Inferential statistics defines statistical error as the amount by which an observation differs from the whole population’s true mean (expected) value. This is in contrast to a residual which is the difference between the observation and the model’s predicted value (such as a regression model). In essence, the residual is an estimate of unobservable statistical error of the model.
Error takes on a different meaning in the context of statistical Hypothesis Testing. Colloquially, a “false positive” is the incorrect rejection of a valid Null Hypothesis and known as a Type I error. “False negatives”, or Type II errors occur when an invalid Null Hypothesis is failed to be rejected.
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