Package {sprtt}

Type:	Package
Title:	Sequential Probability Ratio Tests Toolbox
Version:	0.3.1
Date:	2026-04-13
Maintainer:	Meike Snijder-Steinhilber <Meike.Steinhilber@aol.com>
Description:	A toolbox for Sequential Probability Ratio Tests (SPRT) based on Wald (1945) <doi:10.2134/agronj1947.00021962003900070011x>. SPRTs are applied during the sampling process, ideally after each observation, and at every stage return a decision to either continue sampling or terminate and accept one of the specified hypotheses. The 'seq_ttest()' function performs one-sample, two-sample, and paired t-tests for one- and two-sided hypotheses (Schnuerch & Erdfelder (2019) <doi:10.1037/met0000234>). The 'seq_anova()' function performs a sequential one-way fixed effects ANOVA (Steinhilber et al. (2024) <doi:10.1037/met0000677>). The 'plan_sample_size()' function helps plan sequential studies by simulating required sample sizes across a range of effect sizes. For more information, see the vignettes browseVignettes(package = "sprtt") or the package website https://meikesteinhilber.github.io/sprtt/.
License:	AGPL (≥ 3)
URL:	https://meikesteinhilber.github.io/sprtt/
BugReports:	https://github.com/MeikeSteinhilber/sprtt/issues
Depends:	R (≥ 3.5.0)
Imports:	rappdirs, methods, stats, dplyr, MBESS, purrr, glue, ggplot2, lifecycle, knitr, rmarkdown, gt, ggtext, scales, piggyback
Suggests:	testthat (≥ 3.0.0), testthis, withr, xml2, effsize, effectsize, vdiffr, diffviewer
VignetteBuilder:	knitr
Encoding:	UTF-8
Language:	en-US
LazyData:	yes
LazyDataCompression:	xz
RoxygenNote:	7.3.3
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-05-06 11:58:02 UTC; msteinhi
Author:	Meike Snijder-Steinhilber [aut, cre], Martin Schnuerch [aut, ths], Anna-Lena Schubert [aut, ths]
Repository:	CRAN
Date/Publication:	2026-05-06 12:20:02 UTC

sprtt: Sequential Probability Ratio Tests Toolbox

Description

A toolbox for Sequential Probability Ratio Tests (SPRT) based on Wald (1945) doi:10.2134/agronj1947.00021962003900070011x. SPRTs are applied during the sampling process, ideally after each observation, and at every stage return a decision to either continue sampling or terminate and accept one of the specified hypotheses. The 'seq_ttest()' function performs one-sample, two-sample, and paired t-tests for one- and two-sided hypotheses (Schnuerch & Erdfelder (2019) doi:10.1037/met0000234). The 'seq_anova()' function performs a sequential one-way fixed effects ANOVA (Steinhilber et al. (2024) doi:10.1037/met0000677). The 'plan_sample_size()' function helps plan sequential studies by simulating required sample sizes across a range of effect sizes. For more information, see the vignettes browseVignettes(package = "sprtt") or the package website https://meikesteinhilber.github.io/sprtt/.

Author(s)

Maintainer: Meike Snijder-Steinhilber Meike.Steinhilber@aol.com (ORCID)

Authors:

• Martin Schnuerch (ORCID) [thesis advisor]

• Anna-Lena Schubert (ORCID) [thesis advisor]

See Also

Useful links:

• https://meikesteinhilber.github.io/sprtt/

• Report bugs at https://github.com/MeikeSteinhilber/sprtt/issues

Method to retrieve the contents of a slot of an object of the seq_anova_arguments class.

Description

This method is only used internally to process the input arguments of the seq_anova function. As a normal user, you can ignore this specific documentation.

Usage

## S4 method for signature 'seq_anova_arguments'
x[i, j, drop]

Arguments

Value

Returns the contents of the specified slot. For more information, see the documentation for the seq_anova_arguments class.

Method to retrieve the contents of a slot of an object of the seq_anova_results class.

