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If measurements are Gaussian distributed and independent, and if the weighting factors w_i correspond with the inverse of the measurement variances (), the distribution of J(x ) is a χ² with m + r − n degrees of freedom [8], where r is twice the number of transit buses (exact measurements). Thus, we can write

(2.13)

where 1 − α is the confidence level.

Therefore, for a given α (e.g. 0.01), the value χ²(1 − α, m + r − n) can be computed and the χ² test applied, i.e. if there is no bad measurement at the 1 − α confidence level; otherwise there is. Further details can be found in [7].