One-Sample T-tests

tags: #statistics/inferential/ttest/one_sample

What is a one-sample t-test?

The One Sample T-test examines whether the mean of a population is statistically different from a known or hypothesized value.

To compare the means of multiple groups to each other, use either:

Independent Samples T-test (to compare the means of two groups)
One-Way ANOVA (to compare the means of two or more groups).

This follows the sample assumptions and conditions as a two-sample (independent) t-test.

Hypothesis Model

The hypothesis model for a one-sample t-test for comparing the sample mean to a known or hypothesized value is:

H_{0} : μ = μ_{0}, where the population mean is equal to the [proposed] population mean

H_{A} : μ \neq μ_{0}, where the population mean does NOT equal to the [proposed] population mean

Calculating the test statistic

For calculating the test statistic:

t = \frac{\bar{y} - μ_{0}}{S E (\bar{y})}, where S E (\bar{y}) = \frac{s}{\sqrt{n}}

Running a one-sample t-test in Python

We can conduct a one-sample t-test in Python using the ttest_1samp() function from the scipy.stats library:

from scipy.stats import ttest_1samp

# conduct one-sample t-test
ttest_1samp(a, popmean, alternative="two-sided", alpha=0.05)

Parameters:

a - array-like sample of observations
popmean - hypothesized (expected) population mean (scalar)
alternative - indicate whether the test should be conducted as one- or two-tailed: two-sided, less, greater

This returns the following:

(statistics, p-value)