Description

Method to retrieve the contents of a slot of an object of the seq_anova_results class.

Usage

## S4 method for signature 'seq_anova_results'
x[i, j, drop]

Arguments

Value

Returns the contents of the specified slot. For more information, see the documentation for the seq_anova_results class.

Method to retrieve the contents of a slot of an object of the seq_ttest_arguments class.

Description

This method is only used internally to process the input arguments of the seq_ttest function. As a normal user, you can ignore this specific documentation.

Usage

## S4 method for signature 'seq_ttest_arguments'
x[i, j, drop]

Arguments

Value

Returns the contents of the specified slot of an seq_ttest_arguments object. For more information, see the arguments of the seq_ttest function.

Method to retrieve the contents of a slot of an object of the seq_ttest_results class.

Description

Method to retrieve the contents of a slot of an object of the seq_ttest_results class.

Usage

## S4 method for signature 'seq_ttest_results'
x[i, j, drop]

Arguments

Value

Returns the contents of the specified slot. For more information, see the documentation for the seq_ttest_results class.

Clear cached simulation data

Description

Removes locally cached simulation data (~150 MB) used by plan_sample_size(). Data will be automatically re-downloaded on next use of sample size planning functions.

This function is useful when:

• You want to free up disk space

• The cached data may be outdated and you want to force a fresh download

• Troubleshooting cache-related issues

Usage

cache_clear()

Value

Invisibly returns TRUE if cache was cleared, FALSE if no cache existed.

Examples

## Not run: 
# Clear cache
cache_clear()

## End(Not run)

Cache information

Description

Displays information about cached simulation data (~150 MB) used by plan_sample_size(). Shows the cache directory location, whether data is cached, file size, and dataset version metadata.

The simulation data is automatically downloaded on first use of sample size planning functions and stored locally for faster subsequent access.

Usage

cache_info()

Value

Invisibly returns a list with:

• cache_dir: Character string with the cache directory path

• data_cached: Logical indicating if simulation data is cached

• file_size_mb: Numeric file size in MB (or NA if not cached)

• data_version: GitHub release tag of the cached dataset (or NA if not cached)

• data_created: Date the dataset was created (or NA if not cached)

See Also

• cache_clear() to remove cached data

• download_sample_size_data() to manually download simulation data

• plan_sample_size() which uses the cached data

Test data to run the examples

Description

A dataset that includes 120 individuals.

Usage

df_cancer

Format

A data frame with 2 variables:

treatment_group

control_group

Test data to run the examples

Description

A dataset that includes 120 individuals with sex gender and monthly income.

Usage

df_income

Format

A data frame with 2 variables:

monthly_income

sex

Test data to run the examples

Description

A dataset that includes 120 individuals.

Usage

df_stress

Format

A data frame with 2 variables:

baseline_stress

one_year_stress

Download simulation data for sample size planning

Description

Downloads pre-computed simulation results from GitHub releases. Data is cached locally and only needs to be downloaded once.

Data is hosted at: MeikeSteinhilber/sprtt_plan_sample_size

Usage

download_sample_size_data(force = FALSE)

Arguments

Value

Invisibly returns the path to the cached data file.

Examples

## Not run: 
# Download data (only needed once)
download_sample_size_data()

# Force re-download (e.g., after data update)
download_sample_size_data(force = TRUE)

## End(Not run)

Draw Samples from a Gaussian Mixture Distribution

Description

Draws exemplary samples with a certain effect size for the sequential one-oway ANOVA or the sequential t-test, see Steinhilber et al. (2023) https://doi.org/10.31234/osf.io/m64ne

Usage

draw_sample_mixture(k_groups, f, max_n, counter_n = 100, verbose = FALSE)

Arguments

Value

returns a data.frame with the columns y (observations) and x (factor_A).

