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Use when performing hypothesis testing, A/B testing, data quality checks, time series analysis, or regression model validation. All methods return unified TestResult objects with consistent interface including p-value, statistic, confidence interval, and effect size.\n---\n\n# Pywayne Statistics\n\nComprehensive statistical testing library for hypothesis testing, A/B testing, and data analysis.\n\n## Quick Start\n\n```python\nfrom pywayne.statistics import NormalityTests, LocationTests\nimport numpy as np\n\n# Test data normality\nnt = NormalityTests()\ndata = np.random.normal(0, 1, 100)\nresult = nt.shapiro_wilk(data)\nprint(f\"p-value: {result.p_value:.4f}, is_normal: {not result.reject_null}\")\n\n# Compare two groups\nlt = LocationTests()\ngroup_a = np.random.normal(100, 15, 50)\ngroup_b = np.random.normal(105, 15, 50)\nresult = lt.two_sample_ttest(group_a, group_b)\nprint(f\"Significant difference: {result.reject_null}\")\n```\n\n## Test Categories\n\n### NormalityTests (`NormalityTests`)\n\nTest if data follows a normal distribution or other specified distributions.\n\n| Method | Description | Use Case |\n|---------|-------------|-----------|\n| `shapiro_wilk` | Shapiro-Wilk test | Small-medium samples (n ≤ 5000) |\n| `ks_test_normal` | K-S normality test | Medium-large samples |\n| `ks_test_two_sample` | Two-sample K-S test | Compare two sample distributions |\n| `anderson_darling` | Anderson-Darling test | Tail-sensitive normality test |\n| `dagostino_pearson` | D'Agostino-Pearson K² | Based on skewness and kurtosis |\n| `jarque_bera` | Jarque-Bera test | Large samples, regression residuals |\n| `chi_square_goodness_of_fit` | Chi-square goodness-of-fit | Categorical data |\n| `lilliefors_test` | Lilliefors test | Unknown parameters K-S test |\n\n**Example:**\n```python\nfrom pywayne.statistics import NormalityTests\n\nnt = NormalityTests()\nresult = nt.shapiro_wilk(data)\nif result.p_value < 0.05:\n    print(\"Data is NOT normally distributed\")\nelse:\n    print(\"Data follows normal distribution\")\n```\n\n### LocationTests (`LocationTests`)\n\nCompare means or medians across groups (parametric and non-parametric).\n\n| Method | Description | Use Case |\n|---------|-------------|-----------|\n| `one_sample_ttest` | One-sample t-test | Compare sample mean to a value |\n| `two_sample_ttest` | Two-sample t-test | Compare two independent group means |\n| `paired_ttest` | Paired t-test | Compare before/after measurements |\n| `one_way_anova` | One-way ANOVA | Compare 3+ group means |\n| `mann_whitney_u` | Mann-Whitney U test | Non-parametric two-sample test |\n| `wilcoxon_signed_rank` | Wilcoxon signed-rank | Non-parametric paired test |\n| `kruskal_wallis` | Kruskal-Wallis H test | Non-parametric multi-group test |\n\n**Example (A/B Testing):**\n```python\nfrom pywayne.statistics import LocationTests, NormalityTests\n\nlt = LocationTests()\nnt = NormalityTests()\n\n# Check normality first\nif nt.shapiro_wilk(control).p_value > 0.05:\n    result = lt.two_sample_ttest(control, treatment)\nelse:\n    result = lt.mann_whitney_u(control, treatment)\n\nprint(f\"Effect significant: {result.reject_null}\")\n```\n\n### CorrelationTests (`CorrelationTests`)\n\nTest correlation between variables and independence of categorical variables.\n\n| Method | Description | Use Case |\n|---------|-------------|-----------|\n| `pearson_correlation` | Pearson correlation | Linear relationship |\n| `spearman_correlation` | Spearman's rank | Monotonic relationship |\n| `kendall_tau` | Kendall's tau | Rank correlation, small samples |\n| `chi_square_independence` | Chi-square independence | Categorical variables |\n| `fisher_exact_test` | Fisher's exact test | 2×2 contingency table |\n| `mcnemar_test` | McNemar's test | Paired categorical data |\n\n**Example:**\n```python\nfrom pywayne.statistics import CorrelationTests\n\nct = CorrelationTests()\nresult = ct.pearson_correlation(x, y)\nprint(f\"Correlation: {result.statistic:.3f}, p-value: {result.p_value:.4f}\")\n```\n\n### TimeSeriesTests (`TimeSeriesTests`)\n\nTest time series properties: stationarity, autocorrelation, cointegration.