Basic Statistics
=======================
Finding it difficult to determine what selections to make in the STAGG settings subGUI? Visit the below resources for
help understanding some of the basics about your data. We use the same verbiage in these resources, so it should help
make the right choices for your dataset.

Continuous vs. Discrete Variables
---------------------------------------
`Click here for enlightenment <https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/discrete-vs-continuous-variables/>`_.

Independent, Dependent, and Covariate Variables
---------------------------------------------------
`Covariate variables <https://www.statisticshowto.com/covariate/>`_.

`Independent vs. Dependent Variables <https://statisticsbyjim.com/regression/independent-dependent-variables/>`_.

Advanced statistics
============================

Statistical Modeling and Results
-------------------------------------
For the statistical modeling, we utilize a mixed effects model framework. Each of the crossinteractions
between the categories of the selected independent variables are used as the set of
fixed effects, while the mouse is considered a random effect. Because the independent variables
are categorical, the first group in alphanumeric order from each independent variable is selected to
be part of the overall interaction reference group, whose effect is considered as part of the model
intercept; this is necessary in order for the model to be mathematically identifiable. The resulting
fixed effect table from the modeling step are saved in stat res.xlsx, with separate sheets for each
dependent variable. In particular, each table shows the coefficient estimates, standard errors, and
p-values which correspond to each interaction group in the data. The p-values for the coefficients in
the fixed effects tables are obtained from the hypothesis test for whether each of the corresponding
coefficient estimates is statistically significantly different from 0, i.e. whether the group is significantly
different from the combination of the global mean and the reference group. The p-values
that are less than 10−9 will be rounded to exactly 0 in the output.

For more information on linear mixed-effects modeling, `see this book chapter by Galecki and Burzykowski <https://link.springer.com/chapter/10.1007/978-1-4614-3900-4_13>`_.

Post-Hoc Tukey Testing
-----------------------------
After the mixed effects model is fit to the data, at Tukey’s HSD test is used to run pairwise
comparison tests between each of the different groups with multiple comparison corrections. The
results of each of these tests are saved in tukey res.xlsx, with separate sheets for each dependent
variable. Only the biologically relevant comparisons are saved, i.e. those that compare groups
which are different in one single independent variable. Each table show the estimated difference,
standard errors, and p-values for each biologically relevant pairwise comparison in the model. The
p-values for the estimated differences are obtained from the Tukey HSD test, and they are used to
determine whether the difference between each pair of groups is statistically significantly different
from 0. Note that these are only done for the variables defined as independent variables in the
model, and not for those designated as covariates. The p-values that are less than 10−9 will be
rounded to exactly 0 in the output.

For more information on Tukey post-hoc testing, `see this documentation by Abdi and Williams <https://personal.utdallas.edu/~Herve/abdi-HSD2010-pretty.pdf>`_.