Examples

set.seed(333)

data <- sprtt::draw_sample_mixture(
  k_groups = 2,
  f = 0.40,
  max_n = 2
)
data

data <- sprtt::draw_sample_mixture(
  k_groups = 4,
  f = 1.2, # very large effect size
  max_n = 4,
  counter_n = 1000, # increase of counter is necessary
  verbose = TRUE # prints more information to the console
)
data

Draw Samples from a Normal Distribution

Description

Draws exemplary samples with a certain effect size for the sequential one-oway ANOVA or the sequential t-test, see Steinhilber et al. (2023) https://doi.org/10.31234/osf.io/m64ne

Usage

draw_sample_normal(k_groups, f, max_n, sd = NULL, sample_ratio = NULL)

Arguments

Value

returns a data.frame with the columns y (observations) and x (factor_A).

Examples

set.seed(333)

data <- sprtt::draw_sample_normal(
  k_groups = 2,
  f = 0.20,
  max_n = 2
)
data

data <- sprtt::draw_sample_normal(
  k_groups = 4,
  f = 0,
  max_n = 2,
  sd = c(1, 2, 1, 8)
)
data

data <- sprtt::draw_sample_normal(
  k_groups = 3,
  f = 0.40,
  max_n = 2,
  sd = c(1, 0.8, 1),
  sample_ratio = c(1, 2, 3)
)
data

Get path to cached simulation data directory

Description

Get path to cached simulation data directory

Usage

get_sprtt_cache_dir()

Access sample size simulation data

Description

Loads pre-computed simulation results for SPRT sample size planning. If not already cached locally, the data (~150 MB) will be downloaded automatically from GitHub releases. Use this function to access the complete dataset for custom analysis and visualization. See the Data Structure section below for details on available columns.

Data is hosted at: MeikeSteinhilber/sprtt_plan_sample_size

Usage

load_sample_size_data()

Value

A named list with the following elements:

• description: Short description of the dataset

• version: GitHub release tag of the dataset (e.g., "v0.1.0-data")

• created: Date the dataset was created (as character string)

• n_rep: Number of simulation iterations per condition

• data: A data frame with simulation results (see Data Structure)

Data Structure

The data element contains simulation results with the following columns:

Simulation Metadata:

• batch: Batch identifier for the simulation run

• iteration: Individual simulation iteration within a batch

• source_file: Path to the file containing simulation parameters or results

Input Parameters:

• f_simulated: The true effect size used to generate the simulated data

• f_expected: The expected effect size specified for the SPRT

• k_groups: Number of groups in the design

• alpha: Significance level (Type I error rate)

• power: Desired statistical power (1 - Type II error rate)

• distribution: Data distribution used for simulation

• sd: Standard deviation(s) used in data generation in each group

• sample_ratio: Ratio of sample sizes between groups (e.g., 1:1, 2:1)

• n_raw_data: Total number of raw observations generated in each group

• fix_n: Fixed sample size

Individual Test Results:

• n: Actual sample size at which the SPRT terminated

• decision: Test decision

• decision_error: Whether the decision was erroneous (Type I or Type II error)

• log_lr: Log-likelihood ratio at termination

• f: Calculated effect size from the data

• f_adj: Adjusted effect size

• f_statistic: F-statistic from ANOVA test

Summary Statistics (Aggregated across iterations):

• decision_error_rate: Proportion of incorrect decisions

• mean_n: Mean sample size across all iterations

• sd_error_n: Standard error of the mean sample size (sd(n)/sqrt(n))

• median_n: Median sample size (50th percentile)

• min_n, max_n: Minimum and maximum sample sizes observed

• q25_n, q50_n, q75_n, q90_n, q95_n: Sample size quantiles

• decision_rate_25, decision_rate_50, decision_rate_75, decision_rate_90, decision_rate_95, decision_rate_100: Cumulative decision rates at various percentages of maximum sample size

Examples

## Not run: 
# Load data (downloads automatically if needed)
loaded <- load_sample_size_data()

# Access the simulation data frame
head(loaded$data)

# Check dataset version
loaded$version  # e.g. "v0.1.0-data"
loaded$created

## End(Not run)

Generates HTML reports for sample size planning for sequential ANOVAs.

