How to use this calculator
- Enter or choose 5 (very satisfied).
- Enter or choose 4 (satisfied).
- Enter or choose 3 (neutral).
- Enter or choose 2 (dissatisfied).
- Enter or choose 1 (very dissatisfied).
- The top-box score (5s) updates as you type. Use Copy result or Share to keep it.
Method
Top box = n₅ ÷ n; Mean = Σ k·nₖ ÷ n; Wilson interval = [p + z²/2n ± z√(p(1−p)/n + z²/4n²)] ÷ (1 + z²/n)
- nₖ
- number of responses scoring k
- n
- total responses
- p
- top-box proportion
- z
- 1.645, 1.960 or 2.576 for 90%, 95% or 99% confidence
Worked example
- n = 50 + 35 + 10 + 3 + 2 = 100; top box = 50 ÷ 100 = 50%; top two = 85%.
- Mean = (5×50 + 4×35 + 3×10 + 2×3 + 1×2) ÷ 100 = 4.28.
- Wilson 95% interval for 50 of 100: 40.4% to 59.6%.
Half of 100 patients gave the top score; the true top-box rate is plausibly between about 40% and 60%.
What the result means
Top-box scores are more sensitive to change than means, which bunch near the top of the scale. Wide intervals mean small samples: avoid ranking clinicians or units whose intervals overlap heavily.
Assumptions and limits
- Responses are a random sample of patients and are independent.
- The interval is for the top-box rate only.
- No adjustment for patient mix or survey mode, which official programmes such as HCAHPS apply.
- Non-response bias is not addressed: patients who reply may differ from those who do not.
Questions
Why use top-box rather than the mean?
The mean treats the scale as evenly spaced and hides the share of truly delighted patients. Top-box is easy to explain and to track over time.
Why a Wilson interval?
It behaves well for small samples and for rates near 0% or 100%, where the simple normal approximation gives impossible limits.