Automatic Passenger Counting: Introducing the t-Test Induced Equivalence Test
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Automatic passenger counting in public transport has been emerging rapidly in the last 20 years. However, real-world applications continue to face events that are difficult to classify. The induced imprecision needs to be handled as statistical noise and thus methods have been defined to ensure measurement errors do not exceed certain bounds. Sensible criteria to ensure this in the past have been criteria to limit the bias and the variablilty of the measurement errors. Nevertheless, the still very common misinterpretation of non-significance in classical statistical hypothesis tests for the detection of differences (e.g. Student's t-test) proves to be prevalent in automatic passenger counting as well, although appropriate methods have already been developed under the term equivalence testing in other fields like bioequivalence trials (Schuirmann, 1987). This especially affects calibration and validation of automatic passenger counting systems (APCS) and has been the reason for unexpected results when the sample sizes are not appropriately chosen: Large sample sizes were assumed to improve the assessment of systematic measurement errors of the devices from a users perspective as well as from a manufacturers perspective, but the regular t-test fails to achieve that. We introduce a variant of the t-test, the revised t-test, which addresses both type I and type II errors appropriately, overcomes the mentioned limitations and can be deduced from a long established t-test in an existing industrial recommendation. This test seemed promising, but turned out to be susceptible to numerical instability. However we were able to analytically reformulate it as a numerically stable equivalence test, which is thus easier to use. Our results therefore allow to induce an equivalence test from a t-test and increase the comparability of both tests, especially for decision makers.
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