Description

Renders a parameterized R Markdown report that helps plan sample size for the sequential ANOVA. The function takes expected effect size (f_expected), number of groups (k_groups), the power, and decision rate, then generates a reproducible HTML report summarizing the simulation-based sample size recommendations. The alpha level is always 0.05.

The template is located under: inst/rmarkdown/templates/report_sample_size/skeleton/skeleton.Rmd.

Usage

plan_sample_size(
  f_expected,
  k_groups,
  beta = 0.05,
  decision_rate = 0.85,
  output_dir = tempdir(),
  output_file = "sprtt-report-sample-size-planning.html",
  open = interactive(),
  overwrite = FALSE
)

Arguments

Details

This function is a front-end utility for rendering a pre-defined R Markdown report using rmarkdown::render().

Value

Invisibly returns the path to the rendered HTML file (character string). The report is optionally opened in the default browser.

File Overwrite Behavior

• If the specified output file already exists:

  • and overwrite = FALSE, the user is asked whether to overwrite (in interactive sessions); otherwise, an error is thrown.

  • If overwrite = TRUE, the file is replaced silently.

Examples

## Not run: 
# Generate and open an SPRT sample size planning report:
plan_sample_size(
  f_expected = 0.25,
  k_groups = 3,
  decision_rate = 0.9
)

# Prevent overwriting an existing file:
plan_sample_size(0.25, 3, overwrite = FALSE)

## End(Not run)

Plot Sequential ANOVA Results

Description

Creates a visualization of the sequential probability ratio test (SPRT) for ANOVA results, showing the log-likelihood ratio trajectory across sample sizes and decision boundaries.

Usage

plot_anova(
  anova_results,
  labels = TRUE,
  position_labels_x = 0.15,
  position_labels_y = 0.1,
  position_lr_x = NULL,
  position_lr_y = NULL,
  font_size = 15,
  line_size = 1,
  highlight_color = "#CD2626"
)

Arguments

Value

A ggplot2::ggplot() object showing:

• Log-likelihood ratio trajectory across sample sizes

• Dashed horizontal lines indicating decision boundaries

• Highlighted point showing where decision was reached (or final sample)

• Optional labels for decision regions and likelihood ratio value

Examples

# simulate data for the example ------------------------------------------------
set.seed(3)
data <- sprtt::draw_sample_normal(3, f = 0.25, max_n = 50)

# calculate the SPRT -----------------------------------------------------------
anova_results <- sprtt::seq_anova(y~x, f = 0.25, data = data, plot = TRUE)

# plot the results -------------------------------------------------------------
# default settings
sprtt::plot_anova(anova_results)
# variant 1
sprtt::plot_anova(anova_results,
                 labels = TRUE,
                 position_labels_x = 0.05,
                 position_lr_x = 150,
                 position_lr_y = 0,
                 highlight_color = "green"
                 )
# variant 2
sprtt::plot_anova(anova_results,
                  labels = TRUE,
                  position_labels_x = 0.15,
                  position_labels_y = 0.2,
                  position_lr_x = 60,
                  position_lr_y = 1,
                  font_size = 25,
                  line_size = 2,
                  highlight_color = "darkred"
)
# no labels
sprtt::plot_anova(anova_results,
                 labels = FALSE
                 )
# custom additions
sprtt::plot_anova(anova_results) +
  ggplot2::geom_vline(xintercept = 66, linewidth = 1, linetype = "dashed")

# further information ----------------------------------------------------------
# run this code:
vignette("one_way_anova", package = "sprtt")

Sequential Analysis of Variance

Description

Performs a sequential one-way fixed effects ANOVA, which is a variant of a Sequential Probability Ratio Test (SPRT). The test allows for continuous monitoring of data collection and provides stopping boundaries based on likelihood ratios, offering efficiency gains over traditional fixed-N designs.

