The double triangular test: a sequential test for the two-sided alternative with early stopping under the null hypothesis

The double triangular test is a sequential procedure for testing the null hypothesis that a parameter is zero against the two-sided alternative that it is non-zero The test is devised to produce small samples if the parameter is large in magnitude, whether positive or negative, and also to produce small samples if the parameter is close to zero. In intermediate situations larger samples are likely to be necessary. In this paper some new results concerning the theory of the double triangular test are presented. These are then used to explore in detail its properties, and how data collected using the test may be analysed. In particular, significance levels and point and interval estimates are considered.