Functions for performing various Student's t-tests to compare means of populations.
One-Sample T-Test:
Tests if the population mean differs from a specified assumed_mean.
$$t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}$$
Available in two forms:
one_sample_t_test: Takes a vector of data.one_sample_t_test_params: Takes summary statistics (mean, variance, sample size) directly.
Two-Sample T-Test (two_sample_t_test):
Tests if the means of two independent samples differ.
Automatically handles unequal variances (Welch's t-test) or equal variances based on the data.
Paired Samples T-Test (paired_samples_t_test):
Tests if the means of two dependent (paired) samples differ.
Equivalent to a one-sample t-test on the differences between pairs.
Usage
one_sample_t_test_params(
sample_mean,
sample_variance,
num_samples,
assumed_mean
)
one_sample_t_test(u, assumed_mean)
two_sample_t_test(u, v)
paired_samples_t_test(u, v)Arguments
- sample_mean
Sample mean (for
one_sample_t_test_params).- sample_variance
Sample variance (for
one_sample_t_test_params).- num_samples
Number of samples (for
one_sample_t_test_params).- assumed_mean
The hypothesised population mean to compare against.
- u
A numeric vector of data values for the first sample.
- v
A numeric vector of data values for the second sample.
Examples
# --- One Sample T-Test ---
# Using raw data:
data <- c(5, 6, 7, 5, 6)
one_sample_t_test(data, assumed_mean = 4)
#> [1] 4.810702354 0.008580919
# Using summary statistics:
# Mean = 5.8, Variance = 0.7, N = 5
one_sample_t_test_params(sample_mean = 5.8, sample_variance = 0.7,
num_samples = 5, assumed_mean = 4)
#> [1] 4.810702354 0.008580919
# --- Two Sample T-Test ---
sample1 <- c(5, 6, 7, 5, 6)
sample2 <- c(4, 5, 6, 4, 5)
two_sample_t_test(sample1, sample2)
#> [1] 1.88982237 0.09545201
# --- Paired Samples T-Test ---
# Pre-test vs Post-test
pre <- c(5, 6, 7, 5, 6)
post <- c(6, 7, 8, 6, 7)
paired_samples_t_test(pre, post)
#> [1] -Inf 0