Skip to main content

Sequential Tests of Statistical Hypotheses

  • Chapter
Breakthroughs in Statistics

Part of the book series: Springer Series in Statistics ((PSS))

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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 

  2. Walter Bartky, “Multiple sampling with constant probability”, Annals of Math. Stat., Vol. 14 (1943), pp. 363–377.

    Article  MathSciNet  MATH  Google Scholar 

  3. Harold Hotelling, “Experimental determination of the maximum of a function”, Annals of Math. Stat., Vol. 12 (1941).

    Google Scholar 

  4. Abraham Wald, “On cumulative sums of random variables”, Annals of Math. Star., Vol. 15 (1944).

    Google Scholar 

  5. Z.W. Birnbaum, “An inequality for Mill’s ratio”, Annals of Math. Stat., Vol. 13 (1942).

    Google Scholar 

  6. 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 

  7. 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 

  8. 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 

  9. 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 

  10. 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 

  11. 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 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer Science+Business Media New York

About this chapter

Cite this chapter

Wald, A. (1992). Sequential Tests of Statistical Hypotheses. In: Kotz, S., Johnson, N.L. (eds) Breakthroughs in Statistics. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0919-5_18

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0919-5_18

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94037-3

  • Online ISBN: 978-1-4612-0919-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics