Social Research Methods

Research Question Type -> Recommended Design

"What is the prevalence of X?"     -> Cross-sectional survey
"Does X cause Y?"                   -> Randomized experiment or quasi-experiment
"How does X develop over time?"     -> Longitudinal panel study
"What does X mean to participants?" -> Qualitative (interviews, ethnography)
"How much of Y is explained by X?" -> Correlational / regression study
"Does the effect hold across contexts?" -> Comparative / cross-national study

def operationalize_construct(construct: str, dimensions: list[dict]) -> dict:
    """
    Create an operationalization plan for a theoretical construct.

    Args:
        construct: Name of the abstract concept
        dimensions: List of dicts with 'name', 'indicators', 'measurement_level'
    """
    plan = {
        'construct': construct,
        'dimensions': [],
        'total_items': 0
    }
    for dim in dimensions:
        items = []
        for indicator in dim['indicators']:
            items.append({
                'indicator': indicator,
                'measurement': dim['measurement_level'],
                'source': dim.get('data_source', 'self-report survey')
            })
        plan['dimensions'].append({
            'name': dim['name'],
            'items': items,
            'n_items': len(items)
        })
        plan['total_items'] += len(items)
    return plan

# Example: operationalize "social capital"
social_capital = operationalize_construct(
    construct="Social Capital",
    dimensions=[
        {
            'name': 'bonding_capital',
            'indicators': ['close_friends_count', 'family_support_scale', 'trust_in_neighbors'],
            'measurement_level': 'ordinal (Likert 1-5)'
        },
        {
            'name': 'bridging_capital',
            'indicators': ['diverse_network_size', 'weak_ties_count', 'civic_participation'],
            'measurement_level': 'ratio'
        }
    ]
)

import math

def sample_size_proportion(p: float = 0.5, margin_error: float = 0.05,
                            confidence: float = 0.95, population: int = None) -> int:
    """
    Calculate required sample size for estimating a proportion.

    Args:
        p: Expected proportion (use 0.5 for maximum variance)
        margin_error: Desired margin of error
        confidence: Confidence level
        population: Finite population size (optional)
    """
    z_scores = {0.90: 1.645, 0.95: 1.96, 0.99: 2.576}
    z = z_scores.get(confidence, 1.96)

    n = (z**2 * p * (1 - p)) / margin_error**2

    # Finite population correction
    if population:
        n = n / (1 + (n - 1) / population)

    return math.ceil(n)

print(sample_size_proportion(p=0.5, margin_error=0.03, confidence=0.95))
# Result: 1068

Between-subjects:
  + No carryover effects
  + Simpler analysis
  - Requires more participants
  - Individual differences add noise

Within-subjects:
  + More statistical power
  + Fewer participants needed
  - Carryover/order effects
  - Demand characteristics
  Solution: Counterbalance condition order (Latin square)

# Standard analysis pipeline for survey data
import pandas as pd
from scipy import stats

def analyze_survey(df: pd.DataFrame, iv: str, dv: str,
                    covariates: list[str] = None) -> dict:
    """Run standard analytical checks on survey data."""
    results = {}

    # 1. Descriptive statistics
    results['descriptives'] = df[[iv, dv]].describe().to_dict()

    # 2. Reliability (if scale items provided)
    # Compute Cronbach's alpha for multi-item scales

    # 3. Bivariate test
    if df[iv].nunique() == 2:
        groups = [group[dv].dropna() for _, group in df.groupby(iv)]
        t_stat, p_val = stats.ttest_ind(*groups)
        d = (groups[0].mean() - groups[1].mean()) / df[dv].std()  # Cohen's d
        results['test'] = {'type': 't-test', 't': t_stat, 'p': p_val, 'cohens_d': d}
    else:
        # Correlation for continuous IV
        r, p = stats.pearsonr(df[iv].dropna(), df[dv].dropna())
        results['test'] = {'type': 'correlation', 'r': r, 'p': p}

    return results