Summary and Practical Guide to Hypothesis Testing › Complete Reporting Example

import numpy as np
from scipy import stats

# Research question: Does a new teaching method improve test scores?
np.random.seed(42)
control = np.random.normal(75, 12, 30)  # Traditional method
treatment = np.random.normal(82, 11, 30)  # New method

# 1. Descriptive statistics
print("=" * 60)
print("DESCRIPTIVE STATISTICS")
print("=" * 60)
print(
    f"Control:   n = {len(control)}, M = {np.mean(control):.2f}, SD = {np.std(control, ddof=1):.2f}"
)
print(
    f"Treatment: n = {len(treatment)}, M = {np.mean(treatment):.2f}, SD = {np.std(treatment, ddof=1):.2f}"
)
print()

# 2. Check assumptions
print("=" * 60)
print("ASSUMPTION CHECKS")
print("=" * 60)

# Normality
_, p_norm_ctrl = stats.shapiro(control)
_, p_norm_treat = stats.shapiro(treatment)
print(
    f"Shapiro-Wilk (Control):   W = {stats.shapiro(control)[0]:.3f}, p = {p_norm_ctrl:.3f}"
)
print(
    f"Shapiro-Wilk (Treatment): W = {stats.shapiro(treatment)[0]:.3f}, p = {p_norm_treat:.3f}"
)
print("  → Normality assumption supported (p > 0.05 for both groups)")
print()

# Equal variances
_, p_levene = stats.levene(control, treatment)
print(
    f"Levene's test: F = {stats.levene(control, treatment)[0]:.3f}, p = {p_levene:.3f}"
)
print("  → Equal variances assumption supported (p > 0.05)")
print()

# 3. Conduct test
print("=" * 60)
print("HYPOTHESIS TEST")
print("=" * 60)
t_stat, p_value = stats.ttest_ind(treatment, control, equal_var=True)
df = len(control) + len(treatment) - 2
print(f"Two-sample t-test: t({df}) = {t_stat:.3f}, p = {p_value:.4f}")
print()

# 4. Effect size
mean_diff = np.mean(treatment) - np.mean(control)
pooled_std = np.sqrt(
    (
        (len(control) - 1) * np.var(control, ddof=1)
        + (len(treatment) - 1) * np.var(treatment, ddof=1)
    )
    / (len(control) + len(treatment) - 2)
)
cohens_d = mean_diff / pooled_std
print("=" * 60)
print("EFFECT SIZE")
print("=" * 60)
print(f"Mean difference: {mean_diff:.2f} points")
print(f"Cohen's d = {cohens_d:.3f} (large effect)")
print()

# 5. Confidence interval for difference
se_diff = pooled_std * np.sqrt(1 / len(control) + 1 / len(treatment))
t_crit = stats.t.ppf(0.975, df)
ci_lower = mean_diff - t_crit * se_diff
ci_upper = mean_diff + t_crit * se_diff
print("=" * 60)
print("CONFIDENCE INTERVAL")
print("=" * 60)
print(f"95% CI for difference: [{ci_lower:.2f}, {ci_upper:.2f}]")
print()

# 6. Complete report
print("=" * 60)
print("COMPLETE REPORT (APA STYLE)")
print("=" * 60)
print(
    f"Students in the new teaching method condition (M = {np.mean(treatment):.1f}, "
)
print(
    f"SD = {np.std(treatment, ddof=1):.1f}) scored significantly higher than those in the "
)
print(
    f"traditional method condition (M = {np.mean(control):.1f}, SD = {np.std(control, ddof=1):.1f}), "
)
print(
    f"t({df}) = {t_stat:.2f}, p {'< 0.001' if p_value < 0.001 else f'= {p_value:.3f}'}, "
)
print(f"95% CI [{ci_lower:.1f}, {ci_upper:.1f}], Cohen's d = {cohens_d:.2f}.")