The complete analysis
Proofs, counterexamples, conditional calculations, sensitivity analyses, references, and limitations.
Open report ↗Probability · Psychometrics · Simulation
How much can IQ
test scores differ?
Exact mathematical results and reproducible simulations of differences between correlated IQ scores.
Read, inspect, reproduce.
Start with the report for the proofs and interpretation. The workbook and source package make the underlying work available for inspection.
The numbers behind the report
Tabulated results and numeric source data, with CSV alternatives available in the repository.
Open workbook ↗The editable materials
Report sources and supporting materials for examining and reproducing the analysis.
Open source package ↗Understand the assumptions
Correlation is only part
of the model.
Correlation alone does not determine the mean absolute difference or the highest–lowest range. The reference results assume equal means, a standard deviation of 15, and a jointly normal distribution with equal pairwise correlations.
The signed difference averages to zero because the means are equal. Positive and negative differences cancel; their magnitudes do not.
E|X − Y| = 2σ √((1 − ρ) / π)
Here σ is the common standard deviation and ρ is the Pearson correlation. These population averages are not a prediction of any one person’s score difference.
Run the analysis yourself.
The R programs use packages supplied with R. The report also documents the tools needed to rebuild the PDF and export the workbook.
git clone https://github.com/AndersH3/IQ-test-differences.git
cd IQ-test-differences/iq_report
Rscript code/iq_difference_simulation.R --out=results/main_run_new.txt
Rscript code/iq_report_extensions.R