mds_2025_helper_functions.htv
=============================

.. py:module:: mds_2025_helper_functions.htv


Functions
---------

.. autoapisummary::

   mds_2025_helper_functions.htv.htv


Module Contents
---------------

.. py:function:: htv(test_output, test_type='z', alpha=0.05, tail='two-tailed')

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

   :param test_output: 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)
   :type test_output: dict
   :param test_type: Type of test ('z', 't', 'chi2', 'anova').
   :type test_type: str
   :param alpha: Significance level (Type I error rate).
   :type alpha: float
   :param tail: One-tailed or two-tailed test ("one-tailed" or "two-tailed").
   :type tail: str

   :returns: (fig, ax) Matplotlib figure and axes objects.
   :rtype: tuple

   .. rubric:: 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.