Calculator inputs
Example data table
Sample classroom performance pairs| Pair | Before | After | Difference | Sign |
|---|---|---|---|---|
| 1 | 12 | 15 | 3 | Positive |
| 2 | 10 | 9 | -1 | Negative |
| 3 | 14 | 18 | 4 | Positive |
| 4 | 16 | 16 | 0 | Tie |
| 5 | 11 | 13 | 2 | Positive |
| 6 | 13 | 12 | -1 | Negative |
| 7 | 9 | 11 | 2 | Positive |
| 8 | 15 | 17 | 2 | Positive |
Formula used
The paired sign test reduces each difference to a sign. For every pair, compute di = after - before. Positive differences count as plus signs, negative differences count as minus signs, and zero differences are ties.
The effective sample size is n = plus + minus. Under the null hypothesis of no median shift, the number of positive signs follows X ~ Binomial(n, 0.5).
For a two-sided test, the exact p-value is 2 × min[P(X ≤ plus), P(X ≥ plus)], capped at 1. For one-sided tests, use the corresponding upper or lower binomial tail.
The calculator also reports a continuity-corrected normal approximation, a Wilson interval for the positive direction probability, and a sign-based confidence interval for the median difference when raw paired data are supplied.
How to use this calculator
- Select raw paired values if you have the original observations, or choose summary sign counts if you already counted positives, negatives, and ties.
- Pick the alternative hypothesis that matches your study question. Use two-sided for any shift, greater for improvement, or less for decline.
- Set the significance level, confidence level, and displayed decimals.
- Submit the form to place the result block above the calculator. Review the exact p-value first, then compare it with your significance level.
- Use the CSV or PDF buttons to save the analysis summary. When raw data are entered, the export also includes the parsed pair table.
Frequently asked questions
1. When should I use a paired sign test?
Use it for matched observations such as before-after data, repeated measures, or paired subjects when you want a robust median-direction test without assuming normal differences.
2. What happens to ties?
Tied pairs have zero difference, so they are excluded from the effective sample size. They remain visible in the summary because they still matter for data quality review.
3. Why does the calculator show two p-values?
The exact p-value comes from the binomial distribution and is preferred. The normal approximation is shown as a quick reference, especially when sample size is larger.
4. What does the sign statistic mean?
The statistic S = min(plus, minus) summarizes imbalance in sign counts. Smaller values indicate stronger evidence that the paired median difference is not zero.
5. Can I use summary counts instead of raw data?
Yes. Summary mode is useful when you already know the number of positive signs, negative signs, and ties. Raw mode is better when you also want median summaries.
6. What does “after is greater” test?
It evaluates whether positive differences occur more often than expected under no shift. Choose it when your research question specifically asks whether the second measurement tends to be larger.
7. Is this test resistant to outliers?
Yes. The paired sign test uses only the sign of each difference, not its size. That makes it far less sensitive to extreme values than magnitude-based tests.
8. Why might the exact p-value say “Not available”?
The page computes exact tails directly for practical sample sizes. If the non-tied sample becomes very large, the normal approximation still appears to keep the analysis usable.