Rangetest

Rangetest, or range test, is a statistical method used to determine whether a set of observations falls within a predefined acceptable range. It is commonly employed in quality control, data validation, and experimental analysis to identify measurements that lie outside expected boundaries.

Method: The practitioner defines lower and upper bounds, L and U, representing the acceptable range. For a sample of size n, the number of observations outside the range is K. Under the null hypothesis that observations fall within the range with a known probability of being out-of-range p0, K can be modeled by a binomial distribution Bin(n, p0). A p-value can be computed to assess whether the observed K is unlikely under the null. Alternatively, simple rule-based criteria (for example, if K exceeds a threshold) can be used to flag the sample for review.

Variants and related concepts: Rangetests can be one-sided (only lower or upper bounds) or two-sided. They are related to tolerance intervals, which aim to cover a specified proportion of a population, and to outlier detection and control-chart practices in quality systems.

Applications: In manufacturing, rangetests help flag defective batches or miscalibrated equipment. In data pipelines and sensor networks, they can detect sensor faults or data-entry errors. In experiments, they serve as a quick check that measurements remain within scientifically plausible bounds.

Limitations: Effectiveness depends on the justification of the chosen range. The method assumes independence among observations and, if p0 is unknown, requires estimation. Repeated testing can inflate false-positive rates unless adjusted.