mds_2025_helper_functions.htv

Functions

htv(test_output[, test_type, alpha, tail])

Visualize Type I (α) and Type II (β) errors in hypothesis testing.

Module Contents

mds_2025_helper_functions.htv.htv(test_output, test_type='z', alpha=0.05, tail='two-tailed')[source]

Visualize Type I (α) and Type II (β) errors in hypothesis testing.

Parameters:

test_output (dict) – Dictionary containing hypothesis test parameters: - ‘mu0’: Mean under the null hypothesis (H0) - ‘mu1’: Mean under the alternative hypothesis (H1) - ‘sigma’: Standard deviation (for z or t tests) - ‘sample_size’: Sample size (for z and t tests) - ‘df1’: Degrees of freedom 1 (for F tests, optional) - ‘df2’: Degrees of freedom 2 (for F tests, optional) - ‘df’: Degrees of freedom (for t and chi-squared tests, optional)
test_type (str) – Type of test (‘z’, ‘t’, ‘chi2’, ‘anova’).
alpha (float) – Significance level (Type I error rate).
tail (str) – One-tailed or two-tailed test (“one-tailed” or “two-tailed”).

Returns:

(fig, ax) Matplotlib figure and axes objects.

Return type:

tuple

Example

>>> import numpy as np
>>> from mds_2025_helper_functions.htv import htv
>>>
>>> # Example: Visualizing a two-tailed z-test
>>> test_params = {
...     'mu0': 100,         # Null hypothesis mean
...     'mu1': 105,         # Alternative mean
...     'sigma': 15,        # Standard deviation
...     'sample_size': 30   # Sample size
... }
>>> fig, ax = htv(test_params, test_type="z", alpha=0.05, tail="two-tailed")
>>> plt.show()

# This will plot the null and alternative hypothesis distributions with # shaded regions for Type I and Type II errors, and mark the critical values.

>>> # Example: One-tailed t-test with degrees of freedom
>>> test_params_t = {
...     'mu0': 0,
...     'mu1': 1.5,
...     'sigma': 1,
...     'sample_size': 25
... }
>>> fig, ax = htv(test_params_t, test_type="t", alpha=0.01, tail="one-tailed")
>>> plt.show()

# This will plot a one-tailed t-test diagram with appropriate critical regions.