We have discussed how to handle this test when σ is known. But how should we proceed if it is unknown? One option is the GLRT, discussed above. However, (a) we must estimate μ and (b) Wilk’s theorem only tells us that the test statistic corresponding to maximum likelihood estimates of σ and μ is asymptotically chi-squared. For small n, then, it can be difficult to set a threshold to achieve a d...

Three-stage t-tests of separated one-sided hypotheses are derived, extending Lorden’s optimal three-stage tests for the one-dimensional exponential family by using Lai and Zhang’s generalization of Schwarz’s optimal fully-sequential tests to the multiparameter exponential family. The resulting three-stage t-tests are shown to be asymptotically optimal, achieving the same average sample size as ...

t-Tests are widely used by researchers to compare the average values of a numeric outcome between two groups. If there are doubts about the suitability of the data for the requirements of a t-test, most notably the distribution being non-normal, the Wilcoxon-Mann-Whitney test may be used instead. However, although often applied, both tests may be invalid when discrete and/or extremely skew data...

Otsu's binarization method is one of the most popular image-thresholding methods; Student's t -test is one of the most widely-used statistical tests to compare two groups. This paper aims to stress the equivalence between Otsu's binarization method and the search for an optimal threshold that provides the largest absolute Student's t-statistic. It is then naturally demonstrated that the extensi...