.. _anova_analysis:

ANOVA Analysis
==============

This section explains how to perform an Analysis of Variance (ANOVA) in GeoPopMap, specifically when structure data is available and a quantitative variable is selected in the Map panel.

1. When is ANOVA available?
---------------------------

- **ANOVA is only available if structure data has been uploaded and merged.**
- You must select a **quantitative (numeric) variable** in the Map panel for the analysis to be enabled.

.. figure:: _static/anova1.png
   :alt: ANOVA interface with structure data and variable selection
   :align: center

   The ANOVA interface becomes available when structure data is present and a numeric variable is selected.

2. How to perform the analysis
------------------------------

- Go to the "ANOVA Analysis" tab.
- Select the quantitative variable you want to analyze (from the Map panel).
- The groups are automatically defined by the structure assignation (e.g., population clusters).
- Click the "Run ANOVA" button.

.. figure:: _static/anova2.png
   :alt: Selecting a variable for ANOVA
   :align: center

   Example: Selecting a quantitative variable for ANOVA.

3. Interpreting the Results
---------------------------

- **ANOVA Table**: Shows the F-statistic and p-value. A small p-value (typically < 0.05) indicates a significant difference between group means.
- **Box Plot or Violin Plot**: Visualizes the distribution of the selected variable for each structure group.
- **Post-hoc Test**: Letters indicate which groups are significantly different.

.. figure:: _static/anova3.png
   :alt: ANOVA results and box plot
   :align: center

   Example: ANOVA results and box plot for the selected variable and structure groups.

.. figure:: _static/anova4.png
   :alt: Post-hoc test results
   :align: center

   Example: Post-hoc test results showing group differences.

4. Exporting Results
--------------------

After performing ANOVA analysis, you can export your results in several formats:

- **Export ANOVA Table**: Download the ANOVA results table as a CSV file
- **Export Plot**: Save the box plot or violin plot as a PNG image
- **Export Post-hoc Results**: Download the post-hoc test results as a CSV file

5. Best Practices
-----------------

- Use the Map panel to select a relevant quantitative variable for your biological question.
- Make sure your structure data is correctly merged and the assignation column is present.
- Use the post-hoc letters to interpret which groups differ after a significant ANOVA.
- Export your results for further analysis or inclusion in reports.

6. Limitations
--------------

- ANOVA is not available for qualitative variables or if structure data is missing.
- If you select a non-numeric variable, the app will notify you that ANOVA cannot be performed.

Next Steps
----------

After running ANOVA, you can further explore your data using the :doc:`statistical_analysis` section or visualize the results on the map.