\n\n| Method | Description | Use Case |\n|---------|-------------|-----------|\n| `adf_test` | Augmented Dickey-Fuller | Unit root test for stationarity |\n| `kpss_test` | KPSS test | Stationarity test (complements ADF) |\n| `ljung_box_test` | Ljung-Box Q test | Overall autocorrelation |\n| `runs_test` | Runs test | Randomness testing |\n| `arch_test` | ARCH effect test | Heteroscedasticity |\n| `granger_causality` | Granger causality | Causal relationship |\n| `engle_granger_cointegration` | Engle-Granger cointegration | Long-term equilibrium |\n| `breusch_godfrey_test` | Breusch-Godfrey | Higher-order autocorrelation |\n\n**Example:**\n```python\nfrom pywayne.statistics import TimeSeriesTests\n\ntst = TimeSeriesTests()\nadf_result = tst.adf_test(time_series_data)\nkpss_result = tst.kpss_test(time_series_data)\n\nif adf_result.reject_null:\n    print(\"Series is stationary\")\nelse:\n    print(\"Series has unit root (non-stationary)\")\n```\n\n### ModelDiagnostics (`ModelDiagnostics`)\n\nRegression model diagnostics: heteroscedasticity, autocorrelation, multicollinearity.\n\n| Method | Description | Use Case |\n|---------|-------------|-----------|\n| `breusch_pagan_test` | Breusch-Pagan | Heteroscedasticity test |\n| `white_test` | White's test | General heteroscedasticity |\n| `goldfeld_quandt_test` | Goldfeld-Quandt | Structural break heteroscedasticity |\n| `durbin_watson_test` | Durbin-Watson | First-order autocorrelation |\n| `variance_inflation_factor` | VIF | Multicollinearity diagnosis |\n| `levene_test` | Levene's test | Homogeneity of variance |\n| `bartlett_test` | Bartlett's test | Homogeneity (normal assumption) |\n| `residual_normality_test` | Residual normality | Regression assumption check |\n\n**Example:**\n```python\nfrom pywayne.statistics import ModelDiagnostics\n\nmd = ModelDiagnostics()\nresiduals = y - model.predict(X)\n\n# Check assumptions\nbp_result = md.breusch_pagan_test(residuals, X)\ndw_result = md.durbin_watson_test(residuals)\n\nif bp_result.reject_null:\n    print(\"Warning: Heteroscedasticity detected\")\n```\n\n## TestResult Object\n\nAll test methods return a unified `TestResult` object:\n\n```python\nresult = nt.shapiro_wilk(data)\n\n# Access results\nresult.test_name        # Test method name\nresult.statistic        # Test statistic value\nresult.p_value          # P-value\nresult.reject_null      # True if null hypothesis is rejected\nresult.critical_value   # Critical value (if applicable)\nresult.confidence_interval # Tuple (lower, upper) if applicable\nresult.effect_size      # Effect size if applicable\nresult.additional_info  # Dict with additional information\n```\n\n## Utility Functions\n\n### `list_all_tests()`\n\nList all available test methods across all modules.\n\n```python\nfrom pywayne.statistics import list_all_tests\nprint(list_all_tests())\n```\n\n### `show_test_usage(method_name)`\n\nDisplay usage and documentation for a specific test.\n\n```python\nfrom pywayne.statistics import show_test_usage\nshow_test_usage('shapiro_wilk')\n```\n\n## Method Selection Guide\n\n### Normality Tests\n\n| Sample Size | Recommended Method |\n|-------------|-------------------|\n| n < 30 | Shapiro-Wilk |\n| 30 ≤ n ≤ 300 | Shapiro-Wilk, D'Agostino-Pearson |\n| n > 300 | Jarque-Bera, Kolmogorov-Smirnov |\n\n### Location Tests\n\n| Condition | Parametric | Non-parametric |\n|-----------|-------------|----------------|\n| Normal data | t-test, ANOVA | - |\n| Non-normal data | - | Mann-Whitney U, Kruskal-Wallis |\n| Paired data | Paired t-test | Wilcoxon signed-rank |\n\n## Multiple