# sprtt

## Overview

The `sprtt` package is the implementation of sequential probability ratio tests using the associated t-statistic (sprtt).

The package contains:

• `seq_ttest()` calculates the sequential test statistic and

• three data sets (`df_income`, `df_stress`, `df_cancer`) to run the examples in the documentation

## Installation

### Release version from CRAN

This is the recommended version for a normal user.

``````# installs the package
install.packages("sprtt")``````

### Development version from GitHub

To get a bug fix or to use a feature from the development version, you can install the development version from GitHub.

``````# the installation requires the "devtools" package
# install.packages("devtools")
devtools::install_github("MeikeSteinhilber/sprtt")``````

## Documentation

Detailed documentation can be found on the home page. There are several articles covering the usage of the package, the theoretical background of the test, and also an extended use case.

Short examples can be found in the following paragraph.

### Quick Examples

Note

In the R code sections:

`# comment`: is a comment

`function()`: is R code

`#> results of function()`: is console output

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

library(sprtt)

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

# @ Operator
results@likelihood_ratio
#>  965.0728

# [] Operator
results["likelihood_ratio"]
#>  965.0728

# 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)
#>
#> *****  Sequential  Two Sample t-test *****
#>
#> data: treatment_group and  control_group
#> test statistic:
#>  log-likelihood ratio = 5.347, decision = accept H1
#> SPRT thresholds:
#>  lower log(B) = -2.94444, upper log(A) = 2.94444
#> Log-Likelihood of the:
#>  alternative hypothesis = -4.21063
#>  null hypothesis = -9.55763
#> alternative hypothesis: true difference in means is not equal to 0.
#> specified effect size: Cohen's d = 0.8
#> degrees of freedom: df = 38
#> sample estimates:
#> mean of x mean of y
#>  -0.05204   1.18768
#> Note: to get access to the object of the results use the @ or []
#>           instead of the \$ operator.

# 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)
#>
#> *****  Sequential  Two Sample t-test *****
#>
#> data: stress_level ~ sex
#> test statistic:
#>  log-likelihood ratio = -1.45506, decision = continue sampling
#> SPRT thresholds:
#>  lower log(B) = -2.94444, upper log(A) = 2.94444
#> Log-Likelihood of the:
#>  alternative hypothesis = -1.23287
#>  null hypothesis = 0.2222
#> alternative hypothesis: true difference in means is not equal to 0.
#> specified effect size: Cohen's d = 0.8
#> degrees of freedom: df = 18
#> sample estimates:
#> mean of x mean of y
#>  -0.23286  -0.08217
#> Note: to get access to the object of the results use the @ or []
#>           instead of the \$ operator.

# 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)
#>
#> *****  Sequential  Two Sample t-test *****
#>
#> data: stress_level ~ sex
#> test statistic:
#>  log-likelihood ratio = -0.3585, decision = continue sampling
#> SPRT thresholds:
#>  lower log(B) = -2.94444, upper log(A) = 2.94444
#> Log-Likelihood of the:
#>  alternative hypothesis = -1.923
#>  null hypothesis = -1.5645
#> alternative hypothesis: true difference in means is not equal to 0.
#> specified effect size: Cohen's d = 0.8
#> degrees of freedom: df = 18
#> sample estimates:
#> mean of x mean of y
#>  -0.40818   0.42068
#> Note: to get access to the object of the results use the @ or []
#>           instead of the \$ operator.

# work with dataset (data are in the package included) ------------------------
seq_ttest(monthly_income ~ sex, data = df_income, d = 0.8)
#>
#> *****  Sequential  Two Sample t-test *****
#>
#> data: monthly_income ~ sex
#> test statistic:
#>  log-likelihood ratio = -9.51391, decision = accept H0
#> SPRT thresholds:
#>  lower log(B) = -2.94444, upper log(A) = 2.94444
#> Log-Likelihood of the:
#>  alternative hypothesis = -8.09254
#>  null hypothesis = 1.42137
#> alternative hypothesis: true difference in means is not equal to 0.
#> specified effect size: Cohen's d = 0.8
#> degrees of freedom: df = 118
#> sample estimates:
#> mean of x mean of y
#>  3072.086  3080.715
#> Note: to get access to the object of the results use the @ or []
#>           instead of the \$ operator.``````