A one-sided z-test standardizes the difference between an observed value and its null expectation by the expected standard deviation. The resulting z-score is compared with one tail of a reference normal distribution because the hypothesis predicts a direction, such as more green-list tokens than chance.
The test is only valid when its assumptions and null model are appropriate. Dependence among tokens, selective text sampling, short passages, calibration drift, and multiple testing can change the true error rate and must be addressed by the detector design.
ELI5
A one-sided z-test checks whether an observed result is unusually high or unusually low compared with what a null hypothesis predicts. It looks in one chosen direction because the question was defined that way before the data was examined.
For example, a watermark detector can test whether marked tokens appear more often than chance predicts. The result is trustworthy only if the independence, sample-size and calibration assumptions match the actual text.
Why use a one-sided z-test for text watermark detection?
The watermark predicts a directional increase in keyed preferred outcomes, so only unusually high counts support that specific signal.
What does a large z-score mean in watermark detection?
It means the observed preferred-token count is far above the null expectation relative to the modeled variation.
