personamanagmentlayer__pcl/stdlib/scientific/research-expert/SKILL.md

name, version, description, category, tags, allowed-tools

name	version	description	category	tags	allowed-tools
research-expert	1.1.0	Expert-level research methodology, academic writing, statistical analysis, and scientific investigation. Use when the user mentions methodology, statistics, academic writing, or experimental design, or when the task involves Research Design, Statistical Analysis, or Data Analysis.	scientific	research methodology statistics academic-writing experimental-design	Read Write Edit

Research Methodology Expert

Expert guidance for research methodology, experimental design, statistical analysis, and academic writing.

Core Concepts

Research Design

• Experimental vs observational studies
• Randomized controlled trials (RCTs)
• Cross-sectional, longitudinal, cohort studies
• Case-control studies
• Systematic reviews and meta-analysis
• Sample size determination

Statistical Analysis

• Descriptive statistics
• Hypothesis testing
• Confidence intervals
• Regression analysis
• ANOVA and t-tests
• Non-parametric tests
• Multiple testing correction

Academic Writing

• Literature review
• Research proposals
• Manuscript structure (IMR AD)
• Citation management
• Peer review process
• Publishing ethics

Experimental Design

from dataclasses import dataclass
from typing import List, Optional
import numpy as np
from scipy import stats

@dataclass
class Study:
    name: str
    design_type: str  # 'RCT', 'observational', 'cohort'
    sample_size: int
    groups: List[str]
    primary_outcome: str
    secondary_outcomes: List[str]

class SampleSizeCalculator:
    """Calculate required sample size for studies"""

    @staticmethod
    def two_sample_ttest(effect_size: float, alpha: float = 0.05,
                        power: float = 0.8) -> int:
        """Calculate sample size for two-sample t-test"""
        from statsmodels.stats.power import tt_ind_solve_power

        n = tt_ind_solve_power(
            effect_size=effect_size,
            alpha=alpha,
            power=power,
            alternative='two-sided'
        )

        return int(np.ceil(n))

    @staticmethod
    def proportion_test(p1: float, p2: float, alpha: float = 0.05,
                       power: float = 0.8) -> int:
        """Calculate sample size for comparing proportions"""
        from statsmodels.stats.power import zt_ind_solve_power

        effect_size = (p2 - p1) / np.sqrt(p1 * (1 - p1))

        n = zt_ind_solve_power(
            effect_size=effect_size,
            alpha=alpha,
            power=power,
            alternative='two-sided'
        )

        return int(np.ceil(n))

class ExperimentalDesign:
    """Design and randomize experimental studies"""

    def __init__(self, n_subjects: int, n_groups: int):
        self.n_subjects = n_subjects
        self.n_groups = n_groups

    def simple_randomization(self) -> List[int]:
        """Simple random assignment to groups"""
        return np.random.choice(self.n_groups, size=self.n_subjects)

    def block_randomization(self, block_size: int) -> List[int]:
        """Block randomization for balanced groups"""
        n_blocks = self.n_subjects // block_size
        assignments = []

        for _ in range(n_blocks):
            block = np.repeat(range(self.n_groups),
                            block_size // self.n_groups)
            np.random.shuffle(block)
            assignments.extend(block)

        # Handle remaining subjects
        remainder = self.n_subjects % block_size
        if remainder > 0:
            extra = np.random.choice(self.n_groups, size=remainder)
            assignments.extend(extra)

        return assignments

    def stratified_randomization(self, strata: List[str]) -> List[int]:
        """Stratified randomization by covariates"""
        assignments = np.zeros(self.n_subjects, dtype=int)

        for stratum in set(strata):
            stratum_indices = [i for i, s in enumerate(strata) if s == stratum]
            stratum_n = len(stratum_indices)

            stratum_assignments = np.random.choice(
                self.n_groups,
                size=stratum_n,
                replace=True
            )

            for idx, assignment in zip(stratum_indices, stratum_assignments):
                assignments[idx] = assignment

        return assignments

Statistical Analysis

import pandas as pd
from scipy import stats
import statsmodels.api as sm
from statsmodels.stats.multitest import multipletests

class StatisticalAnalysis:
    """Perform statistical analyses"""

    @staticmethod
    def descriptive_stats(data: pd.Series) -> dict:
        """Calculate descriptive statistics"""
        return {
            "mean": data.mean(),
            "median": data.median(),
            "std": data.std(),
            "min": data.min(),
            "max": data.max(),
            "q25": data.quantile(0.25),
            "q75": data.quantile(0.75),
            "skewness": stats.skew(data),
            "kurtosis": stats.kurtosis(data)
        }

    @staticmethod
    def independent_ttest(group1: np.ndarray, group2: np.ndarray) -> dict:
        """Perform independent samples t-test"""
        statistic, pvalue = stats.ttest_ind(group1, group2)

        # Calculate effect size (Cohen's d)
        pooled_std = np.sqrt((group1.var() + group2.var()) / 2)
        cohens_d = (group1.mean() - group2.mean()) / pooled_std

        return {
            "t_statistic": statistic,
            "p_value": pvalue,
            "cohens_d": cohens_d,
            "mean_diff": group1.mean() - group2.mean(),
            "significant": pvalue < 0.05
        }

    @staticmethod
    def one_way_anova(groups: List[np.ndarray]) -> dict:
        """Perform one-way ANOVA"""
        f_statistic, p_value = stats.f_oneway(*groups)

