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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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Lightweight pattern-driven research ideation with no script dependencies - generates 5-10 candidate ideas from a direction or gap matrix using proven ideation patterns, each with mechanism, falsification plan, and minimal validation experiment. Use for quick brainstorming of research ideas or when the scripted idea-spark skill is unavailable or not yet set up; prefer idea-spark for a single deeply-grounded reviewer-defensible idea card. Do not use for judging an existing idea (use idea-critic) or checking novelty (use scoop-check).
Generate ONE reviewer-defensible, implementable research idea with a concrete method and falsification plan from a stated research direction. Use when the user asks for a research idea, novelty analysis, bottleneck diagnosis, or paper-shape suggestion. Skip code review, debugging, and unconstrained brainstorming without research context.
Search papers across arXiv, DBLP, OpenAlex, OpenReview, Semantic Scholar, and Crossref for a given query and year range, using ./scripts/search_papers.py. Use when the user asks to find papers, related work, prior art, or recent publications on a specific topic, especially when they mention a date range or specific venues like NeurIPS, ICLR, or ICML.
基于 SOC 职业分类
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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 |
本整合包适配（ML/时序实验小样本规则）：
mean ± std，不要写"方差"除非真的报的是 variance）或极差。这是硬策略：
run_comparison 在最小组 n<5 时直接返回描述统计（p_value / significant 置
None），不会返回可被误写进论文的 p 值。correct_pvalues 时手头恰好有的那几个 p 值。在
research_run/<slug>/stage4_experiments/comparison_ledger.md 维护一张累计表
（比较对象 / 数据集 / horizon / 指标 / 原始 p 值 / 所属比较族），投稿前对每个
比较族整体重跑一次校正；表里没登记的检验不得写进论文。run_comparison 已默认 equal_var=False。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
from statsmodels.stats.power import TTestIndPower, FTestAnovaPower
from typing import Union, Optional, Tuple, List, Dict, Any
# ─────────────────────────────────────────────
# 1. Normality Tests
# ─────────────────────────────────────────────
def test_normality(
data: np.ndarray,
alpha: float = 0.05,
verbose: bool = True,
) -> Dict[str, Any]:
"""
Run Shapiro-Wilk, Kolmogorov-Smirnov, and D'Agostino-Pearson normality tests.
Parameters
----------
data : array-like
1-D numeric data.
alpha : float
Significance level.
verbose : bool
Print a summary.
Returns
-------
dict with keys: shapiro, ks, dagostino, is_normal
"""
data = np.asarray(data, dtype=float)
data = data[~np.isnan(data)]
n = len(data)
results: Dict[str, Any] = {}
# Shapiro-Wilk (best for n < 5000)
if n < 5000:
stat_sw, p_sw = stats.shapiro(data)
results["shapiro"] = {"statistic": stat_sw, "p_value": p_sw, "normal": p_sw > alpha}
else:
results["shapiro"] = {"statistic": None, "p_value": None, "normal": None,
"note": "n>=5000; skipped Shapiro-Wilk"}
# Lilliefors-corrected KS (parameters estimated from the same sample — a plain
# stats.kstest with fitted mu/sigma is anti-conservative and must NOT be used)
if n >= 4:
try:
from statsmodels.stats.diagnostic import lilliefors
stat_ks, p_ks = lilliefors(data, dist="norm")
results["ks"] = {"statistic": stat_ks, "p_value": p_ks, "normal": p_ks > alpha,
"note": "Lilliefors-corrected KS"}
except ImportError:
results["ks"] = {"statistic": None, "p_value": None, "normal": None,
"note": "statsmodels missing; skipped KS (do not substitute "
"a plain kstest with fitted parameters)"}
else:
