A test statistic for weighted runs

A new test statistic based on runs of weighted deviations is introduced. Its use for observations sampled from independent normal distributions is worked out in detail. It supplements the classic χ2 test which ignores the ordering of observations and provides additional sensitivity to local deviations from expectations. The exact distribution of the statistic in the non-parametric case is derived and an algorithm to compute p-values is presented. The computational complexity of the algorithm is derived employing a novel identity for integer partitions.