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)
doi: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
- x
Works with two classes:
numericandformula. Therefore you can write"x"or"x~y"."numeric input": a (non-empty) numeric vector of data values."formula input": a formula of the form lhs ~ rhs where lhs is a numeric variable giving the data values and rhs either 1 for a one-sample test or a factor with two levels giving the corresponding groups.
- y
An optional (non-empty) numeric vector of data values. Only used for two-sample tests when
xis numeric.- data
An optional data frame containing the variables specified in the formula. Only used when
xis a formula.- mu
a number indicating the true value of the mean (or difference in means if you are performing a two sample test).
- d
a number indicating the specified (expected) effect size (Cohen's d)
- alpha
Type I error rate (alpha level). The probability of rejecting H0 when it is true. Default is 0.05. Must be between 0 and 1.
- power
Statistical power (1 - beta), where beta is the Type II error rate. The probability of correctly rejecting H0 when H1 is true with effect size d. Default is 0.95. Must be between 0 and 1. Higher values lead to wider stopping boundaries and potentially larger sample sizes.
- alternative
a character string specifying the alternative hypothesis, must be one of
two.sided(default),greaterorless. You can specify just the initial letter.- paired
Logical indicating whether to perform a paired t-test. Default is
FALSE.- na.rm
a logical value indicating whether
NAvalues should be removed before the computation proceeds.- verbose
a logical value whether you want a verbose output or not.
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 ANOVAdraw_sample_normal()for simulating test datavignette("t_test", package = "sprtt")for detailed tutorialvignette("usage_sprtt", package = "sprtt")for package overviewSchnuerch & Erdfelder (2019) doi: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
#> [1] 965.0728
# [] Operator
results["likelihood_ratio"]
#> [1] 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 *****
#>
#> formula: treatment_group and control_group
#> test statistic:
#> log-likelihood ratio = 5.347, decision = accept H1
#> SPRT thresholds:
#> lower log(B) = -2.944, upper log(A) = 2.944
#> Log-Likelihood of the:
#> alternative hypothesis = -4.211
#> null hypothesis = -9.558
#> 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 *****
#>
#> formula: stress_level ~ sex
#> test statistic:
#> log-likelihood ratio = -1.455, decision = continue sampling
#> SPRT thresholds:
#> lower log(B) = -2.944, upper log(A) = 2.944
#> Log-Likelihood of the:
#> alternative hypothesis = -1.233
#> null hypothesis = 0.222
#> 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 *****
#>
#> formula: stress_level ~ sex
#> test statistic:
#> log-likelihood ratio = -0.359, decision = continue sampling
#> SPRT thresholds:
#> lower log(B) = -2.944, upper log(A) = 2.944
#> Log-Likelihood of the:
#> alternative hypothesis = -1.923
#> null hypothesis = -1.564
#> 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 *****
#>
#> formula: monthly_income ~ sex
#> test statistic:
#> log-likelihood ratio = -9.514, decision = accept H0
#> SPRT thresholds:
#> lower log(B) = -2.944, upper log(A) = 2.944
#> Log-Likelihood of the:
#> alternative hypothesis = -8.093
#> null hypothesis = 1.421
#> 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.