Error Propagation

Types of Error

Calculation error refers to mistakes that arise from incorrect executions of arithmetic operations with, or imprecise representations (e.g., rounding) of, numbers. Measurement error refers to incorrect numbers in a data set. It arises from the use of the wrong measurement scale (i.e., nominal, ordinal, interval, ratio) or instruments lacking precision (i.e., the number of digits to the right of a decimal point), and/or recording mistakes. Specification error refers to the use of incorrect assumptions and/or the application of incorrect mathematical formulae or equations in a data analysis. Sampling error refers to differences that are due solely to the use of a subset (a sample) rather than an entire collection of objects (a parent population). Finally, random noise in a geographic landscape represents a haphazard (stochastic) disturbance and is characteristic of ignorance or uncertainty about reality or is the outcome of a goodly number of factors that jointly behave in such a way that random disturbances appear to be introduced into attribute and/or geocode measures.

Controlling Error Propagation

Georeferenced data error rarely averages to zero during data manipulations. Rather, error propagation can be controlled by minimizing or eliminating data input and/or analysis error. The widespread use of computers and hand calculators has minimized calculation error, which today tends to be associated almost solely with rounding and the number of significant digits to the right of a decimal point. Improvements in instruments (e.g., decreasing the pixel size in satellite remote sensors, global positioning system [GPS] technology) and the digital rather than manual handling of data, for example, have reduced measurement error. In particular, the development of spatial statistical theory, statistical theory for non-normal data, and resampling techniques has helped diminish the occurrence of specification error, which continues to be the principal source of error propagation. Experimental design and statistical mixed-model approaches (i.e., including random effects terms) furnish controls for sampling error, which because of its random nature is very controllable. Random noise in a geographic landscape refers to model residuals (i.e., the difference between predicted and observed values) and can be controlled by acquiring a better substantive understanding of geographic phenomena.

Relative Importance of the Origin of Error

Error propagation with georeferenced data is complicated by the presence of pairwise attribute correlation as well as positive spatial autocorrelation (i.e., attribute and error values at adjacent locations tend to be similar). Propagation occurs when these data are manipulated within a geographic information system (e.g., overlay, buffering) or used to construct indexes (e.g., linear combinations or ratios of, say, spectral bands). For univariate overlay, overlay-AND, overlay-OR, and overlay-XOR, attribute error and location error tend to dominate error propagation, with spatial autocorrelation of attribute variables often being the single most important contributor to autocorrelation in propagated error. Attribute error tends to be the single most important contributor to error propagation when addition or ratioing is performed, with interattribute [Page 1012]correlation playing a more important role for addition and location error playing a more important role for ratioing. Synchronized attribute and error map patterns frequently obscure the detection of propagated error.

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