results["ks"] = {"statistic": None, "p_value": None, "normal": None,
"note": "n<4; skipped KS"}
# D'Agostino-Pearson (needs n >= 20)
if n >= 20:
stat_da, p_da = stats.normaltest(data)
results["dagostino"] = {"statistic": stat_da, "p_value": p_da, "normal": p_da > alpha}
else:
results["dagostino"] = {"statistic": None, "p_value": None, "normal": None,
"note": "n<20; skipped D'Agostino"}
# Consensus: normal if at least 2 out of 3 available tests agree
votes = [v["normal"] for v in results.values() if isinstance(v, dict) and v["normal"] is not None]
results["is_normal"] = sum(votes) >= (len(votes) / 2)
results["n"] = n
if verbose:
print(f"Normality tests (n={n}, alpha={alpha})")
for test_name, res in results.items():
if isinstance(res, dict) and "p_value" in res and res["p_value"] is not None:
verdict = "NORMAL" if res["normal"] else "NON-NORMAL"
print(f" {test_name:15s}: stat={res['statistic']:.4f}, p={res['p_value']:.4f} [{verdict}]")
print(f" Consensus: {'NORMAL' if results['is_normal'] else 'NON-NORMAL'}\n")
return results
# ─────────────────────────────────────────────
# 2. Effect Sizes
# ─────────────────────────────────────────────
def cohens_d(group1: np.ndarray, group2: np.ndarray) -> float:
"""Cohen's d for two independent groups."""
g1, g2 = np.asarray(group1), np.asarray(group2)
n1, n2 = len(g1), len(g2)
pooled_sd = np.sqrt(((n1 - 1) * np.var(g1, ddof=1) + (n2 - 1) * np.var(g2, ddof=1)) / (n1 + n2 - 2))
return (np.mean(g1) - np.mean(g2)) / pooled_sd
def eta_squared(f_statistic: float, df_between: int, df_within: int) -> float:
"""Eta-squared from F-statistic for one-way ANOVA."""
ss_between = f_statistic * df_between
ss_total = ss_between + df_within
return ss_between / ss_total
def cramers_v(contingency_table: np.ndarray) -> float:
"""Cramér's V for association in a contingency table."""
chi2 = stats.chi2_contingency(contingency_table, correction=False)[0]
n = contingency_table.sum()
min_dim = min(contingency_table.shape) - 1
return np.sqrt(chi2 / (n * min_dim))
def interpret_effect_size(d: float, measure: str = "cohens_d") -> str:
"""Return a qualitative label for an effect size."""
thresholds = {
"cohens_d": [(0.2, "small"), (0.5, "medium"), (0.8, "large")],
"eta_squared": [(0.01, "small"), (0.06, "medium"), (0.14, "large")],
"cramers_v": [(0.1, "small"), (0.3, "medium"), (0.5, "large")],
}
d = abs(d)
for threshold, label in thresholds.get(measure, []):
if d < threshold:
return label
return "large"
# ─────────────────────────────────────────────
# 3. Automatic Test Selection
# ─────────────────────────────────────────────
def run_comparison(
*groups: np.ndarray,
paired: bool = False,
alpha: float = 0.05,
verbose: bool = True,
) -> Dict[str, Any]:
"""
Automatically select and run the appropriate comparison test.
Parameters
----------
*groups : array-like
Two or more numeric arrays (one per group).
paired : bool
Whether observations are paired / repeated measures.
alpha : float
Significance level.
verbose : bool
Print result summary.
Returns
-------
dict with keys: test_name, statistic, p_value, effect_size, significant
"""
groups = [np.asarray(g, dtype=float) for g in groups]
k = len(groups)
if k < 2:
raise ValueError("Need at least 2 groups.")
min_n = min(len(g) for g in groups)
if min_n < 5:
# HARD policy: below n=5 no p-value is returned at all — a warning is too
# easy to ignore and the p-value would end up in the paper. Descriptive
# statistics only.
note = (f"smallest group has n={min_n} < 5: statistical test not performed "
"(pack policy: no p-values below n=5 — report mean ± std or range, "
"not significance claims).")
