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Select and run the correct hypothesis test based on data properties. Covers parametric/non-parametric tests, effect sizes, and multiple comparison correction.
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| name | statistical-testing |
| description | Select and run the correct hypothesis test based on data properties. Covers parametric/non-parametric tests, effect sizes, and multiple comparison correction. |
| tags | ["statistics","hypothesis-testing","scipy","effect-size","multiple-comparisons","power-analysis"] |
| version | 1.0.0 |
| authors | [{"name":"awesome-rosetta-skills contributors","github":"@awesome-rosetta-skills"}] |
| license | MIT |
| platforms | ["claude-code","codex","gemini-cli","cursor"] |
| dependencies | {"python":["scipy>=1.10.0","numpy>=1.24.0","pandas>=2.0.0","statsmodels>=0.14.0","pingouin>=0.5.3"]} |
| last_updated | 2026-03-17 |
Choose and execute the right statistical test for your data. This skill covers normality checks, parametric and non-parametric tests, effect size computation, and multiple comparison correction.
| Scenario | Groups | Normal? | Recommended Test |
|---|---|---|---|
| Compare means | 2 independent | Yes | Independent t-test |
| Compare means | 2 independent | No | Mann-Whitney U |
| Compare means | 2 paired | Yes | Paired t-test |
| Compare means | 2 paired | No | Wilcoxon signed-rank |
| Compare means | ≥3 independent | Yes | One-way ANOVA |
| Compare means | ≥3 independent | No | Kruskal-Wallis |
| Compare means | ≥3 repeated | Yes | Repeated-measures ANOVA |
| Compare means | ≥3 repeated | No | Friedman test |
| Association | 2 categorical | Expected ≥5 | Chi-square |
| Association | 2 categorical | Expected <5 | Fisher exact |
| Correlation | 2 continuous | Both normal | Pearson r |
| Correlation | 2 continuous | Non-normal | Spearman ρ |
pip install scipy numpy pandas statsmodels pingouin
"""
statistical_testing.py
Complete statistical testing toolkit with automatic test selection.
"""
import warnings
import numpy as np
import pandas as pd
from scipy import stats
from statsmodels.stats import multitest
statsmodels.stats.power TTestIndPower, FTestAnovaPower
typing , , , , ,
() -> [, ]:
data = np.asarray(data, dtype=)
data = data[~np.isnan(data)]
n = (data)
results: [, ] = {}
n < :
stat_sw, p_sw = stats.shapiro(data)
results[] = {: stat_sw, : p_sw, : p_sw > alpha}
:
results[] = {: , : , : ,
: }
mu, sigma = np.mean(data), np.std(data, ddof=)
stat_ks, p_ks = stats.kstest(data, , args=(mu, sigma))
results[] = {: stat_ks, : p_ks, : p_ks > alpha}
n >= :
stat_da, p_da = stats.normaltest(data)
results[] = {: stat_da, : p_da, : p_da > alpha}
:
results[] = {: , : , : ,
: }
votes = [v[] v results.values() (v, ) v[] ]
results[] = (votes) >= ((votes) / )
results[] = n
verbose:
()
test_name, res results.items():
(res, ) res res[] :
verdict = res[]
()
()
results
() -> :
g1, g2 = np.asarray(group1), np.asarray(group2)
n1, n2 = (g1), (g2)
pooled_sd = np.sqrt(((n1 - ) * np.var(g1, ddof=) + (n2 - ) * np.var(g2, ddof=)) / (n1 + n2 - ))
(np.mean(g1) - np.mean(g2)) / pooled_sd
() -> :
ss_between = f_statistic * df_between
ss_total = ss_between + df_within
ss_between / ss_total
() -> :
chi2 = stats.chi2_contingency(contingency_table, correction=)[]
n = contingency_table.()
min_dim = (contingency_table.shape) -
np.sqrt(chi2 / (n * min_dim))
() -> :
thresholds = {
: [(, ), (, ), (, )],
: [(, ), (, ), (, )],
: [(, ), (, ), (, )],
}
d = (d)
threshold, label thresholds.get(measure, []):
d < threshold:
label
() -> [, ]:
groups = [np.asarray(g, dtype=) g groups]
k = (groups)
k < :
ValueError()
all_normal = (test_normality(g, alpha=alpha, verbose=)[] g groups)
result: [, ] = {}
k == :
g1, g2 = groups[], groups[]
paired:
all_normal:
stat, p = stats.ttest_rel(g1, g2)
result[] =
d = np.mean(g1 - g2) / np.std(g1 - g2, ddof=)
result[] = {: (d, )}
:
stat, p = stats.wilcoxon(g1, g2)
result[] =
result[] = {: ( - ( * stat) / ((g1) * ((g1) + )), )}
:
_, p_levene = stats.levene(g1, g2)
equal_var = p_levene > alpha
all_normal:
stat, p = stats.ttest_ind(g1, g2, equal_var=equal_var)
result[] =
d = cohens_d(g1, g2)
result[] = {: (d, ),
: interpret_effect_size(d)}
:
stat, p = stats.mannwhitneyu(g1, g2, alternative=)
result[] =
n1, n2 = (g1), (g2)
rb = - ( * stat) / (n1 * n2)
result[] = {: (rb, )}
:
paired:
all_normal:
:
pingouin pg
df_long = pd.DataFrame({
: np.concatenate(groups),
: np.repeat(np.arange(k), [(g) g groups]),
: np.tile(np.arange((groups[])), k),
})
aov = pg.rm_anova(data=df_long, dv=, within=, subject=)
