Confidence Interval Reporting

A confidence interval communicates the precision of an estimate. A p-value communicates only whether the estimate cleared a threshold. Replacing p-values with CIs —or combining both —is the explicit preference of most major journals, and omitting CIs is a growing cause of manuscript rejection.

STEP 1 —The Pitfall

A p-value of 0.04 with a 95% CI of [0.01, 14.2] and a p-value of 0.04 with a 95% CI of [1.8, 2.3] carry fundamentally different implications for reproducibility and clinical translation. Without the CI, readers cannot distinguish between a precise estimate that barely cleared significance and a wildly imprecise estimate that happened to exclude zero.

In small-sample biology, CIs are often enormous —and reporting them is uncomfortable. Many researchers omit CIs precisely when they are most informative: when the estimate is uncertain.

[Image placeholder: Forest plot style display showing three estimates with identical p=0.04 but very different 95% CIs —one narrow (precise), one wide (uncertain), one skewed. Shows why CI is more informative than p-value alone.]

Identical p-values, entirely different levels of precision. The CI is the information; the p-value is a derived threshold.

STEP 2 —Journal Requirement

CONSORT, STROBE, ARRIVE 2.0, and the ICMJE Uniform Requirements all require CI reporting. Nature's statistics checklist: "Are confidence intervals reported for all key statistics?" The BMJ requires CIs for all main results and treats their absence as a condition for mandatory revision.

STEP 3 —Licklider Solution

Input

Test result and effect size from the analysis pipeline
Sample sizes per group
Declared alpha level (default 0.05 x95% CI)

Output

95% CI auto-calculated for all test statistics using parametric or bootstrap methods
CI for effect size (Cohen's d CI, eta² CI) calculated separately using non-central distributions
CI displayed in figure legend in standard notation: estimate [lower, upper]
Null CI cases (e.g., fixed-parameter descriptive models with no inferential component) explicitly disclosed as "CI not applicable —descriptive analysis"
Validity Score dimension: Fail if CI absent from any inferential result in publication-ready export

Guard

CI reporting is blocking for publication-ready export. The guard is satisfied either by providing the CI value or by explicitly marking the analysis as descriptive (non-inferential) via Outcome Type Lock —in which case CI absence is disclosed, not flagged as an error.

[Image placeholder: Licklider estimation plot (Gardner-Altman style) showing raw data distribution, mean difference, and 95% CI in a dedicated bottom panel. The CI is the visual focus, not the p-value.]

Estimation plot format: CI is the primary display. p-value is supplementary, not the centerpiece.

STEP 4 —Draft Output (Draft / Needs review)

Mean difference = 3.2 units (95% CI [1.8, 4.6]), Cohen's d = 0.82
(95% CI [0.35, 1.27]), t(24) = 4.11, p = 0.0004, two-tailed.
CI computed using the non-central t-distribution.