---
title: "SPRTs"
author: "Meike Steinhilber"
date: "`r Sys.Date()`"
output:
  rmarkdown::html_vignette:
    toc: true
    toc_depth: 4
description: >
  This vignette describes SPRTs in general.
vignette: >
  %\VignetteIndexEntry{SPRTs}
  %\VignetteEncoding{UTF-8}{inputenc}
  %\VignetteEngine{knitr::rmarkdown}
bibliography: references.bib
csl: "apa.csl"
---


## Overview

The `sprtt` package is a **s**equential **p**robability **r**atio **t**ests **t**oolbox (**sprtt**). This vignette describes the theoretical background of these tests.

Other recommended vignettes cover:

-   a [general guide](https://meikesteinhilber.github.io/sprtt/articles/usage-sprtt.html), how to use the package and

-   an extended [use case](https://meikesteinhilber.github.io/sprtt/articles/use-case.html).


## 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 [@wald1945]:

-   The data collection is *terminated* because enough evidence has been collected for the null hypothesis (H~0~).

-   The data collection is *terminated* because enough evidence has been collected for the alternative hypothesis (H~1~).

-   The data collection *will continue* as there is not yet enough evidence for either of the two hypotheses.

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 [@schnuerch2020a].

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 [@wald1945; @schnuerch2020a]. Sequential hypothesis testing is therefore particularly suitable when resources are limited because the required sample size is reduced without compromising predefined error probabilities.