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Sign Test Calculator

Perform a sign test on paired data using only the direction of differences.

About Sign Test Calculator

The sign test is the simplest paired test, requiring only the direction of each difference. Tied pairs are discarded, which reduces the effective sample size. Discarding magnitude makes the sign test less powerful than Wilcoxon, but it requires almost no assumptions and works on purely ordinal data.

Formula

Sign Test

Under the no-effect hypothesis positives follow a binomial with p = 0.5; z = (positives − n/2) ÷ √(n/4)

sign test
Uses only the direction of each difference, discarding magnitude

Worked example

With the default values below, Sign Test Calculator returns Z Statistic of 2.35702. Change any input above and every figure here is recalculated in your browser.

Inputs used

Positive differencesminimum 0
14
Negative differencesminimum 0
4
Significance levelaccepts 0.1–20 %
5 %

Results

Z Statistic
2.35702
Non-Tied Pairs
18
Expected Positives Under the Null
9.00
Proportion Positive
77.778%
Decision
Reject H0 — the direction of change is not random

Step by step

  1. 1Values used
  2. 2Sign Test
  3. 3Z Statistic= 2.35702
  4. 4Non-Tied Pairs= 18
  5. 5Expected Positives Under the Null= 9.00
  6. 6Proportion Positive= 77.778
  7. 7Decision= Reject H0 — the direction of change is not random

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Sign Test calculated?

Under the no-effect hypothesis positives follow a binomial with p = 0.5; z = (positives − n/2) ÷ √(n/4) The sign test is the simplest paired test, requiring only the direction of each difference. Tied pairs are discarded, which reduces the effective sample size.

Why does Sign Test matter?

Discarding magnitude makes the sign test less powerful than Wilcoxon, but it requires almost no assumptions and works on purely ordinal data.

What values do I need to enter?

This calculator takes 3 inputs: Positive differences, Negative differences, Significance level. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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