result = {
"test_name": None,
"statistic": None,
"p_value": None,
"significant": None,
"alpha": alpha,
"effect_size": {},
"descriptives": [
{"n": int(len(g)),
"mean": round(float(np.mean(g)), 4),
"std": round(float(np.std(g, ddof=1)), 4) if len(g) > 1 else None,
"min": round(float(np.min(g)), 4),
"max": round(float(np.max(g)), 4)}
for g in groups
],
"note": note,
}
if verbose:
print(f"No test run: {note}")
for i, d in enumerate(result["descriptives"]):
print(f" group {i}: n={d['n']}, mean={d['mean']}, std={d['std']}, "
f"range=[{d['min']}, {d['max']}]")
print()
return result
# Check normality for each group
all_normal = all(test_normality(g, alpha=alpha, verbose=False)["is_normal"] for g in groups)
result: Dict[str, Any] = {}
if k == 2:
g1, g2 = groups[0], groups[1]
if paired:
if all_normal:
stat, p = stats.ttest_rel(g1, g2)
result["test_name"] = "Paired t-test"
d = np.mean(g1 - g2) / np.std(g1 - g2, ddof=1)
result["effect_size"] = {"cohens_d": round(d, 4)}
else:
stat, p = stats.wilcoxon(g1, g2)
result["test_name"] = "Wilcoxon signed-rank"
# matched-pairs rank-biserial r = (T+ - T-)/(T+ + T-), computed from
# the signed ranks directly (robust to scipy's choice of W statistic)
diff = g1 - g2
diff = diff[diff != 0]
ranks = stats.rankdata(np.abs(diff))
t_plus = float(ranks[diff > 0].sum())
t_minus = float(ranks[diff < 0].sum())
rb = (t_plus - t_minus) / (t_plus + t_minus)
result["effect_size"] = {"rank_biserial": round(rb, 4)}
else:
if all_normal:
# Welch by default — the two-step "Levene pretest then choose
# equal_var" procedure inflates error rates and is not robust;
# Welch loses almost nothing when variances happen to be equal.
stat, p = stats.ttest_ind(g1, g2, equal_var=False)
result["test_name"] = "Welch's t-test"
d = cohens_d(g1, g2)
result["effect_size"] = {"cohens_d": round(d, 4),
"interpretation": interpret_effect_size(d)}
else:
stat, p = stats.mannwhitneyu(g1, g2, alternative="two-sided")
result["test_name"] = "Mann-Whitney U"
n1, n2 = len(g1), len(g2)
rb = 1 - (2 * stat) / (n1 * n2)
result["effect_size"] = {"rank_biserial_r": round(rb, 4)}
else:
# k >= 3
if paired:
if all_normal:
# Repeated-measures via pingouin if available, else warn
try:
import pingouin as pg
df_long = pd.DataFrame({
"value": np.concatenate(groups),
"group": np.repeat(np.arange(k), [len(g) for g in groups]),
"subject": np.tile(np.arange(len(groups[0])), k),
})
aov = pg.rm_anova(data=df_long, dv="value", within="group", subject="subject")
stat = aov["F"].iloc[0]
p = aov["p-unc"].iloc[0]
result["test_name"] = "Repeated-measures ANOVA (pingouin)"
result["effect_size"] = {"eta_squared": round(aov["np2"].iloc[0], 4)}
except ImportError:
warnings.warn("pingouin not installed; falling back to Friedman test.")