Testing Correction\n\nWhen performing multiple tests, apply p-value correction:\n\n```python\nfrom statsmodels.stats.multitest import multipletests\n\np_values = [r.p_value for r in results]\nrejected, p_corrected, _, _ = multipletests(\n    p_values, alpha=0.05, method='fdr_bh'\n)\n```\n\n## Common Applications\n\n### Data Quality Check\n\n```python\ndef data_quality_check(data):\n    nt = NormalityTests()\n    lt = LocationTests()\n\n    normality = nt.shapiro_wilk(data)\n\n    # Outlier detection (IQR)\n    Q1, Q3 = np.percentile(data, [25, 75])\n    IQR = Q3 - Q1\n    outliers = data[(data < Q1 - 1.5*IQR) | (data > Q3 + 1.5*IQR)]\n\n    return {\n        'size': len(data),\n        'is_normal': not normality.reject_null,\n        'p_value': normality.p_value,\n        'outliers': len(outliers)\n    }\n```\n\n### A/B Testing Workflow\n\n```python\ndef ab_test_analysis(control, treatment):\n    nt = NormalityTests()\n    lt = LocationTests()\n\n    # Check normality\n    norm_c = nt.shapiro_wilk(control[:100])\n    norm_t = nt.shapiro_wilk(treatment[:100])\n\n    # Choose appropriate test\n    if norm_c.p_value > 0.05 and norm_t.p_value > 0.05:\n        result = lt.two_sample_ttest(control, treatment)\n    else:\n        result = lt.mann_whitney_u(control, treatment)\n\n    return {\n        'test_used': result.test_name,\n        'p_value': result.p_value,\n        'significant': result.reject_null,\n        'effect_size': result.effect_size\n    }\n```\n\n### Regression Model Diagnostics\n\n```python\ndef diagnose_model(y, X, model):\n    md = ModelDiagnostics()\n    residuals = y - model.predict(X)\n\n    return {\n        'heteroscedasticity_bp': md.breusch_pagan_test(residuals, X).reject_null,\n        'autocorrelation_dw': md.durbin_watson_test(residuals).statistic,\n        'residuals_normal': md.residual_normality_test(residuals).p_value,\n        'vif_max': max(md.variance_inflation_factor(X))\n    }\n```\n\n## Notes\n\n- All methods accept `np.ndarray` or list as input\n- All methods return `TestResult` with consistent interface\n- Always validate test assumptions before applying parametric tests\n- Apply multiple testing correction when performing several tests\n- Report effect sizes alongside p-values for complete interpretation\n\nFile v0.1.0:_meta.json\n\n{\n  \"ownerId\": \"kn7d2b8vpaw5d7bq2ybbb9sqjh8143nf\",\n  \"slug\": \"statistics-2\",\n  \"version\": \"0.1.0\",\n  \"publishedAt\": 1771259011974\n}\n\nFile v0.1.0:skill-card.md\n\n## Description:\n\nPywayne Statistics is a usage guide for a Python statistical testing library with methods for normality, location, correlation, time series, and model diagnostics.\n\nThis skill is ready for commercial/non-commercial use.\n\n## Publisher:\n\n[wangyendt](https://clawhub.ai/user/wangyendt)\n\n### License/Terms of Use:\n\n\n## Use Case:\n\nDevelopers, analysts, and data scientists use this skill to choose and apply pywayne.statistics tests for hypothesis testing, A/B testing, data quality checks, time series analysis, and regression diagnostics.\n\n### Deployment Geography for Use:\n\nGlobal\n\n## Known Risks and Mitigations:\n\nRisk: Statistical results can be misleading when test assumptions, sample size, or multiple comparisons are handled incorrectly.\n\nMitigation: Validate test assumptions, apply multiple testing correction where relevant, and report effect sizes alongside p-values.\n\nRisk: The skill references an external Python package whose implementation was not covered by the skill security review.\n\nMitigation: Review and pin the external package before running it in production or sensitive environments.\n\n## Reference(s):\n\n- [ClawHub skill page](https://clawhub.ai/wangyendt/skills/statistics-2)\n- [ClawHub publisher profile](https://clawhub.ai/user/wangyendt)\n\n## Skill Output:\n\n**Output Type(s):** [text, markdown, code, guidance]\n\n**Output Format:** [Markdown with Python code examples]\n\n**Output Parameters:** [1D]\n\n**Other Properties Related to Output:** [Provides statistical method-selection guidance, result interpretation notes, and example Python snippets.]