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 assignmentsStatistical 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/