Step 1: Pick a mode


Step 2: Paste your data

Instructions:

  • One number per line, or comma/space separated.
  • Bootstrap mode: one column (sample). Permutation mode: two columns (Group A on top, Group B below — or use the second textarea).
  • Non-numeric entries are skipped with a warning.
10,000 is plenty for most teaching examples. More = smoother histogram, slower run.

Results

How to read this

Bootstrap CI (percentile method): resample the data with replacement to approximate the sampling distribution of the mean. The CI is the middle X% of the resampled means. More accurate variants (BCa, studentized) exist; for approximately symmetric data they agree closely with the percentile method.

Permutation p-value: under H0 of "the two distributions are identical" (so group labels are interchangeable), randomly reshuffle the labels many times and see how often the resulting difference is as extreme as what you observed. Note: strictly, this tests distributional equality, not just equality of means — when variances or shapes differ under a "same-mean" H0, the permutation test becomes a test of a stronger hypothesis.

Comparison to formula: for approximately-normal, equal-variance data with moderate n, the bootstrap CI matches the t-CI closely and the permutation p matches the t-test p closely. Divergence is informative — it points to skew, outliers, or unequal variances.

Reproducibility: each run uses fresh random seeds, so results differ by Monte Carlo noise. For 10,000 iterations this is about ~±0.002 on a p-value or ~±0.5% on a CI endpoint. That's expected, not a bug.