Hypothesis testing preview

Hypothesis tests answer: is this pattern likely under a null model? SciPy returns a test statistic and p-value. Always pair with effect size and domain context from Data Science ethics.

Null and alternative

• Null (H₀) — default claim (e.g. two groups have equal means)
• Alternative (H₁) — what you seek evidence for
• α — significance threshold (often 0.05)—not a magic line
• p-value — evidence against H₀ given the data and model assumptions

Common tests

• ttest_ind — two independent samples (Welch variant for unequal variance)
• ttest_rel — paired measurements
• mannwhitneyu — nonparametric two-sample
• chi2_contingency — categorical association

Two-sample example

import numpy as np
from scipy import stats

a = np.array([1.2, 1.5, 1.1, 1.4])
b = np.array([1.8, 1.9, 2.0, 1.7])
t = stats.ttest_ind(a, b, equal_var=False)
print(t)

Important interview questions and answers

1. Q: p-value = 0.03 means?
   A: If H₀ were true, ~3% of repeats would show a statistic at least this extreme—not 3% chance H₀ is false.
2. Q: When nonparametric?
   A: Skewed data, outliers, or ordinal scales—Mann-Whitney instead of t-test.

Self-check

1. Define null hypothesis in one sentence.
2. When use Welch's t-test (equal_var=False)?

Tip: Always report effect size and sample n—not only p-values from ttest_ind.