        # Calculate effect size (eta-squared)
        grand_mean = np.mean(np.concatenate(groups))
        ss_between = sum(len(g) * (g.mean() - grand_mean)**2 for g in groups)
        ss_total = sum(((g - grand_mean)**2).sum() for g in groups)
        eta_squared = ss_between / ss_total

        return {
            "f_statistic": f_statistic,
            "p_value": p_value,
            "eta_squared": eta_squared,
            "significant": p_value < 0.05
        }

    @staticmethod
    def linear_regression(X: pd.DataFrame, y: pd.Series) -> dict:
        """Perform linear regression"""
        X_with_const = sm.add_constant(X)
        model = sm.OLS(y, X_with_const).fit()

        return {
            "coefficients": model.params.to_dict(),
            "r_squared": model.rsquared,
            "adj_r_squared": model.rsquared_adj,
            "f_statistic": model.fvalue,
            "p_value": model.f_pvalue,
            "summary": model.summary()
        }

    @staticmethod
    def multiple_testing_correction(p_values: List[float],
                                    method: str = 'fdr_bh',
                                    alpha: float = 0.05) -> dict:
        """Apply multiple testing correction"""
        reject, pvals_corrected, alphacSidak, alphacBonf = multipletests(
            p_values,
            alpha=alpha,
            method=method
        )

        return {
            "rejected": reject,
            "corrected_pvalues": pvals_corrected,
            "n_significant": reject.sum(),
            "method": method
        }

class EffectSize:
    """Calculate effect sizes"""

    @staticmethod
    def cohens_d(group1: np.ndarray, group2: np.ndarray) -> float:
        """Cohen's d for two groups"""
        pooled_std = np.sqrt((group1.var() + group2.var()) / 2)
        return (group1.mean() - group2.mean()) / pooled_std

    @staticmethod
    def hedges_g(group1: np.ndarray, group2: np.ndarray) -> float:
        """Hedges' g (corrected effect size)"""
        n1, n2 = len(group1), len(group2)
        df = n1 + n2 - 2

        correction = 1 - (3 / (4 * df - 1))
        d = EffectSize.cohens_d(group1, group2)

        return d * correction

    @staticmethod
    def r_squared_to_cohens_f(r_squared: float) -> float:
        """Convert R² to Cohen's f"""
        return np.sqrt(r_squared / (1 - r_squared))

Literature Review

from typing import Dict, List
from dataclasses import dataclass

@dataclass
class Citation:
    authors: List[str]
    year: int
    title: str
    journal: str
    volume: Optional[int] = None
    pages: Optional[str] = None
    doi: Optional[str] = None

    def format_apa(self) -> str:
        """Format citation in APA style"""
        authors_str = self._format_authors_apa()
        citation = f"{authors_str} ({self.year}). {self.title}. {self.journal}"

        if self.volume:
            citation += f", {self.volume}"
        if self.pages:
            citation += f", {self.pages}"
        if self.doi:
            citation += f". https://doi.org/{self.doi}"

        return citation + "."

    def _format_authors_apa(self) -> str:
        """Format authors in APA style"""
        if len(self.authors) == 1:
            return self.authors[0]
        elif len(self.authors) == 2:
            return f"{self.authors[0]} & {self.authors[1]}"
        else:
            return f"{self.authors[0]} et al."

class LiteratureReview:
    """Manage literature review"""

    def __init__(self):
        self.citations: List[Citation] = []
        self.themes: Dict[str, List[Citation]] = {}

    def add_citation(self, citation: Citation, themes: List[str]):
        """Add citation and categorize by themes"""
        self.citations.append(citation)

        for theme in themes:
            if theme not in self.themes:
                self.themes[theme] = []
            self.themes[theme].append(citation)

    def get_bibliography(self, style: str = 'apa') -> List[str]:
        """Generate bibliography"""
        if style == 'apa':
            return [c.format_apa() for c in sorted(
                self.citations,
                key=lambda x: (x.authors[0], x.year)
            )]

    def get_summary_by_theme(self, theme: str) -> List[Citation]:
        """Get citations for specific theme"""
        return self.themes.get(theme, [])

Best Practices

Research Design

• Pre-register studies when possible
• Calculate adequate sample sizes
• Use appropriate controls
• Randomize when applicable
• Blind assessors to reduce bias
• Consider confounding variables
• Document protocol deviations

Data Analysis

• Pre-specify analysis plan
• Check statistical assumptions
• Report effect sizes, not just p-values
• Apply multiple testing corrections
• Use appropriate statistical tests
• Report confidence intervals
• Make data and code available

Academic Writing

• Follow journal guidelines
• Use clear, precise language
• Report methodology in detail
• Discuss limitations openly
• Acknowledge conflicts of interest
• Properly cite all sources
• Use reference management software

Anti-Patterns

❌ P-hacking and data dredging ❌ HARKing (Hypothesizing After Results are Known) ❌ Cherry-picking results ❌ Inadequate sample sizes ❌ Ignoring failed experiments ❌ No pre-registration ❌ Selective reporting of outcomes

Resources

• ClinicalTrials.gov: https://clinicaltrials.gov/
• CONSORT Statement: http://www.consort-statement.org/
• Cochrane Handbook: https://training.cochrane.org/handbook
• APA Style: https://apastyle.apa.org/
• StatsModels: https://www.statsmodels.org/