stat = aov[].iloc[]
p = aov[].iloc[]
result[] =
result[] = {: (aov[].iloc[], )}
ImportError:
warnings.warn()
stat, p = stats.friedmanchisquare(*groups)
result[] =
result[] = {}
:
stat, p = stats.friedmanchisquare(*groups)
result[] =
result[] = {}
:
all_normal:
stat, p = stats.f_oneway(*groups)
result[] =
total_n = ((g) g groups)
df_between = k -
df_within = total_n - k
es = eta_squared(stat, df_between, df_within)
result[] = {: (es, ),
: interpret_effect_size(es, )}
:
stat, p = stats.kruskal(*groups)
result[] =
result[] = {}
result[] = ((stat), )
result[] = ((p), )
result[] = p < alpha
result[] = alpha
verbose:
()
()
()
result.get():
()
()
result
() -> pd.DataFrame:
reject, p_corrected, _, _ = multitest.multipletests(p_values, alpha=alpha, method=method)
pd.DataFrame({
: p_values,
: p_corrected,
: reject,
: method,
})
() -> [, ]:
analysis = TTestIndPower()
n_per_group :
n = analysis.solve_power(effect_size=effect_size, alpha=alpha, power=power, ratio=)
{: np.ceil(n), : effect_size,
: alpha, : power}
:
achieved_power = analysis.solve_power(effect_size=effect_size, alpha=alpha,
nobs1=n_per_group, ratio=)
{: n_per_group, : effect_size,
: alpha, : (achieved_power, )}
() -> [, ]:
chi2, p, dof, expected = stats.chi2_contingency(contingency)
v = cramers_v(contingency)
result = {
: expected.() >= ,
: (chi2, ),
: (p, ),
: dof,
: (v, ),
: p < alpha,
}
expected.() < :
contingency.shape == (, ):
_, p_fisher = stats.fisher_exact(contingency)
result[] = (p_fisher, )
result
import numpy as np
from statistical_testing import run_comparison, correct_pvalues, power_analysis_ttest
rng = np.random.default_rng(42)
# Simulate three treatment groups (non-normal distributions)
control = rng.exponential(scale=5, size=40)
treatment1 = rng.exponential(scale=7, size=38)
treatment2 = rng.exponential(scale=9, size=42)
# Automatic test selection
result = run_comparison(control, treatment1, treatment2, alpha=0.05)
# → Kruskal-Wallis H (non-normal data detected automatically)
# If significant, run post-hoc pairwise tests with FDR correction
from scipy.stats import mannwhitneyu
pairs = [
("control vs t1", mannwhitneyu(control, treatment1, alternative="two-sided").pvalue),
("control vs t2", mannwhitneyu(control, treatment2, alternative="two-sided").pvalue),
("t1 vs t2", mannwhitneyu(treatment1, treatment2, alternative="two-sided").pvalue),
]
labels, raw_p = zip(*pairs)
correction_df = correct_pvalues(list(raw_p), method="fdr_bh")
correction_df.index = labels
print(correction_df)
import numpy as np
from statistical_testing import (
test_normality, run_comparison, cohens_d, power_analysis_ttest
)
rng = np.random.default_rng(0)
pre = rng.normal(loc=100, scale=15, size=30)
post = pre + rng.normal(loc=8, scale=10, size=30) # ~0.5 SD improvement
# Step 1: Check normality of the difference
diff = post - pre
norm_result = test_normality(diff)
# Step 2: Run the appropriate test
result = run_comparison(pre, post, paired=True)
# Step 3: Retrospective power
d = result["effect_size"].get("cohens_d", cohens_d(pre, post))
power_report = power_analysis_ttest(effect_size=abs(d), alpha=0.05, n_per_group=30)
print(f"Achieved power: {power_report['achieved_power']:.2f}")
# Step 4: How many participants for 90% power?
needed = power_analysis_ttest(effect_size=abs(d), alpha=0.05, power=0.90)
print(f"N needed for 90% power: {int(needed['required_n_per_group'])}")
import numpy as np
from statistical_testing import chi_square_test_with_effect, correct_pvalues
# 2x2 contingency: treatment vs outcome
table = np.array([[45, 15],
[30, 30]])
result = chi_square_test_with_effect(table)
print(result)
# {'test_name': 'Chi-square', 'chi2': ..., 'p_value': ..., 'cramers_v': ..., 'significant': True}
# 3x3 contingency across three centres
multi_table = np.array([[50, 20, 10],
[40, 25, 15],
[35, 30, 20]])
result3 = chi_square_test_with_effect(multi_table)
print(result3)
| Measure | Small | Medium | Large |
|---|---|---|---|
| Cohen's d | 0.2 | 0.5 | 0.8 |
| η² (eta-squared) | 0.01 | 0.06 | 0.14 |
| Cramér's V (2×2) | 0.1 | 0.3 | 0.5 |
| Pearson r | 0.1 | 0.3 | 0.5 |
| Method | Controls | Best For |
|---|---|---|
| Bonferroni | Family-wise error rate (FWER) | Few comparisons, strict control |
| Holm | FWER (less conservative) | General use |
| Benjamini-Hochberg (FDR) | False discovery rate | Many comparisons (genomics, etc.) |
| Benjamini-Yekutieli | FDR under dependence | Correlated tests |
No API keys required. All computation is local.
# Optional: set random seed for reproducibility in scripts
export STATS_RANDOM_SEED=42
基于 SOC 职业分类
