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Updated documentation of existing functions and am adding documentation for the new functions
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Corey-Bryant committed Mar 7, 2022
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43 changes: 43 additions & 0 deletions source/anova_documentation.rst
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Effect size measures formulas
=============================
By default, this method will return the measures of :math:`R^2`, :math:`\text{Adj. }R^2`, :math:`\eta^2`, and :math:`\omega^2`;
note that for the factor terms the reported :math:`\eta^2` and :math:`\omega^2` will be partial, i.e. :math:`\eta^2_p` and :math:`\omega^2_p` respectively.
Additionally, :math:`R^2` and :math:`\eta^2` are the same but have different names due to coming from different frameworks
which uses different terminology. Formulas for how to calculate these effect sizes
comes from :cite:`grissomkim2012`.

Eta-squared (:math:`\eta^2`) and :math:`R^2`
""""""""""""""""""""""""""""""""""""""""""""
.. math::
\eta^2 = \frac{\text{SS}_{model}}{\text{SS}_{total}}
Adjusted :math:`R^2`
""""""""""""""""""""
.. math::
\text{Adj. }R^2 = 1 - \frac{\text{df}_{total}}{\text{df}_{error}} * \frac{\text{SS}_{error}}{\text{SS}_{total}}
Partial Eta-squared (:math:`\eta^2_p`)
""""""""""""""""""""""""""""""""""""""
.. math::
\eta^2_p = \frac{\text{SS}_{effect}}{\text{SS}_{effect} + \text{SS}_{error}}
Omega-squared (:math:`\omega^2`)
"""""""""""""""""""""""""""""""""
.. math::
\omega^2 = \frac{\text{SS}_{effect} - (\text{df}_{effect} * \text{MS}_{error})}{\text{SS}_{total} + \text{MS}_{error}}
Partial Omega-squared (:math:`\omega^2_p`)
"""""""""""""""""""""""""""""""""""""""""""
.. math::
\omega^2_p = \frac{\text{SS}_{effect} - (\text{df}_{effect} * \text{MS}_{error})}{\text{SS}_{effect} + (\text{N} - \text{df}_{effect}) * \text{MS}_{error}}
Where N is the total number of observations included in the model.



Examples
========
First to load required libraries for this example. Below, an example data set will be loaded
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9 changes: 9 additions & 0 deletions source/refs.bib
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% Encoding: UTF-8
@book{grissomkim2012,
title = {Effect Sizes for Research: Univariate and Multivariate Applications},
publisher = {Routledge},
year = {2012},
author = {Grissom, R. J. and Kim, J. J.},
edition = {Second},
isbn = {978-0-415-87769-5}
}

@article{Satterthwaite1946,
ISSN = {00994987},
URL = {http://www.jstor.org/stable/3002019},
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