Hypothesis Testing, T-tests & Chi-square

1from scipy import stats
2import numpy as np
3
4x_bar, mu_0, sigma, n, alpha = 490, 500, 30, 36, 0.05
5z = (x_bar - mu_0) / (sigma / np.sqrt(n))
6p_value = 2 * stats.norm.cdf(z)
7
8print(f"Z-statistic: {z:.4f}")
9print(f"P-value: {p_value:.4f}")
10print(f"→ {'Reject' if p_value < alpha else 'Fail to Reject'} H₀")

1from scipy import stats
2import numpy as np
3
4sample = [192, 198, 190, 195, 202, 188, 197, 194, 199, 195]
5mu_0, alpha = 200, 0.05
6
7t_stat, p_value = stats.ttest_1samp(sample, mu_0)
8print(f"Mean: {np.mean(sample):.2f}, t: {t_stat:.4f}, P: {p_value:.4f}")
9print(f"→ {'Reject' if p_value < alpha else 'Fail to Reject'} H₀")

1from scipy import stats
2import numpy as np
3
4class_A = [85, 90, 78, 92, 88, 76, 95, 89, 82, 91]
5class_B = [72, 85, 80, 78, 88, 70, 82, 75, 79, 84]
6alpha = 0.05
7
8print(f"A: mean={np.mean(class_A):.2f}, B: mean={np.mean(class_B):.2f}")
9
10# Standard t-test
11t_stat, p_value = stats.ttest_ind(class_A, class_B)
12print(f"t: {t_stat:.4f}, P: {p_value:.4f}")
13
14# Welch's t-test (unequal variances)
15t_welch, p_welch = stats.ttest_ind(class_A, class_B, equal_var=False)
16print(f"Welch: t={t_welch:.4f}, P={p_welch:.4f}")
17
18# Check equal variances with Levene's test
19stat, p_lev = stats.levene(class_A, class_B)
20print(f"Levene: p={p_lev:.4f} → {'Equal' if p_lev > 0.05 else 'Unequal'} variances")

1from scipy import stats
2import numpy as np
3
4before = [85, 90, 78, 92, 88, 76, 95, 89, 82, 91]
5after = [82, 86, 75, 88, 84, 74, 90, 85, 79, 87]
6alpha = 0.05
7
8diff = np.array(before) - np.array(after)
9print(f"Mean difference: {np.mean(diff):.2f}")
10
11t_stat, p_value = stats.ttest_rel(before, after)
12print(f"t: {t_stat:.4f}, P: {p_value:.4f}")
13print(f"→ {'Reject' if p_value < alpha else 'Fail to Reject'} H₀")

1from scipy import stats
2
3observed = [95, 105, 98, 110, 92, 100]  # 600 lần tung xúc xắc
4expected = [100] * 6
5
6chi2, p_value = stats.chisquare(observed, expected)
7print(f"Chi-square: {chi2:.4f}, P-value: {p_value:.4f}")
8print(f"→ {'Reject' if p_value < 0.05 else 'Fail to Reject'} H₀")

1from scipy import stats
2import numpy as np
3import pandas as pd
4
5observed = np.array([[30, 45],   # Male: A, B
6                     [40, 35]])  # Female: A, B
7
8chi2, p_value, dof, expected = stats.chi2_contingency(observed)
9
10print("Observed:")
11print(pd.DataFrame(observed, index=['Male', 'Female'], columns=['A', 'B']))
12print(f"\nChi-square: {chi2:.4f}, P: {p_value:.4f}, df: {dof}")
13print(f"→ {'Reject' if p_value < 0.05 else 'Fail to Reject'} H₀")

1def cramers_v(table):
2    chi2, p, dof, exp = stats.chi2_contingency(table)
3    n = table.sum()
4    return np.sqrt(chi2 / (n * (min(table.shape) - 1)))
5
6v = cramers_v(observed)
7print(f"Cramér's V: {v:.4f}")