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This is not the case for random errors, but these can be reduced by averaging over a number of observations. Systematic errors can, however, be controlled by careful (and repeated) calibration of the observer and measuring apparatus against a known standard. Without knowing the true value of the quantity being measured, it is not possible to determine the magnitude of any systematic error that may exist.
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Random errors lead to variable differences from the true value and give rise, unpredictably, to measurements that are greater or smaller than the true value. Systematic errors (also known as ‘bias’) are reproducible inaccuracies that lead to a measured value that is consistently larger or smaller than the true value. For this reason, it has become standard practice to include a statistical estimate of the measurement error in published reports of laboratory and clinical studies.įor reasons of mathematical and conceptual convenience, the total measurement error is generally partitioned into two separate classes of error: systematic and random. In comparative studies, measurement errors complicate interpretation of the results by potentially concealing important differences between groups or by indicating differences, which, in reality, do not exist. If the errors are significant in relation to the measurements being made, they reduce the usefulness of those measurements. This is particularly so for anthropometric measurements of the type that commonly occur in clinical orthodontic research. Unless one can be absolutely sure that no bias exists between the replicate measurements, Dahlberg's formula should be avoided and the MME formula used instead.Īll physical measurements are approached with some degree of error. In these circumstances, it would be helpful if a confidence interval for the true error was also quoted. Where the original study contains fewer than 20 cases, the estimate of error will be unreliable. A sample of at least 25–30 cases should be replicated to provide an estimate of the random error. No such distorting effect was found for the MME formula, which provided estimates of error that were not meaningfully different from the true value even where relatively large biases existed between the replicates. Where, however, a bias exists between the replicate measurements, Dahlberg's formula can be expected to overestimate the true value of the random error even where the biases are small and difficult to detect by standard statistical tests. The results indicate that with a sample of less than 25–30 replicated measurements, the resulting estimates of error are potentially unreliable and may under or overestimate the true error, irrespective of the formula used in the calculation. In each case, the estimates of the random error were based on the distribution of 5000 separate simulations. Nine different sample sizes ( n = 2, 5, 10, 15, 20, 25, 30, 50, and 100) and two different types of bias (additive and multiplicative) were examined for their effect on the estimated error. Dahlberg's and the MME formula were applied to these paired data sets and the resulting estimates of error compared with the ‘true’ error. For each simulation, two sets of ‘measured values’ were generated to provide the replicated data necessary for the estimation of the random error. Computer-based numerical simulations were used to generate clinically realistic measurements involving random errors with a known distribution. This study examined the effects of different sample sizes and different levels of bias (systematic error) between replicated measurements on the accuracy of estimates of random error calculated using two common formulae: Dahlberg's and the ‘method of moments’ estimator (MME).