the estimate of the true value of the unknown quantity. We can put some reasonable numbers on these estimates of uncertainty, which where statistics comes into the picture in surveying and geomatics.
Statistics is used to provide an estimate of the size and variation in the gap between the measurements and the true value of the quantity being measured. Another way to look at this is that statistical information provides a quantification of the uncertainty of our knowledge of the required quantity. As measurements are fundamental to everything we do in all of the geospatial disciplines, so to is the discipline of statistics.
It is possible to measure anything, once you realize that any effort that reduced uncertainty is a useful measurement. This includes rough estimates, such as we used to reduce our estimate of the distance between points A and B to “less than 20,000 km.” With practice, it is possible to make a reasonable and quantitative estimate of how good one’s measurements or estimates are, permitting a quantified estimate of how good the estimate of the unknown value is.
Douglas W. Hubbard (2014) wrote a book about this, extending the process to a wide range of intangibles (e.g., customer satisfaction, public perception and process effectiveness), as well as the more definite things that surveyors measure. The process works for anything, including the attribute data for GIS.
There is a huge body of work and knowledge about determining the quality of the spatial location of surveyed points, but nothing about the quality of derived quantities like lines and polygons. Similarly, the degree of uncertainty of the values in pixels, the location of pixels, and the values of attributes (and the boundaries between different regions of attributes) is largely an untouched area of study. Yet it is these latter pieces of data that make up the largest part of a GIS database. How then are we to provide a quantitative estimate of the quality of the decisions that are derived from GIS data? This is one of the largest unknown areas facing surveying, geomatics and the geospatial sciences generally.
Hubbard, D.W, 2014. How to Measure Anything. 3rd Ed. Hoboken, NJ: John Wiley and Sons, Inc.