Summary  
This chapter explains how to implement code in Python to perform one-way ANOVA using SciPy’s stats.f_oneway function, compute and print the F-statistic and p-value, and interpret whether group means differ significantly.

General domain of usage  
Education (e.g., comparing student test scores across different teaching methods)

This video introduces **ANOVA (Analysis of Variance)**, covering its core purpose of comparing means across three or more groups. You will learn the assumptions underlying ANOVA—including **independence**, **normality**, and **homogeneity of variances**—and discover when ANOVA is the appropriate statistical test. The video also explains how to interpret the **F-statistic** and **p-value** to determine if group means differ significantly.

When you need to determine whether three or more groups have significantly different means, **ANOVA** (Analysis of Variance) is the statistical method to use. Unlike t-tests, which compare only two groups at a time, **ANOVA** allows you to analyze all groups in a single test, reducing the risk of **Type I errors** that can occur when performing multiple pairwise comparisons.

The **one-way ANOVA** examines the effect of a single categorical independent variable (**factor**) on a continuous dependent variable. The main question it answers is: "Are the means of the groups all equal, or is at least one group different?"

For **ANOVA** results to be valid, several assumptions must be met:
- Independence: the observations in each group must be independent of each other;
- Normality: the data in each group should be approximately normally distributed;
- Homogeneity of variances: the variance among the groups should be roughly equal.

If these assumptions are satisfied, you can use **ANOVA** to compare means across multiple groups. The test produces an **F-statistic** and a **p-value**. The **F-statistic** measures the ratio of variance between the group means to the variance within the groups. A large **F-statistic** suggests that group means are more spread out than you would expect by chance. The **p-value** tells you whether the differences among group means are statistically significant. If the **p-value** is below your chosen significance level (commonly `0.05`), you reject the null hypothesis that all group means are equal.

import numpy as np
from scipy import stats

# Simulate data for three groups
group_a = [23, 20, 22, 30, 25]
group_b = [35, 40, 38, 37, 36]
group_c = [29, 27, 32, 30, 28]

# Perform one-way ANOVA
f_statistic, p_value = stats.f_oneway(group_a, group_b, group_c)

print("F-statistic:", f_statistic)
print("p-value:", p_value)

if p_value < 0.05:
    print("There is a statistically significant difference between group means.")
else:
    print("There is no statistically significant difference between group means.")

import unittest
import ast
import re
import io
import sys
import numpy as np
from scipy import stats

class TestTask(unittest.TestCase):
    def test_default_values(self):
        with open('user_code.py', 'r') as f:
            code = f.read()
            
        ns = {}
        try:
            exec(code, ns)
            f_stat = ns.get('f_stat')
            p_val = ns.get('p_val')
            anova_result = ns.get('anova_result')
            
            group1 = [19, 22, 20, 23, 21]
            group2 = [30, 29, 32, 31, 28]
            group3 = [24, 25, 23, 22, 26]
            expected = stats.f_oneway(group1, group2, group3)
            
            is_correct = False
            if f_stat is not None and p_val is not None and isinstance(anova_result, tuple):
                is_correct = np.isclose(f_stat, expected.statistic, atol=1e-5) and \
                             np.isclose(p_val, expected.pvalue, atol=1e-5) and \
                             len(anova_result) == 2
        except Exception:
            is_correct = False
            f_stat = None
            p_val = None
            
        _dynamic_test(
            self,
            is_correct,
            "Correctly computes the F-statistic and p-value for the default groups.",
            f"Expected F-stat ~42.26 and p-val ~2.11e-06. Got F-stat: {f_stat}, p-val: {p_val}.",
        )

    def test_dynamic_values(self):
        with open('user_code.py', 'r') as f:
            code = f.read()
            
        # Подменяем группы на новые значения
        code = change_var(code, 'group1', '[10, 12, 11, 13, 14]')
        code = change_var(code, 'group2', '[20, 22, 19, 21, 23]')
        code = change_var(code, 'group3', '[30, 29, 31, 32, 28]')
        
        ns = {}
        try:
            exec(code, ns)
            f_stat = ns.get('f_stat')
            p_val = ns.get('p_val')
            
            g1 = [10, 12, 11, 13, 14]
            g2 = [20, 22, 19, 21, 23]
            g3 = [30, 29, 31, 32, 28]
            expected = stats.f_oneway(g1, g2, g3)
            
            is_correct = False
            if f_stat is not None and p_val is not None:
                is_correct = np.isclose(f_stat, expected.statistic, atol=1e-5) and \
                             np.isclose(p_val, expected.pvalue, atol=1e-5)
        except Exception:
            is_correct = False
            
        _dynamic_test(
            self,
            is_correct,
            "ANOVA computation dynamically handles arbitrary lists.",
            "Failed to evaluate dynamically. Ensure you are passing the variables directly into stats.f_oneway().",
        )

    

def _dynamic_test(test_case, condition, success_message, failure_message):
    if condition:
        test_case._testMethodName = success_message
        test_case.assertTrue(True, success_message)
    else:
        test_case._testMethodName = failure_message
        test_case.fail(failure_message)

def gsub_spaces(text):
    text = re.sub(r"\s+", "", text)
    text = text.replace("'", "")
    text = text.replace('"', "")
    return text

def change_var(code: str, var_name: str, value: str) -> str:
    tree = ast.parse(code)
    lines = code.splitlines()
    changed = False
    assign_nodes = [
        (i, node)
        for i, node in enumerate(tree.body)
        if isinstance(node, ast.Assign)
        and any(isinstance(target, ast.Name) and target.id == var_name for target in node.targets)
    ]
    if not assign_nodes:
        return code
    for i, node in reversed(assign_nodes):
        start_line = node.lineno - 1
        line = lines[start_line]
        indent = ' ' * (len(line) - len(line.lstrip()))
        lines[start_line] = f"{indent}{var_name} = {value}"
        next_line = len(lines)
        for next_node in tree.body[i+1:]:
            if hasattr(next_node, 'lineno'):
                next_line = next_node.lineno - 1
                break
        if next_line > start_line + 1:
            lines[start_line+1:next_line] = []
        changed = True
        
    return chr(10).join(lines) if changed else code

if __name__ == "__main__":
    unittest.main()

test_main.py

This course provides a comprehensive introduction to statistical methods using Python. You will learn how to apply core statistical concepts, perform hypothesis testing, analyze data distributions, and interpret results using Python's scientific libraries. The course emphasizes practical application through real-world examples and hands-on exercises.

A comprehensive section covering the core concepts and practical applications of statistical methods using Python.

ANOVA: Analysis of Variance

Solution