\n\n## Skill Version(s):\n\n0.1.0 (source: server release metadata)\n\n## Ethical Considerations:\n\nUsers should evaluate whether this skill is appropriate for their environment, review any generated or modified files before relying on them, and apply their organization's safety, security, and compliance requirements before deployment.","readmeExcerpt":"Skill: Pywayne Statistics Owner: wangyendt Summary: Comprehensive statistical testing library with 37+ methods for normality tests, location tests, correlation tests, time series tests, and model diagnostics.... Tags: latest:0.1.0 Version history: v0.1.0 | 2026-02-16T16:23:31.974Z | auto Initial release of pywayne-statistics. - Introduces a unified statistical testing library supporting 37+ tests across normality, lo","codeSnippets":[],"executableExamples":[{"language":"python","snippet":"from pywayne.statistics import NormalityTests, LocationTests\nimport numpy as np\n\n# Test data normality\nnt = NormalityTests()\ndata = np.random.normal(0, 1, 100)\nresult = nt.shapiro_wilk(data)\nprint(f\"p-value: {result.p_value:.4f}, is_normal: {not result.reject_null}\")\n\n# Compare two groups\nlt = LocationTests()\ngroup_a = np.random.normal(100, 15, 50)\ngroup_b = np.random.normal(105, 15, 50)\nresult = lt.two_sample_ttest(group_a, group_b)\nprint(f\"Significant difference: {result.reject_null}\")"},{"language":"python","snippet":"from pywayne.statistics import NormalityTests\n\nnt = NormalityTests()\nresult = nt.shapiro_wilk(data)\nif result.p_value < 0.05:\n    print(\"Data is NOT normally distributed\")\nelse:\n    print(\"Data follows normal distribution\")"},{"language":"python","snippet":"from pywayne.statistics import LocationTests, NormalityTests\n\nlt = LocationTests()\nnt = NormalityTests()\n\n# Check normality first\nif nt.shapiro_wilk(control).p_value > 0.05:\n    result = lt.two_sample_ttest(control, treatment)\nelse:\n    result = lt.mann_whitney_u(control, treatment)\n\nprint(f\"Effect significant: {result.reject_null}\")"},{"language":"python","snippet":"from pywayne.statistics import CorrelationTests\n\nct = CorrelationTests()\nresult = ct.pearson_correlation(x, y)\nprint(f\"Correlation: {result.statistic:.3f}, p-value: {result.p_value:.4f}\")"},{"language":"python","snippet":"from pywayne.statistics import TimeSeriesTests\n\ntst = TimeSeriesTests()\nadf_result = tst.adf_test(time_series_data)\nkpss_result = tst.kpss_test(time_series_data)\n\nif adf_result.reject_null:\n    print(\"Series is stationary\")\nelse:\n    print(\"Series has unit root (non-stationary)\")"},{"language":"python","snippet":"from pywayne.statistics import ModelDiagnostics\n\nmd = ModelDiagnostics()\nresiduals = y - model.predict(X)\n\n# Check assumptions\nbp_result = md.breusch_pagan_test(residuals, X)\ndw_result = md.durbin_watson_test(residuals)\n\nif bp_result.reject_null:\n    print(\"Warning: Heteroscedasticity detected\")"}],"parameters":null,"dependencies":[],"permissions":[],"extractedFiles":[{"path":"SKILL.md","content":"---\nname: pywayne-statistics\ndescription: Comprehensive statistical testing library with 37+ methods for normality tests, location tests, correlation tests, time series tests, and model diagnostics. Use when performing hypothesis testing, A/B testing, data quality checks, time series analysis, or regression model validation. All methods return unified TestResult objects with consistent interface including p-value, statistic, confidence interval, and effect size.\n---\n\n# Pywayne Statistics\n\nComprehensive statistical testing library for hypothesis testing, A/B testing, and data analysis.