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Scientific observations are marred by two distinct types of errors, systematic errors on the one hand, and random, on the other hand. The effects of random errors can be mitigated by the repeated measurements.
The statistical errors, on the other hand, are independent, and their sum within the random sample is almost surely not zero. One can standardize statistical errors (especially of a normal distribution) in a z-score (or "standard score"), and standardize residuals in a t-statistic, or more generally studentized residuals.
An increasing positive correlation will decrease the variance of the difference, converging to zero variance for perfectly correlated variables with the same variance. On the other hand, a negative correlation ( ρ A B → − 1 {\displaystyle \rho _{AB}\to -1} ) will further increase the variance of the difference, compared to the uncorrelated ...
There will be an uncertainty associated with the estimate, even if the estimate is zero, as is often the case. Instances of systematic errors arise in height measurement, when the alignment of the measuring instrument is not perfectly vertical, and the ambient temperature is different from that prescribed.
While precision is a description of random errors (a measure of statistical variability), accuracy has two different definitions: More commonly, a description of systematic errors (a measure of statistical bias of a given measure of central tendency, such as the mean). In this definition of "accuracy", the concept is independent of "precision ...
If errors have the essential characteristics of random variables, then it is reasonable to assume that errors are equally likely to be positive or negative, and that they are not correlated with true scores or with errors on other tests.
Systematic errors in the measurement of experimental quantities leads to bias in the derived quantity, the magnitude of which is calculated using Eq(6) or Eq(7). However, there is also a more subtle form of bias that can occur even if the input, measured, quantities are unbiased; all terms after the first in Eq(14) represent this bias.
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