Normal-approximation interval around a reported effect

Read the equation

Multiplying the stated standard error 2.1 by 1.96 and adding and subtracting it from 11.3 yields [7.184,15.416] percentage points. The calculation is a conventional approximate 95% interval under a normal sampling approximation. Its coverage depends on the reported standard error and study design being appropriate.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

Subtracting the rounded marginals gives 11.4 points, while the separately published gap is 11.3. Independent rounding can account for this 0.1-point difference; it is not evidence of a calculation error in the source. We preserve the published contrast for interval arithmetic rather than silently replacing it.

Using a normal approximation with the reported standard error:

11.3±1.962.1=7.184,15.416 percentage points.

This interval is approximate. It is not a new bootstrap, does not account for uncertainties not captured by the source standard error, and does not establish a mechanism for the difference.

Published condition

Alignment-faking reasoning

11.3±1.96\left(2.1\right)=\left[7.184,15.416\right] percentage points.