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Sample study · multilevel design

Homework and Math Scores Across Schools

Research information

Statement of the problem

This study examines how weekly homework hours relate to students' math scores, acknowledging that students are nested within schools so any raw relationship may confound within-school effects with between-school differences.

Objectives

To describe the math_score and homework_hours across the participating schools.
To fit a multilevel (mixed-effects) model of math_score on homework_hours with a random intercept per school, so within-school and between-school variation are separated.

Dataset

school_math.csv289 rows × 3 cols

Column	Kind	Distinct
math_score	numeric	196
school_id	categorical	10
homework_hours	numeric	76

Feasibility & estimateFree

✓ Feasibledesign: multilevel · via heuristic

Detected a multilevel design with 2 analyzable variable(s) and 2 analytical question(s). Recommended 2 statistical test(s). Estimated cost: 26 credits.

Recommended analysis

To describe the math_score and homework_hours across the participating schools.

Descriptive Statistics(math_score, homework_hours)

To fit a multilevel (mixed-effects) model of math_score on homework_hours with a random intercept per school, so within-school and between-school variation are separated.

Linear Mixed-Effects Model(math_score, school_id, homework_hours)

Dataset Complexity8

Statistical Tests5

AI Interpretation6

Visualizations2

Report Generation5

Total to run26 credits

Estimated runtime: ~40-80 seconds

ResultsComputed

2 tests26 credits

Descriptive Statistics (math_score, homework_hours)

n	max	min	std	mean	mode	range	median	variable	variance
289	87	40.900	9.518	68.060	66.800	46.100	68.900	math_score	90.599
289	8	0.500	2.168	4.481	5.500	7.500	4.600	homework_hours	4.700

Linear Mixed-Effects Model (math_score, school_id, homework_hours)

significant

N289p< .001

ICC0.806

large

coef	ci low	ci high	p value	predictor
2.483	2.302	2.664	0.000	homework_hours

Mixed model on 10 groups: ICC = 0.81 of variance sits between groups. Per-predictor coefficients + 95% CIs are in the table.

Report

Publication-ready report

Tests used · Results · Discussion — generated from the computed statistics.

Numeric-claim check passed · 11 numbers verified · prose: llm:gemini

Open report ↗Download DOCX Download PDF

Reproducible code

Download the exact Jupyter notebook or Python script that reproduces these results with widely-used libraries (scipy, statsmodels, lifelines).

Download Jupyter notebook Download Python script

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