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A sequential test for two binomial populations.

H Robbins1

  • 1Columbia University, New York, N.Y. 10027.

Proceedings of the National Academy of Sciences of the United States of America
|November 1, 1974
PubMed
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This study introduces a sequential procedure to compare success probabilities in Bernoulli trials. The method is effective even when data is collected at different rates, aiding in medical treatment comparisons.

Area of Science:

  • Statistics
  • Biostatistics
  • Sequential Analysis

Background:

  • Comparing success probabilities is crucial in various fields, including medical treatment evaluation.
  • Sequential procedures offer efficient data collection and analysis compared to fixed-sample methods.
  • Handling observations at different rates presents a challenge in comparative studies.

Purpose of the Study:

  • To propose a novel sequential procedure for comparing success probabilities of two Bernoulli sequences.
  • To accommodate scenarios with unequal observation rates for the sequences.
  • To evaluate the procedure's performance, particularly its error probability characteristics.

Main Methods:

  • Development of a sequential probability ratio test framework.

Related Experiment Videos

  • Adaptation of the procedure for asynchronous or unequally sampled Bernoulli trials.
  • Theoretical analysis of the procedure's error probability.

    • Main Results:

    • The proposed sequential procedure effectively determines which Bernoulli sequence has a higher success probability.
    • The procedure is robust to differing observation rates between the two sequences.
    • The error probability is shown to be primarily dependent on the odds ratio of the success probabilities.

    Conclusions:

    • The developed sequential procedure provides a statistically sound and efficient method for comparing Bernoulli success probabilities.
    • Its applicability extends to real-world scenarios with varying data collection frequencies, such as clinical trials.
    • The odds ratio dependency offers a desirable and interpretable characteristic for decision-making in comparative effectiveness research.