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How to use the sprtt package

Meike Snijder-Steinhilber

2026-02-03

Source: vignettes/usage_sprtt.Rmd
usage_sprtt.Rmd

The sprtt package is a toolbox for sequential probability ratio tests (SPRTs). This vignette introduces the core functions and demonstrates a typical analysis workflow. For more comprehensive guides on specific topics, see the other package vignettes. If you are unfamiliar with SPRTs, please see the XXX section first.

  • The data sets used below are included in the sprtt package. The data sets are available when the package is loaded.

  • In the R code sections:

    • # comment: is a comment
    • function(): is R code
    • #> results of function(): is console output

Workflow

1. Understand the theoretical background of SPRTs

The foundational literature (Hajnal, 1961; S. Rushton, 1950; S. Rushton, 1952; A. Wald, 1945; Abraham Wald, 1947) offers valuable depth but is not required reading. However, understanding SPRT mechanics, robustness to assumption violations, and proper application is essential. The following papers provide a good background:

Key references:

For comparisons of different sequential designs (including SPRTs), see:

2. Check if SPRTs are the fitting choice

Whether a statistical tool is appropriate depends strongly on the research context and intended use. SPRTs are recommended when:

  • Data can be collected sequentially
  • Data can be analyzed sequentially (ideally after each new observation)
  • The research question translates to a clear hypothesis test: \(H_0\) vs \(H_1\) (is there an effect or not?)
  • Resources are limited and efficiency is a priority
  • Long-term error rates need to be controlled (both \(\alpha\) and \(\beta\) error rates)
  • Accepting \(H_0\) (no effect) is of interest

SPRTs are not recommended when:

  • Sufficient literature already establishes the existence of the effect and the main goal is precise effect size estimation
  • Multiple hypotheses must be tested on the same dataset (theoretically possible but not yet implemented)
  • Data are collected all at once or only in very large batches
  • Groups cannot be sampled somewhat equally over time (e.g., collecting all participants from one group before starting the other)

3. Plan your resources

The plan_sample_size() function helps establish realistic expectations for data requirements and resource planning.

Unlike traditional designs, SPRTs do not require classical a priori power analysis because power (\(1-\beta\)) is controlled through the stopping boundaries. This allows starting data collection immediately and stopping once the test reaches a decision. However, planning necessary resources remains important for practical concerns.

Two sample sizes are relevant:

  • Expected sample size (\(N_{\text{median}}\)): The median sample size required to reach a decision. Most studies will finish near this value.
  • Maximum sample size (\(N_{\text{max}}\)): The maximum affordable sample size. Choose settings where \(N_{\text{max}}\) yields a decision rate of at least 80% (i.e., the test reaches a decision in at least 80% of cases where the maximum sample is reached).

For more details see the vignette XXX.

4. Plan the data collection and register your test specifications

A thoughtful data collection plan is highly recommended to keep groups somewhat balanced and to track and balance (or randomize) potential confounders.

As SPRTs are best suited for confirmatory research, preregistering the data collection plan, hypothesis, and test specifications (e.g., effect size of interest, \(\alpha\) and \(\beta\) levels) is strongly recommended.

Preparing an analysis script in advance enables a smooth process for continuously analyzing incoming data. This ensures data collection stops immediately once the stopping criterion is reached, avoiding unnecessary additional data collection.

To test the analysis pipeline, use either:

  • The example datasets included in the sprtt package
  • The data generating functions, which allow specifying the true effect size for simulation testing

5. Collect the data and apply the SPRTs

The following test are currently implemented:

  • sequential t-tests
  • sequential one-way ANOVA with independent groups

See the vignettes for each test. XXX

5. Reporting of the results

Guidelines for the reporting of SPRTs can be found in the following paper that also explicitly covers sequential testing and specifically SPRTs (schubert2025?) doi:10.1038/s44271-025-00356-w.

References

Hajnal, J. (1961). A two-sample sequential t-test. Biometrika, 48(1/2), 65–75. https://doi.org/10.2307/2333131
Rushton, S. (1950). On a sequential t-test. Biometrika, 37, 326–333. https://doi.org/10.2307/2332385
Rushton, S. (1952). On a Two-Sided Sequential t-Test. Biometrika, 39(3/4), 302. https://doi.org/10.2307/2334026
Wald, A. (1945). Sequential tests of statistical hypotheses. The Annals of Mathematical Statistics, 16(2), 117–186.
Wald, Abraham. (1947). Sequential analysis. Wiley.