[Term Entry] Python: ANOVA & Hypothesis Testing

content/python/concepts/statsmodels/terms/anova-and-hypothesis-testing/anova-and-hypothesis-testing.md

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+---
+Title: 'ANOVA and Hypothesis Testing'
+Description: 'ANOVA (Analysis of Variance) tests if group means differ significantly.'
+Subjects:
+  - 'Data Science'
+  - 'Data Visualization'
+  - 'Computer Science'
+Tags:
+  - 'Comparison'
+  - 'Data'
+  - 'Datasets'
+  - 'Linear Regression'
+  - 'Pandas'
+  - 'Python'
+  - 'Statsmodels'
+  - 'Tables'
+CatalogContent:
+  - 'learn-python-3'
+  - 'paths/data-science'
+---
+
+**ANOVA (Analysis of Variance)** is a statistical method used to compare the means of multiple groups in a dataset. It helps determine if there are significant differences between the group means.
+
+ANOVA tests the null hypothesis, which assumes that all group means are equal. If the test finds a significant difference, it suggests that at least one group mean is different from the others.
+
+This method is commonly used in hypothesis testing to evaluate relationships between variables and identify patterns in the data.
+
+In Python, the `statsmodels` library provides tools to perform ANOVA and other hypothesis tests. These tools are widely used in data analysis to uncover meaningful insights about relationships in a dataset.
+
+## Syntax
+
+The basic syntax for performing ANOVA using `statsmodels` is as follows:
+
+```pseudo
+import statsmodels.api as sm
+from statsmodels.formula.api import ols
+
+# Define the model
+model = ols('dependent_variable ~ C(independent_variable)', data=dataset).fit()
+
+# Perform ANOVA
+anova_table = sm.stats.anova_lm(model, typ=1)
+print(anova_table)
+```
+
+- `import statsmodels.api as sm`: This imports the `statsmodels` library, which is a Python module for performing statistical analysis.
+- `from statsmodels.formula.api import ols`: This imports the `ols` (**[Ordinary Least Squares](https://www.codecademy.com/resources/docs/python/statsmodels/ols)**) function from the module. The `ols` function is used to define a linear regression model.
+- `dependent_variable ~ C(independent_variable)`: This formula specifies the relationship between variables for the model:
+  - `dependent_variable`: This is the variable you are trying to explain or predict (the outcome variable).
+  - `independent_variable`: This is the categorical variable (factor) that you believe affects the `dependent_variable`.
+  - `C()`: This tells the function to treat the `independent_variable` as a categorical variable.
+- `data=dataset`: This specifies the dataset being analyzed. It must be a structured data format, such as a **[Pandas DataFrame](https://www.codecademy.com/resources/docs/pandas/dataframe)**, where the variables in the formula are columns in the dataset.
+- `model = ols(...)`: This creates a linear regression model using the specified formula and dataset.
+- `.fit()`: This method fits the model to the data, meaning it estimates the parameters of the regression model.
+- `sm.stats.anova_lm(model, typ=1)`: This function performs an [ANOVA analysis](https://www.codecademy.com/resources/docs/python/statsmodels/anova-lm) on the fitted model:
+  - `model`: This is the fitted model created by the `ols` function.
+  - `typ=1`: This specifies the type of sum of squares to use in the ANOVA calculation. Type 1 is a sequential sum of squares, which evaluates each variable in the order it appears in the formula.
+
+## Example
+
+The following example demonstrates how to analyze whether average test scores differ among three teaching methods:
+
+```py
+import pandas as pd
+import statsmodels.api as sm
+from statsmodels.formula.api import ols
+
+# Sample data
+data = pd.DataFrame({
+    'Score': [85, 89, 76, 71, 80, 78, 93, 95, 88],
+    'Method': ['A', 'A', 'A', 'B', 'B', 'B', 'C', 'C', 'C']
+})
+
+# Define the model
+model = ols('Score ~ C(Method)', data=data).fit()
+
+# Perform ANOVA
+anova_table = sm.stats.anova_lm(model, typ=1)
+print(anova_table)
+```
+
+The output for this example is the following table:
+
+![ANOVA Table Result](https://raw.githubusercontent.com/Codecademy/docs/main/media/anova-result.png)