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Part of a series on statistics: Probability theory; Probability. Axioms; Determinism. System; Indeterminism; Randomness; Probability space; Sample space; Event ...
The statistical errors are then =, with expected values of zero, [4] whereas the residuals are = ¯. The sum of squares of the statistical errors, divided by σ 2, has a chi-squared distribution with n degrees of freedom:
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If the probability distribution of the variable is known or can be assumed, in theory it is possible to get any of its statistics. In particular, it is possible to derive confidence limits to describe the region within which the true value of the variable may be found.
The probability of type I errors is called the "false reject rate" (FRR) or false non-match rate (FNMR), while the probability of type II errors is called the "false accept rate" (FAR) or false match rate (FMR). If the system is designed to rarely match suspects then the probability of type II errors can be called the "false alarm rate". On the ...
For a value that is sampled with an unbiased normally distributed error, ... The Student's probability distribution is approximated well by the Gaussian distribution ...
The procedures of Bonferroni and Holm control the FWER under any dependence structure of the p-values (or equivalently the individual test statistics).Essentially, this is achieved by accommodating a `worst-case' dependence structure (which is close to independence for most practical purposes).