analysis/sampling_correlation_report.md

Bernoulli sampling-noise correlation simulation

• Calibration data: results_128
• Tasks per simulated experiment: 100
• Monte Carlo draws: 20,000
• True correlation 1 uses the same latent task accuracy in both modalities but independent Bernoulli trials.
• True correlation 0 uses independent latent task accuracies with the same fitted marginal distribution.

Pooled canonical calibration

True latent corr.	Trials/task	Metric	Mean observed	95% simulation interval
0	8	pearson	-0.001	[-0.196, 0.199]
0	8	spearman	-0.001	[-0.197, 0.199]
0	128	pearson	-0.000	[-0.199, 0.200]
0	128	spearman	-0.000	[-0.199, 0.200]
1	8	pearson	0.848	[0.780, 0.902]
1	8	spearman	0.833	[0.759, 0.891]
1	128	pearson	0.989	[0.983, 0.993]
1	128	spearman	0.984	[0.977, 0.990]