Sequential One-Way ANOVA

Meike Steinhilber



The sprtt package is a sequential probability ratio tests toolbox (sprtt). This vignette describes the theoretical background of these tests.

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What is a sequential test procedure?

With a sequential approach, data is continuously collected and an analysis is performed after each data point, which can lead to three different results (A. Wald, 1945):

Basically it is not necessary to perform an analysis after each data point — several data points can also be added at once. However, this affects the sample size (N) and the error rates (Schnuerch et al., 2020).

The efficiency of sequential designs has already been examined. Reductions in the sample by 50% and more were found in comparison to analyses with fixed sample sizes (Schnuerch et al., 2020; A. Wald, 1945). Sequential hypothesis testing is therefore particularly suitable when resources are limited because the required sample size is reduced without compromising predefined error probabilities.

What is the sequential one-way ANOVA?

The sequential one-way fixed effects ANOVA is based on the Sequential Probability Ratio Test (SPRT) by Abraham Abraham Wald (1947), which is a highly efficient sequential hypothesis test. It can be used instead of t-tests if the means of two or more groups are compared. For detailed information see the public preprint (Steinhilber et al., 2023).


Schnuerch, M., Erdfelder, E., & Heck, D. W. (2020). Sequential hypothesis tests for multinomial processing tree models. Journal of Mathematical Psychology, 95, 102326.
Steinhilber, M., Schnuerch, M., & Schubert, A.-L. (2023). Sequential one-way ANOVA: Increasing efficiency in psychological hypothesis testing using a variant of sequential probability ratio tests. PsyArXiv.
Wald, A. (1945). Sequential tests of statistical hypotheses. The Annals of Mathematical Statistics, 16(2), 117–186.
Wald, Abraham. (1947). Sequential analysis. Wiley.