Student's t-Test

Performs one and two sample t-tests. The mosaic t.test provides wrapper functions around the function of the same name in stats. These wrappers provide an extended interface that allows for a more systematic use of the formula interface.

Usage

t_test(x, ...)

t.test(x, ...)

# S3 method for class 'formula'
t_test(formula, data, ..., groups = NULL)

# Default S3 method
t_test(
  x,
  y = NULL,
  alternative = c("two.sided", "less", "greater"),
  mu = 0,
  paired = FALSE,
  var.equal = FALSE,
  conf.level = 0.95,
  ...
)

Arguments

x: a (non-empty) numeric vector of data values.
...: further arguments to be passed to or from methods. For the formula method, this includes arguments of the default method, but not paired.
formula: 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 or paired test or a factor with two levels giving the corresponding groups. If lhs is of class "Pair" and rhs is 1, a paired test is done, see Examples.
data: an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula).
groups: When x is a formula, groups can be used to compare groups: x = ~ var, groups = g is equivalent to x = var ~ g. See the examples.
y: an optional (non-empty) numeric vector of data values.
alternative: a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.
mu: a number indicating the true value of the mean (or difference in means if you are performing a two sample test).
paired: a logical indicating whether you want a paired t-test.
var.equal: a logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used.
conf.level: confidence level of the interval.

Value

an object of class htest

Details

This is a wrapper around stats::t.test() from the stats package to extend the functionality of the formula interface. In particular, one can now use the formula interface for a 1-sample t-test. Before, the formula interface was only permitted for a 2-sample test. The type of formula that can be used for the 2-sample test has also be broadened. See the examples.

Examples

  t.test(HELPrct$age)
#> 
#> 	One Sample t-test
#> 
#> data:  HELPrct$age
#> t = 98.419, df = 452, p-value < 2.2e-16
#> alternative hypothesis: true mean is not equal to 0
#> 95 percent confidence interval:
#>  34.94150 36.36534
#> sample estimates:
#> mean of x 
#>  35.65342 
#> 
  # We can now do this with a formula
  t.test(~ age, data = HELPrct)
#> 
#> 	One Sample t-test
#> 
#> data:  age
#> t = 98.419, df = 452, p-value < 2.2e-16
#> alternative hypothesis: true mean is not equal to 0
#> 95 percent confidence interval:
#>  34.94150 36.36534
#> sample estimates:
#> mean of x 
#>  35.65342 
#> 
  # data = can be omitted, but it is better to use it
  t.test(~ age, HELPrct)
#> 
#> 	One Sample t-test
#> 
#> data:  age
#> t = 98.419, df = 452, p-value < 2.2e-16
#> alternative hypothesis: true mean is not equal to 0
#> 95 percent confidence interval:
#>  34.94150 36.36534
#> sample estimates:
#> mean of x 
#>  35.65342 
#> 
  # the original 2-sample formula
  t.test(age ~ sex, data = HELPrct)
#> 
#> 	Welch Two Sample t-test
#> 
#> data:  age by sex
#> t = 0.92976, df = 179.74, p-value = 0.3537
#> alternative hypothesis: true difference in means between group female and group male is not equal to 0
#> 95 percent confidence interval:
#>  -0.8800365  2.4482932
#> sample estimates:
#> mean in group female   mean in group male 
#>             36.25234             35.46821 
#> 
  # alternative 2-sample formulas
  t.test(~ age | sex, data = HELPrct)
#> 
#> 	Welch Two Sample t-test
#> 
#> data:  age by sex
#> t = 0.92976, df = 179.74, p-value = 0.3537
#> alternative hypothesis: true difference in means between group female and group male is not equal to 0
#> 95 percent confidence interval:
#>  -0.8800365  2.4482932
#> sample estimates:
#> mean in group female   mean in group male 
#>             36.25234             35.46821 
#> 
  t.test(~ age, groups = sex, data = HELPrct)
#> 
#> 	Welch Two Sample t-test
#> 
#> data:  age by sex
#> t = 0.92976, df = 179.74, p-value = 0.3537
#> alternative hypothesis: true difference in means between group female and group male is not equal to 0
#> 95 percent confidence interval:
#>  -0.8800365  2.4482932
#> sample estimates:
#> mean in group female   mean in group male 
#>             36.25234             35.46821 
#> 
  # 2-sample t from vectors
  with(HELPrct, t.test(age[sex == "male"], age[sex == "female"]))
#> 
#> 	Welch Two Sample t-test
#> 
#> data:  age[sex == "male"] and age[sex == "female"]
#> t = -0.92976, df = 179.74, p-value = 0.3537
#> alternative hypothesis: true difference in means is not equal to 0
#> 95 percent confidence interval:
#>  -2.4482932  0.8800365
#> sample estimates:
#> mean of x mean of y 
#>  35.46821  36.25234 
#> 
  # just the means
  mean(age ~ sex, data = HELPrct)
#>   female     male 
#> 36.25234 35.46821

Usage

Arguments

Value

Details

See also

Examples