Error randomization

When an analyst performs a single analysis on a sample, the difference between the experimentally determined value and the expected value is influenced by three sources of error random error, systematic errors inherent to the method, and systematic errors unique to the analyst. If enough replicate analyses are performed, a distribution of results can be plotted (Figure 14.16a). The width of this distribution is described by the standard deviation and can be used to determine the effect of random error on the analysis. The position of the distribution relative to the sample s true value, p, is determined both by systematic errors inherent to the method and those systematic errors unique to the analyst. For a single analyst there is no way to separate the total systematic error into its component parts. 

Random error arises as the result of chance variations in factors that influence the value of the quantity being measured but which are themselves outside of the control of the person making the measurement. Such things as electrical noise and thermal effects contribute towards this type of error. Random error causes results to vary in an unpredictable way from one measurement to the next. It is therefore not possible to correct individual results for random error. However, since random error should sum to zero over many measurements, such an error can be reduced by making repeated measurements and calculating the mean of the results. 

Because measurements always contain some type of error, it is necessary to correct their values to know objectively the operating state of the process. Two types of errors can be identified in plant data random and systematic errors. Random errors are small errors due to the normal fluctuation of the process or to the random variation inherent in instrument operation. Systematic errors are larger errors due to incorrect calibration or malfunction of the instruments, process leaks, etc. The systematic errors, also called gross errors, occur occasionally, that is, their number is small when compared to the total number of instruments in a chemical plant. 

Random error is the divergence, due to chance alone, of an observation on a sample from the true population value, leading to lack of precision in the measurement of an association. There are three major sources of random error individual/biological variation, sampling error, and measurement error. Random error can be minimized but can never be completely eliminated since only a sample of the population can be studied, individual variation always occurs, and no measurement is perfectly accurate. 

SYSTEMATIC ERRORS RANDOM ERROR STATISTICS (A Primer)... 

Define Quality Control, Quality Assurance, sample, analyte, validation study, accuracy, precision, bias, calibration, calibration curve, systematic error, determinate error, random error, indeterminate error, and outlier. 

As already mentioned in the introduction, ruggedness is a part of the precision evaluation. Precision is a measure for random errors. Random errors cause imprecise measurements. Another kind of errors that can occur are systematic errors. They cause inaccurate results and are measured in terms of bias. The total error is defined as the sum of the systematic and random errors. 

There are three types of data error random error in the reference laboratory values, random error in the optical data, and systematic error in the relationship between the two. The proper approach to data error depends on whether the affected variables are reference values or spectroscopic data. Calibrations are usually performed empirically and are problem specific. In this situation, the question of data error becomes an important issue. However, it is difficult to decide if the spectroscopic error is greater than the reference laboratory method error, or vice versa. The noise of current NIR instrumentation is usually lower than almost anything else in the calibration. The total error of spectroscopic data includes... 

Random error (commonly referred to as noise) produces results that are spread about the average value. The greater the degree of randomness, the larger the spread. Statistics are often used to describe random errors. Random errors are typically ones that we have no control over, such as electrical noise in a transducer. These errors affect the precision or reproducibility of the experimental results. The goal is to have small random errors that lead to good precision in our measurements. The precision of a method is determined from replicate measurements taken at a similar time. 

One may ask how much drug outcome (concentration/effect) varies across a modeling cycle within an individual. To answer this question, yet other random-effect population parameters are needed the variance of the combined random intraindividual and measurement error random because outcome fluctuations and measurement errors are also regarded as occurring according to chance mechanisms. 

The proper implementation of calibration is to a large extent determined by careful and correct preparation of calibration solutions and samples for measurements. This is especially important in trace analysis because even the smallest errors, random or systematic, at the laboratory stage of the calibration procedure can significantly influence the precision and accuracy of the obtained results. 

When a sample is repeatedly analyzed in the laboratory using the same measuring method, results are collected that deviate from each other to some extent. The deviations, representing a scatter of individual values around a mean value, are denoted as statistical or random errors, a measure of which is the precision. Deviations from the true content of a sample are caused by systematic errors. An analytical method only provides true values if it is free of systematic errors. Random errors make an analytical result less precise while systematic errors give incorrect values. Hence, precision of a measuring method has to be considered separately. Statements relative to the accuracy are only feasible if the true value is known. 

We also discuss the analysis of the accuracy of experimental data. In the case that we can directly measure some desired quantity, we need to estimate the accuracy of the measurement. If data reduction must be carried out, we must study the propagation of errors in measurements through the data reduction process. The two principal types of experimental errors, random errors and systematic errors, are discussed separately. Random errors are subject to statistical analysis, and we discuss this analysis. 

The first type are called random errors, random because they cause repeat measurements on the same sample to go up and down. 

Sources of uncertainty in analytical measurements are random and systematic errors. Random errors are determined by the limited precision of measurements. They can be diminished by repetitive measurements. To characterize random errors, probabUity-based approaches are used where the measurements are considered as random, independent events. 

In the process of experimentation, there exist two types of errors random errors and bias errors. Random error is experimental error for which the numerical vtilues change from one run to another without a consistent pattern. It can be thought of as inherent noise in measured responses. Bias error is experimental error for which the numerical values tend to follow a consistent pattern over a number of experimental runs. It is attributed to an assignable cause. To reduce the effects of both types of errors, it is strongly adviced that the following good experimented practices be taken into consideration. 

These are deviations or components that are frequently called error. Random deviations are -I- or - values that have an expected mean of zero over the long run. The distribution of these terms is assumed to be approximately normal but in practice it is usually sufficient if the distribution is unimodal. The value of each random term influences the measured r, value on an individual measurement basis. However in the long run. when r, values are averaged over a substantial number of measurements, the influence of the random terms may be greatly diminished or eliminated depending on the sampling and replication plan, since each term averages out to zero (or approximately zero) and the mean y, is essentially unperturbed. 

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