psychometrics

## What I do - Design and analyze psychological measurements - Build and validate questionnaires - Measure latent traits - Assess reliability and validity - Create scoring systems - Handle survey data analysis ## When to use me Use me when: - Building assessment tools - Measuring user attitudes/personality - Validating questionnaires - Creating scoring models ## Key Concepts ### Psychometric Models ```python import numpy as np from scipy import stats # Classical Test Theory def cronbach_alpha(items): """Calculate Cronbach's alpha for reliability""" item_scores = np.array(items) n_items = item_scores.shape[1] # Item variances item_vars = item_scores.var(axis=0, ddof=1) total_var = item_scores.sum(axis=1).var(ddof=1) alpha = (n_items / (n_items - 1)) * (1 - item_vars.sum() / total_var) return alpha # Item Response Theory (Simplified) # 1PL Model: P(correct) = 1 / (1 + exp(-(theta - b))) def logistic_1pl(theta, difficulty): return 1 / (1 + np.exp(-(theta - difficulty))) ``` ### Reliability Measures - **Cronbach's Alpha**: Internal consistency - **Test-retest**: Stability over time - **Inter-rater**: Agreement between raters - **Split-half**: Correlation between halves ### Validity Types - **Content**: Measures intended construct - **Criterion**: Correlates with outcome - **Construct**: Theoretical underpinning - **Face**: Appears valid to examinees ### Factor Analysis ```python from sklearn.decomposition import FactorAnalysis # Exploratory factor analysis fa = FactorAnalysis(n_components=3) factor_scores = fa.fit_transform(X) # Interpretation loadings = fa.components_.T # High loadings indicate strong factor relationships ``` ### Item Analysis - Difficulty index (p-value) - Discrimination index - Item-total correlation - Response distribution