\n\n## Quick Start\n\n```python\nfrom pywayne.statistics import NormalityTests, LocationTests\nimport numpy as np\n\n# Test data normality\nnt = NormalityTests()\ndata = np.random.normal(0, 1, 100)\nresult = nt.shapiro_wilk(data)\nprint(f\"p-value: {result.p_value:.4f}, is_normal: {not result.reject_null}\")\n\n# Compare two groups\nlt = LocationTests()\ngroup_a = np.random.normal(100, 15, 50)\ngroup_b = np.random.normal(105, 15, 50)\nresult = lt.two_sample_ttest(group_a, group_b)\nprint(f\"Significant difference: {result.reject_null}\")\n```\n\n## Test Categories\n\n### NormalityTests (`NormalityTests`)\n\nTest if data follows a normal distribution or other specified distributions.\n\n| Method | Description | Use Case |\n|---------|-------------|-----------|\n| `shapiro_wilk` | Shapiro-Wilk test | Small-medium samples (n ≤ 5000) |\n| `ks_test_normal` | K-S normality test | Medium-large samples |\n| `ks_test_two_sample` | Two-sample K-S test | Compare two sample distributions |\n| `anderson_darling` | Anderson-Darling test | Tail-sensitive normality test |\n| `dagostino_pearson` | D'Agostino-Pearson K² | Based on skewness and kurtosis |\n| `jarque_bera` | Jarque-Bera test | Large samples, regression residuals |\n| `chi_square_goodness_of_fit` | Chi-square goodness-of-fit | Categorical data |\n| `lilliefors_test` | Lilliefors test | Unknown parameters K-S test |\n\n**Example:**\n```python\nfrom pywayne.statistics import NormalityTests\n\nnt = NormalityTests()\nresult = nt.shapiro_wilk(data)\nif result.p_value < 0.05:\n    print(\"Data is NOT normally distributed\")\nelse:\n    print(\"Data follows normal distribution\")\n```\n\n### LocationTests (`LocationTests`)\n\nCompare means or medians across groups (parametric and non-parametric).\n\n| Method | Description | Use Case |\n|---------|-------------|-----------|\n| `one_sample_ttest` | One-sample t-test | Compare sample mean to a value |\n| `two_sample_ttest` | Two-sample t-test | Compare two independent group means |\n| `paired_ttest` | Paired t-test | Compare before/after measurements |\n| `one_way_anova` | One-way ANOVA | Compare 3+ group means |\n| `mann_whitney_u` | Mann-Whitney U test | Non-parametric two-sample test |\n| `wilcoxon_signed_rank` | Wilcoxon signed-rank | Non-parametric paired test |\n| `kruskal_wallis` | Kruskal-Wallis H test | Non-parametric multi-group test |\n\n**Example (A/B Testing):**\n```python\nfrom pywayne.statistics import LocationTests, NormalityTests\n\nlt = L"},{"path":"_meta.json","content":"{\n  \"ownerId\": \"kn7d2b8vpaw5d7bq2ybbb9sqjh8143nf\",\n  \"slug\": \"statistics-2\",\n  \"version\": \"0.1.0\",\n  \"publishedAt\": 1771259011974\n}"},{"path":"skill-card.md","content":"## Description:\n\nPywayne Statistics is a usage guide for a Python statistical testing library with methods for normality, location, correlation, time series, and model diagnostics.\n\nThis skill is ready for commercial/non-commercial use.\n\n## Publisher:\n\n[wangyendt](https://clawhub.ai/user/wangyendt)\n\n### License/Terms of Use:\n\n\n## Use Case:\n\nDevelopers, analysts, and data scientists use this skill to choose and apply pywayne.statistics tests for hypothesis testing, A/B testing, data quality checks, time series analysis, and regression diagnostics.\n\n### Deployment Geography for Use:\n\nGlobal\n\n## Known Risks and Mitigations:\n\nRisk: Statistical results can be misleading when test assumptions, sample size, or multiple comparisons are handled incorrectly.\n\nMitigation: Validate test assumptions, apply multiple testing correction where relevant, and report effect sizes alongside p-values.\n\nRisk: The skill references an external Python package whose implementation was not covered by the skill security review.\n\nMitigation: Review and pin the external package before running it in production or sensitive environments.