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Bootstrap Confidence Intervals

Analyze → Bootstrap Confidence Intervals. A confidence interval for a statistic without a formula for its standard error: the nonparametric bootstrap resamples your cases with replacement many times, recomputes the statistic on each resample, and reads the interval off the spread of those values. Use it for a median, a coefficient of variation, or any statistic whose textbook interval assumes more than you are willing to.

Filling the dialog

  • Statistic: one of Mean, Median, Standard deviation, Variance or Coefficient of variation of one variable; the Pearson or Spearman correlation of two (Variable (X) and Variable (Y)); or the Mean difference (2 groups) of a variable across a Grouping factor (2 levels) (the second level minus the first).
  • Resamples (B): how many resamples to draw (default 1,000; capped at 1,000,000). More resamples steady the interval's ends; BCa in particular wants 1,000 or more.
  • Interval method: Percentile (default) or BCa (bias-corrected and accelerated), which adjusts for a skewed or biased bootstrap distribution.
  • Confidence (0–1): default 0.95.
  • Seed: the random seed (default 1). The same data, statistic, seed, resample count and method give the same interval, digit for digit, on every run and every platform.

Reading the output

One table, Bootstrap Confidence Interval, with the Observed statistic on your data, the bootstrap Bias (the resamples' mean minus the observed value), the bootstrap Std. Error (their standard deviation), and CI Lower / CI Upper. The note names the method, the level, the resample count, the seed and n. A resample on which the statistic is undefined (a correlation of a constant column; a mean difference with one group empty) is degenerate: it is excluded, and the note says how many were.

How this is computed

This section names which method each procedure prints: the estimator, the statistic, its degrees of freedom, and the tie, missing-value and weight rules. Each line links the recorded convention that explains the choice. The full index is the convention inventory; every number here is validated against independent packages per the validation suite.

  • Resampling: n cases drawn with replacement per resample, all cases together (a mean difference is not resampled within groups); the SplitMix64 generator seeded by Seed, drawn in a fixed order, so results are reproducible (resampling conventions).
  • Statistics: the standard deviation and variance use the n − 1 divisor; the coefficient of variation is SD / mean (a ratio, not a percentage; undefined at a zero mean).
  • Intervals. Percentile: the resamples' quantiles at (1 − level)/2 and (1 + level)/2. BCa: those quantiles shifted by the bias correction z₀ (from the share of resamples below the observed value) and the acceleration a, which is the jackknife of the same statistic (deterministic).
  • Missing values: listwise over the variables the statistic uses; cases an active Select Cases filter excludes are left out.
  • Weights: the bootstrap is unweighted: with Weight Cases on it resamples cases equally and says so in a note.

Reproducibility

Each run journals a syntax command, for example:

bootstrap_ci variable=income, statistic=median, ci_method=bca, replicates=2000

This is the tool bootstrap_ci, available to the AI assistant, MCP and batch scripts like every analysis. See the command reference for every argument.