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Critical values for the Z-test, the t-test, the χ²-test, the F-test, the common outlier tests and tests of constraints for parameters in an adjustment model are computed. The observations should be approximately independently normally distributed or their number should be sufficiently large.

The computation is based on the linear or linearised model of by least squares, possibly with constraints (restrictions) for parameters.

l+v=Ax,   B^Tx=b,   v^TPv = min!

• l is the known n-vector of (linearized) observations
• v is the unknown n-vector of residuals
• A is the known n×u-design matrix of the adjustment model
• x is the unknown u-vector of (linearized) parameters
• B is the known u×m-matrix of the constraints
• b is the known m-vector of (linearized) constraints
• P is the known n×n-weight matrix of the observations

The model contains as a special case also the model of a statistical sample, e.g. in the form of . For this case let u=1,m=0.

Probability of type I decision error

number of	adjustment model	comparative adjustment model
observations	n =	n´ = (only for
parameters	u =	u´ = two-sample t-test
constraints	m =	m´ = and F-test)

For singular models let u be the range space of A and m be the range space of B.

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