Error in Measurements of Environmental Quantities

Two types of errors of observation exist systematic and random. The total error associated with a measurement is a function of the systematic error, commonly called bias, and the random error. Systematic errors in environmental measurements can be divided into three general categories instrument errors (e g., nonideal functioning of an instrument) interference from envi- 

Even if all systematic error could be eliminated, the exact value of a chemical or physical quantity still would not be obtained through repeated measurements, due to the presence of random error (Barford, i985). Random error refers to random differences between the measured value and the exact value the magnitude of the random error is a reflection of the precision of the measuring device used in the analysis. Often, random errors are assumed to follow a Gaussian, or normal, distribution, and the precision of a measuring device is characterized by the sample standard deviation of the distribution of repeated measurements made by the device. [By contrast, systematic errors are not subject to any probability distribution law (Velikanov, 1965).] A brief review of the normal distribution is provided below to provide background for a discussion of the quantification of random error. 

The Gaussian distribution has a symmetrical, bell shape and is sufficiently characterized by its mean (/jl) and variance (cr2). Its standard deviation (cr) is the square root of the variance. The symbols pi and cr refer to the mean and standard deviation of a population (i.e., the set of all possible measurements of a particular quantity). In practice, /x, and cr often are not known because a population is too large to sample in its entirety. A subset of measurements of a particular quantity represents a sample of a population. If the sample is drawn from a normal population, the parameters characterizing the sample distribution are the sample mean of the measurements or observations (y) and the sample standard deviation (s). Both of these parameters are calculated based on the values of the sample observations and the number of observations, 

For greater detail on the Gaussian distribution and its statistical properties, the reader is referred to Dingman (1994), Davis (1986), or McCuen (1985). 

Random error for repeated measurements of a particular quantity can be estimated as a multiplicative function of a t statistic, which reflects the probability that a value falls within a certain interval, and the standard error of the mean, 

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