Recently, Billard (1977) introduced a truncated partial sequential procedure for testing a null hypothesis about a normal mean with known variance against a two-sided alternative hypothesis. That procedure had the disadvantage that a large number of observations is necessary if the null hypothesis is to be accepted. A new procedure is introduced which reduces the expected sample size for all mean values with considerable reductions for values near the null mean value. Theoretical operating characteristic and average sample number functions are derived, and the empirical distribution of the sample size in some special cases is obtained. / For the case of unknown variance and a one-sided alternative hypothesis, there are a number of tests, the best known of which are those of Wald (1947) and Barnard (1952). These tests have concerned themselves with tests for units of (mu)/(sigma). In this work, a partial sequential test procedure is introduced for hypotheses concerned only with (mu). An advantage of this new procedure is its relative simplicity and ease of execution when compared to the above tests. This is essentially due to the fact that in the present procedure the transformed observations follow a central t-distribution as distinct from the noncentral t-distribution. The difficulties caused by the noncentral distribution explain the relative lack of progress in obtaining the results about the properties, such as the operating characteristic and average sample number functions, of the tests of Barnard and Wald. The key element in the present procedure is that a number of observations is taken initially before any decision is made; subsequent observations are then taken in batches, the sizes of which depend on the estimate for the variance obtained from the initial set of observations. Some properties of the procedure are studied. In particular, an approximation to the theoretical operating characteristic function is derived and the sensitivity of the average sample number function to changes in some of the test parameters is investigated. / The ideas developed for the partial sequential t-test are extended to develop tests of hypotheses concerning the parameters of a simple linear regression equation, general linear hypotheses and hypotheses about the mean of special cases of the multivariate normal. / Source: Dissertation Abstracts International, Volume: 42-06, Section: B, page: 2435. / Thesis (Ph.D.)--The Florida State University, 1981.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_74568 |
| Contributors | ARGHAMI, NASSER REZA., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 131 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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