Wijsman RA (1967) General proof of termination with probability one of invariant sequential probability ratio tests based on multivariate normal observations. Wald A, Wolfowitz J (1948) Optimum character of the sequential probability ratio test. Wald A (1946) Some improvements in setting limits for the expected number of observations required by a sequential probability ratio test. Wald A (1945b) Some generalizations of the theory of cumulative sums of random variables. Wald A (1945a) Sequential tests of statistical hypotheses. Wald A (1944) On cumulative sums of random variables. Stuart A, Ord JK, Arnold S (1999) Kendall’s advanced theory of statistics: Volume 2A-Classical inference and the linear model, 6th edn. Siegmund D (1985) Sequential analysis: tests and confidence intervals. Savage IR, Savage LJ (1965) Finite stopping time and finite expected stopping time. In: Armitage P, Colton T (eds) Encyclopedia of biostatistics, vol 2. Mukhopadhyay N, de Silva BM (2008) Sequential methods and their applications. In: El-Shaarawi AH, Piegorsch WW (eds) Encyclopedia of environmetrics, vol 4. Mukhopadhyay N (2002) Sequential sampling. Lindgren BW (1976) Statistical theory, 3rd edn. Lehmann EL (1959) Testing statistical hypotheses, 1st edn. Lai TL (2004) Likelihood ratio identities and their applications to sequential analysis (with discussion). Initially developed as a tool for product quality control, the process begins, first, with the sampling of a single observation or a group of observations. Lai TL (2001) Sequential analysis: some classical problems and new challenges (with discussion). Sequential sampling is a non-probabilistic sampling technique, in which the sample size, n, is not fixed in advanced, nor is the timeframe of data collection. In: Armitage P, Colton T (eds) Encyclopedia of biostatistics, vol 5. J Roy Stat Soc Ser A (General) 124:372–411 Johnson NL (1961) Sequential analysis: a survey. Jennison C, Turnbull BW (1991) Exact calculations for sequential t, χ 2 and F tests. Ghosh BK, Sen PK (eds) (1991) Handbook of sequential analysis, M. In: Kotz S, Read CB, Balakrishnan N, Vidakovic B (eds) Encyclopedia of statistical sciences vol 11, 2nd edn. It is possible that the auditor will not be willing to proceed through every group of sampling units, and instead will accept the conclusion that the planned confidence and tolerable rate of deviation cannot be achieved.David HT, Kruskal WH (1956) The WAGR sequential t-test reaches a decision with probability one. When it appears necessary to proceed to the next group of sampling units, the auditor should consider the cost-benefit of continuing to engage in testing. Engaging in the examination of further groups of sampling units will not improve the situation, so the auditor stops the sampling process. An analysis of the first group uncovers four deviations, which is too many deviations. This second group is found to contain one additional deviation, so the audit continues to the third group of samples in her continuing quest for more information, to see if the increased sample results will eventually support the assessed level of control risk. An analysis of the first group uncovers two deviations, so the auditor decides to continue with the sampling, using the next sampling group. Accordingly, she decides not to examine any additional sampling units. An analysis of the first group uncovers no deviations, so the auditor concludes that the sample supports the planned assessed level of control risk. The sampling plan is to continue to the next group of sampling units if the preceding group contains at least one deviation. Halt any further sampling, because the planned confidence and tolerable rate of deviation cannot be achieved, due to the presence of too many deviations orĮngage in the examination of additional sampling units in order to gather more information about whether the planned assessed level of control risk can be supported.Īn auditor develops a set of three groups of sampling units, where each successive group contains the same number of units to be sampled. Based on the results of this examination, the auditor decides whether to:Īccept the assessed level of control risk, without engaging in any additional sampling The sequential sampling process begins with the auditor examining the first group of sampling units. The auditor uses a computer program to determine the size of each of these groups, based on the tolerable rate of deviation, the risk of overreliance, and the expected rate of population deviation. Consequently, sequential sampling plans work best when few deviations are expected.Ī sequential sample is usually comprised of anywhere from two to four groups of sampling units. This approach can result in fewer sampling units being examined, though the sampling will continue if any deviations are found. Sequential sampling is a sampling technique that involves the evaluation of each sample taken from a population to see if it fits a desired conclusion the auditor stops evaluating samples as soon as there is sufficient support for the conclusion.
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