stat, p = stats.friedmanchisquare(*groups)
result["test_name"] = "Friedman test (fallback)"
result["effect_size"] = {}
else:
stat, p = stats.friedmanchisquare(*groups)
result["test_name"] = "Friedman test"
result["effect_size"] = {}
else:
if all_normal:
stat, p = stats.f_oneway(*groups)
result["test_name"] = "One-way ANOVA"
total_n = sum(len(g) for g in groups)
df_between = k - 1
df_within = total_n - k
es = eta_squared(stat, df_between, df_within)
result["effect_size"] = {"eta_squared": round(es, 4),
"interpretation": interpret_effect_size(es, "eta_squared")}
else:
stat, p = stats.kruskal(*groups)
result["test_name"] = "Kruskal-Wallis H"
result["effect_size"] = {}
result["statistic"] = round(float(stat), 4)
result["p_value"] = round(float(p), 6)
result["significant"] = p < alpha
result["alpha"] = alpha
if verbose:
print(f"Test: {result['test_name']}")
print(f" Statistic = {result['statistic']}, p = {result['p_value']}")
print(f" Significant at alpha={alpha}: {result['significant']}")
if result.get("effect_size"):
print(f" Effect size: {result['effect_size']}")
print()
return result
# ─────────────────────────────────────────────
# 4. Multiple Comparison Correction
# ─────────────────────────────────────────────
def correct_pvalues(
p_values: List[float],
method: str = "fdr_bh",
alpha: float = 0.05,
) -> pd.DataFrame:
"""
Apply multiple comparison correction.
Parameters
----------
p_values : list of float
method : str
One of: bonferroni, holm, fdr_bh (Benjamini-Hochberg),
fdr_by (Benjamini-Yekutieli), sidak
alpha : float
Returns
-------
DataFrame with original p-values, corrected p-values, and rejection flags.
"""
reject, p_corrected, _, _ = multitest.multipletests(p_values, alpha=alpha, method=method)
return pd.DataFrame({
"p_original": p_values,
"p_corrected": p_corrected,
"reject_H0": reject,
"method": method,
})
# ─────────────────────────────────────────────
# 5. Power Analysis
# ─────────────────────────────────────────────
def power_analysis_ttest(
effect_size: float = 0.5,
alpha: float = 0.05,
power: float = 0.80,
n_per_group: Optional[int] = None,
) -> Dict[str, float]:
"""
Two-sample t-test power analysis — for **a priori** planning only (choose n
before running the experiment, using an effect size from pilot data or the
literature). Do NOT compute "achieved/post-hoc power" from the observed effect
size of the same experiment: it is a monotone transform of the p-value and adds
no information. Note this solver is for *independent* two-sample designs; a
paired design has different power characteristics (use
statsmodels TTestPower on the difference scores instead).
Provide any three of (effect_size, alpha, power, n_per_group) to solve for the fourth.
"""
analysis = TTestIndPower()
if n_per_group is None:
n = analysis.solve_power(effect_size=effect_size, alpha=alpha, power=power, ratio=1.0)
return {"required_n_per_group": np.ceil(n), "effect_size": effect_size,
"alpha": alpha, "power": power}
else:
achieved_power = analysis.solve_power(effect_size=effect_size, alpha=alpha,
nobs1=n_per_group, ratio=1.0)
return {"n_per_group": n_per_group, "effect_size": effect_size,
"alpha": alpha, "achieved_power": round(achieved_power, 4)}
def chi_square_test_with_effect(
contingency: np.ndarray,
alpha: float = 0.05,
) -> Dict[str, Any]:
"""Chi-square test with Cramér's V effect size."""
chi2, p, dof, expected = stats.chi2_contingency(contingency)
v = cramers_v(contingency)
result = {
"test_name": "Chi-square" if expected.min() >= 5 else "Fisher exact (recommended)",
"chi2": round(chi2, 4),
"p_value": round(p, 6),
"dof": dof,
"cramers_v": round(v, 4),
"significant": p < alpha,
}
if expected.min() < 5:
if contingency.shape == (2, 2):
_, p_fisher = stats.fisher_exact(contingency)
result["fisher_p"] = round(p_fisher, 6)
return 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, 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 and report effect size + CI
result = run_comparison(pre, post, paired=True)
# Step 3 (planning the NEXT experiment): a-priori power using an effect size
# from pilot data or the literature — never "achieved power" from this sample.
d_planned = 0.5 # e.g., smallest effect size of interest
needed = power_analysis_ttest(effect_size=d_planned, alpha=0.05, power=0.90)
print(f"N needed for 90% power at d={d_planned}: {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