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In statistical hypothesis testing, there are various notions of so-called type III errors (or errors of the third kind), and sometimes type IV errors or higher, by analogy with the type I and type II errors of Jerzy Neyman and Egon Pearson. Fundamentally, type III errors occur when researchers provide the right answer to the wrong question, i.e ...
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 .
If the probability of obtaining a result as extreme as the one obtained, supposing that the null hypothesis were true, is lower than a pre-specified cut-off probability (for example, 5%), then the result is said to be statistically significant and the null hypothesis is rejected.
When either randomness or uncertainty modeled by probability theory is attributed to such errors, they are "errors" in the sense in which that term is used in statistics; see errors and residuals in statistics. Every time a measurement is repeated, slightly different results are obtained.
More recent research has used Statcheck on papers published in Canadian psychology journals, finding similar rates of statistical reporting errors as the original authors based on a 30-year sample of such articles. The same study also found many typographical errors in online versions of relatively old papers, and that correcting for these ...
Statistical tests (e.g. t-test and the related ANOVA family of tests) rely on appropriate replication to estimate statistical significance. Tests based on the t and F distributions assume homogeneous, normal, and independent errors. Correlated errors can lead to false precision and p-values that are too small. [6]
Linear errors-in-variables models were studied first, probably because linear models were so widely used and they are easier than non-linear ones. Unlike standard least squares regression (OLS), extending errors in variables regression (EiV) from the simple to the multivariable case is not straightforward, unless one treats all variables in the same way i.e. assume equal reliability.
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