The sequential ANOVA continuously evaluates the likelihood ratio after each observation (or group of observations), stopping when sufficient evidence accumulates for either H0 or H1.

For methodological details, see Steinhilber et al. (2024) https://doi.org/10.1037/met0000677. For practical guidance, see vignette("one_way_anova", package = "sprtt").

Usage

seq_anova(
  formula,
  f,
  alpha = 0.05,
  power = 0.95,
  data,
  verbose = TRUE,
  plot = FALSE,
  seq_steps = "single"
)

Arguments

Value

An object of the S4 class seq_anova_results. Click on the class link to see the full description of the slots. To get access to the object use the @-operator or ⁠[]⁠-brackets instead of $. See the examples below.

Limitations

• Only one-way fixed effects ANOVA is currently supported

• Repeated measures ANOVA is not yet implemented

See Also

• plot_anova() for visualizing sequential ANOVA results

• plan_sample_size() for sample size planning

• seq_ttest() for sequential t-tests

• vignette("one_way_anova", package = "sprtt") for detailed tutorial

• vignette("plan_sample_size", package = "sprtt") for planning guidance

• Steinhilber et al. (2023) for theoretical background

Examples

# simulate data ----------------------------------------------------------------
set.seed(333)
data <- sprtt::draw_sample_normal(k_groups = 3,
                    f = 0.25,
                    sd = c(1, 1, 1),
                    max_n = 50)


# calculate sequential ANOVA ---------------------------------------------------
results <- sprtt::seq_anova(y ~ x, f = 0.25, data = data)
# test decision
results@decision
# test results
results

# calculate sequential ANOVA ---------------------------------------------------
results <- sprtt::seq_anova(y ~ x,
                            f = 0.25,
                            data = data,
                            alpha = 0.01,
                            power = .80,
                            verbose = TRUE)
results

# calculate sequential ANOVA ---------------------------------------------------
results <- sprtt::seq_anova(y ~ x,
                            f = 0.15,
                            data = data,
                            alpha = 0.05,
                            power = .80,
                            verbose = FALSE)
results

An S4 class to represent the results of a sequential anova.

Description

An S4 class to represent the results of a sequential anova.

Arguments

Slots

likelihood_ratio_log

the logarithmic test statistic.

decision

the test decision: "accept H1", "accept H0", or "continue sampling".

A_boundary_log

the lower logarithmic boundary of the test.

B_boundary_log

the upper logarithmic boundary of the test.

f

a number indicating the specified effect size (Cohen's f).

effect_sizes

a list with effect sizes (Cohen's f, eta squared, ...).

alpha

the type I error. A number between 0 and 1.

power

1 - beta (beta is the type II error probability). A number between 0 and 1.

likelihood_ratio

the likelihood ratio of the test without logarithm.

likelihood_1

the likelihood of the alternative Hypothesis (H1).

likelihood_0

the likelihood of the null Hypothesis (H0).

likelihood_1_log

the logarithmic likelihood of the alternative Hypothesis (H1).

likelihood_0_log

the logarithmic likelihood of the null Hypothesis (H0).

non_centrality_parameter

parameter to calculate the likelihoods

F_value

the F-value of the F-statistic.

df_1

degrees of freedom.

df_2

degrees of freedom.

ss_effect

ss_effect.

ss_residual

ss_residual.

ss_total

ss_total.

total_sample_size

total sample size.

data_name

a character string giving the name(s) of the data.

verbose

a logical value whether you want a verbose output or not.

Sequential Probability Ratio Test using t-statistic

Description

Performs one-sample, two-sample, and paired sequential t-tests, which are variants of Sequential Probability Ratio Tests (SPRT). The test allows for continuous monitoring of data collection and provides stopping boundaries based on likelihood ratios, offering efficiency gains over traditional fixed-N designs.

The sequential t-test continuously evaluates the likelihood ratio after each observation (or pair of observations), stopping when sufficient evidence accumulates for either H0 or H1.

