KONSİLCalculator · deterministic
Paired t-test sample size calculator
Before–after in the same person, or two methods on the same subjects: complete records from dz.
Calculator
No AI, no sign-up — the arithmetic runs in the server-side deterministic solver, validated against G*Power and R pwr.
When to use it
Use this when every participant is their own control: pre–post measurements, two imaging methods in the same patient, two lab techniques on the same sample. The denominator is different here: what enters the calculation is the SD of the change scores, which depends on the pre–post correlation — not the raw measurement SD.
Where the inputs come from
- dz: SDchange = √(SD₁² + SD₂² − 2r·SD₁·SD₂). With pre/post SD 3 and r = 0.70 the change SD is 2.32, so a 1.5-point target change gives dz ≈ 0.65. The derivation is in the effect size guide.
- Where r comes from: publications that applied the same measure twice, or a cautious pilot; otherwise run a sensitivity scenario across 0.5–0.7.
Worked example
With dz = 0.50, two-sided α = 0.05 and 80% power the solver requires 34 complete records (participants with both measurements). At 20% attrition the recruitment target becomes 43. Chase the same goal with dz = 0.20 and the number rises to 199 — that is the price of the denominator.
How to write it in the protocol
“For the primary outcome [measure], the target mean change [Δ] and the change-score SD [value, with source] gave dz = [value]. A paired t test with two-sided α = 0.05 and 80% power required [n] complete records; allowing [x]% attrition, [N] participants were targeted.”
Sources
- Cohen J. Statistical Power Analysis for the Behavioral Sciences, 2nd ed. Lawrence Erlbaum; 1988.
- Faul F, Erdfelder E, Lang A-G, Buchner A. G*Power 3: a flexible statistical power analysis program. Behav Res Methods. 2007;39:175–191.
- Champely S. pwr: Basic Functions for Power Analysis (R package).