Comprehensive t-test with Cohen's d

This function wraps stats::t.test() to provide a consistent interface for independent-samples, paired-samples, and one-sample t-tests. It always calculates Cohen's d as a measure of effect size and returns results in a tidy format.

t_test(
  x,
  y = NULL,
  data = NULL,
  paired = FALSE,
  mu = 0,
  var.equal = FALSE,
  conf.level = 0.95,
  alternative = c("two.sided", "less", "greater"),
  ...
)

Arguments

x: A numeric vector of data values, or a formula of the form outcome ~ group for independent samples tests.
y: An optional numeric vector of data values. For independent samples, this should be NULL if x is a formula. For paired samples, this should be a vector of the same length as x.
data: An optional data frame containing the variables in the formula (for independent samples tests only).
paired: Logical indicating whether to perform a paired samples t-test. Default is FALSE.
mu: A number indicating the true value of the mean (for one-sample tests) or difference in means (for paired and independent samples tests). Default is 0.
var.equal: Logical indicating whether to treat the two variances as equal for independent samples tests. Default is FALSE (Welch's t-test).
conf.level: Confidence level for the confidence interval. Default is 0.95.
alternative: A character string specifying the alternative hypothesis: "two.sided" (default), "less", or "greater".
...: Additional arguments passed to stats::t.test().

Value

An object of class "timesaveR_t_test" containing:

test_type: Type of t-test performed
statistic: The t-statistic
parameter: Degrees of freedom
p.value: The p-value
estimate: The estimated mean or mean difference
conf.low: Lower bound of confidence interval
conf.high: Upper bound of confidence interval
cohens_d: Cohen's d effect size
alternative: Alternative hypothesis
method: Description of the test method
data.name: Description of the data
htest: The original htest object from t.test()

Details

Cohen's d is calculated as follows:

For independent samples: (mean1 - mean2) / pooled_sd (or using separate SDs if var.equal = FALSE)
For paired samples: mean_diff / sd_diff
For one sample: (mean - mu) / sd

Examples

# One-sample t-test
t_test(mtcars$mpg, mu = 20)
#> 
#> One Sample t-test 
#> 
#> data:  mtcars$mpg 
#> t = 0.085, df = 31, p-value = .933
#> alternative hypothesis: true mean is not equal to 20 
#> 95% confidence interval:
#>  17.918 22.264
#> sample estimate:
#>  mean of x
#>  20.091
#> 
#> Cohen's d: 0.015
#> 

# Independent samples t-test (formula interface)
t_test(mpg ~ am, data = mtcars)
#> 
#> Welch Two Sample t-test 
#> 
#> data:  mpg by am 
#> t = -3.767, df = 18.33, p-value = .001
#> alternative hypothesis: true mean is not equal to 0 
#> 95% confidence interval:
#>  -11.280 -3.210
#> sample estimates:
#>  mean of x    mean of y
#>  17.147    24.392
#> 
#> Cohen's d: -1.411
#> 

# Independent samples t-test (vector interface)
t_test(mtcars$mpg[mtcars$am == 0], mtcars$mpg[mtcars$am == 1])
#> 
#> Welch Two Sample t-test 
#> 
#> data:  mtcars$mpg[mtcars$am == 0] and mtcars$mpg[mtcars$am == 1] 
#> t = -3.767, df = 18.33, p-value = .001
#> alternative hypothesis: true mean is not equal to 0 
#> 95% confidence interval:
#>  -11.280 -3.210
#> sample estimates:
#>  mean of x    mean of y
#>  17.147    24.392
#> 
#> Cohen's d: -1.411
#> 

# Paired samples t-test
t_test(iris$Sepal.Width, iris$Petal.Length, paired = TRUE)
#> 
#> Paired t-test 
#> 
#> data:  iris$Sepal.Width and iris$Petal.Length 
#> t = -4.309, df = 149, p-value < .001
#> alternative hypothesis: true mean is not equal to 0 
#> 95% confidence interval:
#>  -1.022 -0.379
#> sample estimate:
#>  mean difference
#>  -0.701
#> 
#> Cohen's d: -0.352
#>

Arguments

Value

Details

See also

Examples