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A Modified Sequential Probability Ratio Test.

ABSTRACT: We describe a modified sequential probability ratio test that can be used to reduce the average sample size required to perform statistical hypothesis tests at specified levels of significance and power. Examples are provided for z tests, t tests, and tests of binomial success probabilities. A description of a software package to implement the test designs is provided. We compare the sample sizes required in fixed design tests conducted at 5% significance levels to the average sample sizes required in sequential tests conducted at 0.5% significance levels, and we find that the two sample sizes are approximately equal.

SUBMITTER: Pramanik S

PROVIDER: S-EPMC9053723 | biostudies-literature | 2021 Apr

REPOSITORIES: biostudies-literature

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A Modified Sequential Probability Ratio Test.

Pramanik Sandipan S Johnson Valen E VE Bhattacharya Anirban A

Journal of mathematical psychology 20210304

We describe a modified sequential probability ratio test that can be used to reduce the average sample size required to perform statistical hypothesis tests at specified levels of significance and power. Examples are provided for <i>z</i> tests, <i>t</i> tests, and tests of binomial success probabilities. A description of a software package to implement the test designs is provided. We compare the sample sizes required in fixed design tests conducted at 5% significance levels to the average samp ...[more]

PMID: 35496657

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Project description:Introduction: Functional magnetic resonance imaging (fMRI) often involves long scanning durations to ensure the associated brain activity can be detected. However, excessive experimentation can lead to many undesirable effects, such as from learning and/or fatigue effects, discomfort for the subject, excessive motion artifacts and loss of sustained attention on task. Overly long experimentation can thus have a detrimental effect on signal quality and accurate voxel activation detection. Here, we propose dynamic experimentation with real-time fMRI using a novel statistically driven approach that invokes early stopping when sufficient statistical evidence for assessing the task-related activation is observed. Methods: Voxel-level sequential probability ratio test (SPRT) statistics based on general linear models (GLMs) were implemented on fMRI scans of a mathematical 1-back task from 12 healthy teenage subjects and 11 teenage subjects born extremely preterm (EPT). This approach is based on likelihood ratios and allows for systematic early stopping based on target statistical error thresholds. We adopt a two-stage estimation approach that allows for accurate estimates of GLM parameters before stopping is considered. Early stopping performance is reported for different first stage lengths, and activation results are compared with full durations. Finally, group comparisons are conducted with both early stopped and full duration scan data. Numerical parallelization was employed to facilitate completion of computations involving a new scan within every repetition time (TR). Results: Use of SPRT demonstrates the feasibility and efficiency gains of automated early stopping, with comparable activation detection as with full protocols. Dynamic stopping of stimulus administration was achieved in around half of subjects, with typical time savings of up to 33% (4 min on a 12 min scan). A group analysis produced similar patterns of activity for control subjects between early stopping and full duration scans. The EPT group, individually, demonstrated more variability in location and extent of the activations compared to the normal term control group. This was apparent in the EPT group results, reflected by fewer and smaller clusters. Conclusion: A systematic statistical approach for early stopping with real-time fMRI experimentation has been implemented. This dynamic approach has promise for reducing subject burden and fatigue effects.

Dataset Information

A Modified Sequential Probability Ratio Test.

Publications

A Modified Sequential Probability Ratio Test.

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