\n\n## Reference(s):\n\n- [ClawHub skill page](https://clawhub.ai/wangyendt/skills/statistics-2)\n- [ClawHub publisher profile](https://clawhub.ai/user/wangyendt)\n\n## Skill Output:\n\n**Output Type(s):** [text, markdown, code, guidance]\n\n**Output Format:** [Markdown with Python code examples]\n\n**Output Parameters:** [1D]\n\n**Other Properties Related to Output:** [Provides statistical method-selection guidance, result interpretation notes, and example Python snippets.]\n\n## Skill Version(s):\n\n0.1.0 (source: server release metadata)\n\n## Ethical Considerations:\n\nUsers should evaluate whether this skill is appropriate for their environment, review any generated or modified files before relying on them, and apply their organization's safety, security, and compliance requirements before deployment."}],"languages":[],"docsSourceLabel":"CLAWHUB","editorialOverview":"Comprehensive statistical testing library with 37+ methods for normality tests, location tests, correlation tests, time series tests, and model diagnostics.... Skill: Pywayne Statistics Owner: wangyendt Summary: Comprehensive statistical testing library with 37+ methods for normality tests, location tests, correlation tests, time series tests, and model diagnostics.... Tags: latest:0.1.0 Version history: v0.1.0 | 2026-02-16T16:23:31.974Z | auto Initial release of pywayne-statistics. - Introduces a unified statistical testing library supporting 37+ tests across normality, lo","editorialQuality":{"score":100,"threshold":65,"status":"ready","wordCount":955,"uniquenessScore":51,"reasons":[]}},"media":{"evidence":{"source":"no-media","verified":false,"confidence":"low","updatedAt":"2026-10-10T03:01:08.152Z","emptyReason":"No screenshots, media assets, or demo links are available."},"primaryImageUrl":null,"mediaAssetCount":0,"assets":[],"demoUrl":null},"ownerResources":{"evidence":{"source":"unclaimed","verified":false,"confidence":"low","updatedAt":"2026-10-10T03:01:08.152Z","emptyReason":"This page has not been claimed by the agent owner."},"hasCustomPage":false,"customPageUpdatedAt":null,"customLinks":[],"structuredLinks":{"docsUrl":null,"demoUrl":null,"supportUrl":null,"pricingUrl":null,"statusUrl":null},"customPage":null},"relatedAgents":{"evidence":{"source":"protocol-neighbors","verified":false,"confidence":"medium","updatedAt":"2026-10-10T07:53:40.196Z","emptyReason":null},"items":[{"id":"8ebccd8e-3863-4187-8355-c3f14e1f9edf","entityType":"agent","canonicalPath":"/agent/iofficeai-aionui","slug":"iofficeai-aionui","name":"AionUi","description":"Free, local, open-source 24/7 Cowork app and OpenClaw for Gemini CLI, Claude Code, Codex, OpenCode, Qwen Code, Goose CLI, Auggie, and more | 🌟 Star if you like it!","url":"https://github.com/iOfficeAI/AionUi","homepage":"https://www.aionui.com","source":"GITHUB_REPOS","protocols":["MCP","OPENCLAW"],"capabilities":[],"safetyScore":100,"overallRank":70,"updatedAt":"2026-10-09T19:11:12.944Z","createdAt":"2026-02-25T03:38:16.584Z","downloads":null},{"id":"b917f68a-ebff-438e-84f8-3f4b2494c0bc","entityType":"agent","canonicalPath":"/agent/activepieces-activepieces","slug":"activepieces-activepieces","name":"activepieces","description":"AI Agents & MCPs & AI Workflow Automation • (~400 MCP servers for AI agents) • AI Automation / AI Agent with MCPs • AI Workflows & AI Agents • MCPs for AI Agents","url":"https://github.com/activepieces/activepieces","homepage":"https://www.activepieces.com","source":"GITHUB_REPOS","protocols":["OPENCLAW"],"capabilities":[],"safetyScore":100,"overallRank":70,"updatedAt":"2026-04-15T02:22:12.426Z","createdAt":"2026-02-25T03:38:12.412Z","downloads":null},{"id":"5cb26759-3a39-483f-94cf-276a98c13bb8","entityType":"agent","canonicalPath":"/agent/cherryhq-cherry-studio","slug":"cherryhq-cherry-studio","name":"cherry-studio","description":"AI productivity studio with smart chat, autonomous agents, and 300+ assistants. 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