statBasics (version 0.2.3)

ht_2pop_mean: Hypothesis testing mean for two populations

Description

Performs a hypothesis testing for the difference in means of two populations.

Usage

ht_2pop_mean(
  x,
  y,
  delta = 0,
  sd_pop_1 = NULL,
  sd_pop_2 = NULL,
  var_equal = FALSE,
  alternative = "two.sided",
  conf_level = NULL,
  sig_level = 0.05,
  na_rm = TRUE
)

Value

a tibble with the following columns:

statistic

the value of the test statistic.

p_value

the p-value for the test.

critical_value

critical value in the General Procedure for Hypothesis Testing.

critical_region

critical region in the General Procedure for Hypothesis Testing.

delta

a scalar value indicating the value of \(\Delta_0\).

alternative

character string giving the direction of the alternative hypothesis.

lower_ci

lower bound of the confidence interval. It is presented only if !is.null(conf_level).

upper_ci

upper bound of the confidence interval. It is presented only if !is.null(conf_level).

Arguments

x

a (non-empty) numeric vector.

y

a (non-empty) numeric vector.

delta

a scalar value indicating the difference in means (\(\Delta_0\)). Default value is 0.

sd_pop_1

a number specifying the known standard deviation of the first population. Default value is NULL.

sd_pop_2

a number specifying the known standard deviation of the second population. Default value is NULL.

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. Default value is FALSE.

alternative

a character string specifying the alternative hypothesis, must be one of ‘"two.sided"’ (default), ‘"greater"’ or ‘"less"’.

conf_level

a number indicating the confidence level to compute the confidence interval. If conf_level = NULL, then confidence interval is not included in the output. Default value is NULL.

sig_level

a number indicating the significance level to use in the General Procedure for Hypothesis Testing.

na_rm

a logical value indicating whether NA values should be removed before the computation proceeds.

Details

We have wrapped the t.test and the BSDA::z.test in a function as explained in the book of Montgomery and Runger (2010) <ISBN: 978-1-119-74635-5>.

Examples

# t-test: var_equal == FALSE
x <- rnorm(1000, mean = 10, sd = 2)
y <- rnorm(500, mean = 5, sd = 1)
# H0: mu_1 - mu_2 == -1 versus H1: mu_1 - mu_2 != -1
ht_2pop_mean(x, y, delta = -1)
# t-test: var_equal == TRUE
x <- rnorm(1000, mean = 10, sd = 2)
y <- rnorm(500, mean = 5, sd = 2)
# H0: mu_1 - mu_2 == -1 versus H1: mu_1 - mu_2 != -1
ht_2pop_mean(x, y, delta = -1, var_equal = TRUE)

# z-test
x <- rnorm(1000, mean = 10, sd = 3)
x <- rnorm(500, mean = 5, sd = 1)
# H0: mu_1 - mu_2 >= 0 versus H1: mu_1 - mu_2 < 0
ht_2pop_mean(x, y, delta = 0, sd_pop_1 = 3, sd_pop_2 = 1)