pisa-international

name	pisa-international
description	Use this Skill to analyze PISA/TIMSS international large-scale assessment data: plausible values averaging, Fay's BRR variance estimation, and cross-national SES gradients.
tags	["education","PISA","TIMSS","large-scale-assessment","plausible-values","international-comparison"]
version	1.0.0
authors	[{"name":"awesome-rosetta-skills contributors","github":"@xjtulyc"}]
license	MIT
platforms	["claude-code","codex","gemini-cli","cursor"]
dependencies	{"python":["pandas>=1.5","numpy>=1.23","scipy>=1.9","matplotlib>=3.6","statsmodels>=0.14"]}
last_updated	2026-03-18
status	stable

PISA/TIMSS International Large-Scale Assessment Analysis

TL;DR — Correctly analyse PISA and TIMSS data with all 10 plausible values, Fay's BRR variance estimation (80 replicate weights), ESCS gradient regressions, and cross-national comparison figures.

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When to Use

Use this Skill when you need to:

• Compute country-level mean performance estimates on PISA or TIMSS using the statistically correct combination of all plausible values.
• Estimate standard errors that account for both sampling variance (BRR replicate weights) and imputation variance (between-plausible-value spread).
• Analyse SES gradients (score ~ ESCS regression) and gender gaps across countries.
• Produce cross-national comparison figures with proper error bars.
• Check proficiency level distributions (PISA Levels 1–6).

Do NOT use naive averaging of plausible values without BRR weights — this underestimates standard errors and produces invalid significance tests.

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Background

Why Plausible Values Exist

PISA does not administer every item to every student (matrix sampling design). Each student answers only a booklet subset, so the full proficiency scale cannot be directly estimated. Instead, PISA generates M = 10 plausible values (PV1MATH–PV10MATH) per student — random draws from the posterior distribution of proficiency given the student's responses and background.

Correct Estimation Protocol (Rubin's Rules)

For statistic Q (e.g., country mean):

1. For each plausible value m = 1..M:
       Q_m  = estimate using PV_m with BRR replicate weights → Var_BRR_m

2. Point estimate:   Q = (1/M) * Σ Q_m

3. Sampling variance:  U = (1/M) * Σ Var_BRR_m

4. Imputation variance: B = (1/(M-1)) * Σ (Q_m - Q)²

5. Total variance:  Var_total = U + (1 + 1/M) * B

6. SE = sqrt(Var_total)

Fay's BRR Variance Estimation

PISA provides 80 balanced repeated replication (BRR) weights (W_FSTR1–W_FSTR80). For each replicate r:

Var_BRR(Q) = (1 / (80 * k²)) * Σ_r (Q_r - Q_full)²

where k = 0.5 (Fay coefficient used in PISA).

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Environment Setup

conda create -n pisa_analysis python=3.11 -y
conda activate pisa_analysis
pip install pandas>=1.5 numpy>=1.23 scipy>=1.9 matplotlib>=3.6 statsmodels>=0.14

# Download PISA 2022 student data (SPSS format) from OECD:
# https://www.oecd.org/pisa/data/2022database/
# Convert .sav to parquet for efficiency:
pip install pyreadstat pyarrow
python -c