Paired mean difference interval worksheet
StatMedAnalysis | Version 2026-11-05

Instructions: save a working copy, fill blank fields, retain assumptions and
record an independent arithmetic check. Use fictional or aggregate values;
do not enter patient identifiers. This is a planning aid, not clinical advice.

1. Define pairs and direction
Pairing unit and why pairs are independent of other pairs: ________
Difference definition (e.g. after minus before) and units: _________
Eligible pairs: ______ Complete pairs: ______ Missing pairs: ______
Reasons for missing measurements and possible selection: __________

2. Audit the summary
Mean within-pair difference: _____________________________________
Sample SD of within-pair differences: _____________________________
Source of SD (not a marginal SD and not an SE): ____________________
Distribution/outlier review, especially for small n: ______________
Normal differences are required for exact small-sample t inference.
A large sample does not remove dependence or selection bias.

3. Calculate a two-sided 95% interval
Require n >= 2 whole complete pairs and SDdiff > 0.
n complete pairs: ______ df=n-1: ______ SE=SDdiff/sqrt(n): _________
t critical = t quantile(.975, df): _______________________________
Margin = critical * SE: __________________________________________
Lower = mean difference-margin: _____ Upper=mean difference+margin: ___
Hypothetical n=25, mean difference=2, SDdiff=5: SE=1, df=24,
t=2.063899, interval approximately -0.063899 to 4.063899.

4. Interpret
Estimate and interval in original units: _________________________
Meaningful effect threshold and justification: ____________________
Avoid saying a CI crossing zero proves no effect. A paired summary
alone does not establish causality or predict an individual's change.
If SD=0, investigate the data and measurement resolution; this tool
rejects the degenerate input rather than returning false precision.
Prepared by/date/version: __________ Independent check: __________

Guide and primary-source links (verified 2026-11-05):
https://www.statmedanalysis.com/blog/paired-mean-confidence-interval
https://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm
https://www.statmedanalysis.com/tools/paired-t-summary