Sequential Tests of Statistical Hypotheses
By a sequential test of a statistical hypothesis is meant any statistical test procedure which gives a specific rule, at any stage of the experiment (at the n-th trial for each integral value of n), for making one of the following three decisions: (1) to accept the hypothesis being tested (null hypothesis), (2) to reject the null hypothesis, (3) to continue the experiment by making an additional observation. Thus, such a test procedure is carried out sequentially. On the basis of the first trial, one of the three decisions mentioned above is made. If the first or the second decision is made, the process is terminated. If the third decision is made, a second trial is performed. Again on the basis of the first two trials one of the three decisions is made and if the third decision is reached a third trial is performed, etc. This process is continued until either the first or the second decision is made.
KeywordsSequential Test Statistical Hypothesis Powerful Test Moment Generate Function Sequential Probability Ratio Test
Unable to display preview. Download preview PDF.
- H.F. Dodge and H.G. Romig, “A method of sampling inspection,” The Bell System Tech. Jour., Vol. 8 (1929), pp. 613–631.Google Scholar
- Harold Hotelling, “Experimental determination of the maximum of a function”, Annals of Math. Stat., Vol. 12 (1941).Google Scholar
- Abraham Wald, “On cumulative sums of random variables”, Annals of Math. Star., Vol. 15 (1944).Google Scholar
- Z.W. Birnbaum, “An inequality for Mill’s ratio”, Annals of Math. Stat., Vol. 13 (1942).Google Scholar
- P.C. Mahalanobis, “A sample survey of the acreage under jute in Bengal, with discussion on planning of experiments,” Proc. 2nd Ind. Stat. Conf., Calcutta, Statistical Publishing Soc. (1940).Google Scholar
- Abraham Wald, Sequential Analysis of Statistical Data: Theory. A report submitted by the Statistical Research Group, Columbia University to the Applied Mathematics Panel, National Defense Research Committee, Sept. 1943.Google Scholar
- Harold Freeman, Sequential Analysis of Statistical Data: Applications. A Report submitted by the Statistical Research Group, Columbia University to the Applied Mathematics Panel, National Defense Research Committee, July 1944.Google Scholar
- G.A. Barnard, M.A., Economy in Sampling with Reference to Engineering Experimentation (British) Ministry of Supply, Advisory Service on Statistical Method and Quality Control, Technical Report, Series ‘R’ No. Q.C./R/7 Part 1.Google Scholar
- CM. Stockman, A Method of Obtaining an Approximation for the Operating Characteristic of a Wald Sequential Probability Ratio Test Applied to a Binomial Distribution, (British) Ministry of Supply, Advisory Service on Statistical Method and Quality Control, Technical Report, Series ‘R’ No. Q.C./R/19.Google Scholar
- Abraham Wald, A General Method of Deriving the Operating Characteristics of any Sequential Probability Ratio Test. A Memorandum submitted to the Statistical Research Group, Columbia University, April 1944.Google Scholar