For methodological details, see Schnuerch & Erdfelder (2019) https://doi.org/10.1037/met0000234. For practical guidance, see vignette("t_test", package = "sprtt").

Usage

seq_ttest(
  x,
  y = NULL,
  data = NULL,
  mu = 0,
  d,
  alpha = 0.05,
  power = 0.95,
  alternative = "two.sided",
  paired = FALSE,
  na.rm = TRUE,
  verbose = TRUE
)

Arguments

Value

An object of the S4 class seq_ttest_results. Click on the class link to see the full description of the slots. To get access to the object use the @-operator or ⁠[]⁠-brackets instead of $. See the examples below.

See Also

• seq_anova() for sequential one-way ANOVA

• draw_sample_normal() for simulating test data

• vignette("t_test", package = "sprtt") for detailed tutorial

• vignette("usage_sprtt", package = "sprtt") for package overview

• Schnuerch & Erdfelder (2019) https://doi.org/10.1037/met0000234 for theoretical background

Examples

# set seed --------------------------------------------------------------------
set.seed(333)

# load library ----------------------------------------------------------------
library(sprtt)

# one sample: numeric input ---------------------------------------------------
treatment_group <- rnorm(20, mean = 0, sd = 1)
results <- seq_ttest(treatment_group, mu = 1, d = 0.8)

# get access to the slots -----------------------------------------------------
# @ Operator
results@likelihood_ratio

# [] Operator
results["likelihood_ratio"]

# two sample: numeric input----------------------------------------------------
treatment_group <- stats::rnorm(20, mean = 0, sd = 1)
control_group <- stats::rnorm(20, mean = 1, sd = 1)
seq_ttest(treatment_group, control_group, d = 0.8)

# two sample: formula input ---------------------------------------------------
stress_level <- stats::rnorm(20, mean = 0, sd = 1)
sex <- as.factor(c(rep(1, 10), rep(2, 10)))
seq_ttest(stress_level ~ sex, d = 0.8)

# NA in the data --------------------------------------------------------------
stress_level <- c(NA, stats::rnorm(20, mean = 0, sd = 2), NA)
sex <- as.factor(c(rep(1, 11), rep(2, 11)))
seq_ttest(stress_level ~ sex, d = 0.8, na.rm = TRUE)

# work with dataset (data are in the package included) ------------------------
seq_ttest(monthly_income ~ sex, data = df_income, d = 0.8)

An S4 class to represent the results of a sequential t-test.

Description

An S4 class to represent the results of a sequential t-test.

Slots

likelihood_ratio_log

the logarithmic test statistic.

decision

the test decision: "accept H1", "accept H0", or "continue sampling".

A_boundary_log

the lower logarithmic boundary of the test.

B_boundary_log

the upper logarithmic boundary of the test.

d

a number indicating the specified effect size (Cohen's d).

mu

a number indicating the true value of the mean (or difference in means if you are performing a two sample test).

alpha

the type I error. A number between 0 and 1.

power

1 - beta (beta is the type II error probability). A number between 0 and 1.

likelihood_ratio

the likelihood ratio of the test without logarithm.

likelihood_1

the likelihood of the alternative Hypothesis (H1).

likelihood_0

the likelihood of the null Hypothesis (H0).

likelihood_1_log

the logarithmic likelihood of the alternative Hypothesis (H1).

likelihood_0_log

the logarithmic likelihood of the null Hypothesis (H0).

non_centrality_parameter

parameter to calculate the likelihoods

t_value

the t-value of the t-statistic.

p_value

the p-value of the t-test.

df

degrees of freedom.

mean_estimate

the estimated mean or difference in means depending on whether it was a one-sample test or a two-sample test.

alternative

a character string specifying the alternative hypothesis: "two.sided" (default), "greater" or "less".

one_sample

"true" if it is a one-sample test, "false" if it is a two-sample test.

ttest_method

a character string indicating what type of t-test was performed.

data_name

a character string giving the name(s) of the data.

verbose

a logical value whether you want a verbose output or not.