Signed Rank Sum Calculator
Calculates the signed rank sum after removing zero paired differences and ranking absolute differences. The form displays W+−W− from nonzero paired differences beside signed-rank sum, using a worked condition that can be recalculated with the labeled inputs.
Describe the observed sequence under the stated assumptions
Signed-rank sum
What signed-rank sum answers
The signed rank sum page calculates the signed rank sum after removing zero paired differences and ranking absolute differences.
Signed-rank sum is limited to the statistical quantity named by the result panel. The signed-rank sum calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
Inputs that define signed-rank sum
- Before values: For signed-rank sum, the displayed before values sequence is 20, 18, 25, 22, 19, 24. Preserve before values order when signed-rank sum depends on pairing, lag, rank, or time position, and distinguish an observed zero from a missing before values entry.
- After values: For signed-rank sum, the displayed after values sequence is 22, 19, 27, 21, 20, 26. Preserve after values order when signed-rank sum depends on pairing, lag, rank, or time position, and distinguish an observed zero from a missing after values entry.
The entries used for signed-rank sum must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid signed-rank sum arithmetic for a nonexistent study.
From inputs to signed-rank sum
For signed-rank sum, match every symbol in the relationship to a labeled field before substituting numbers. Signed-rank sum is reported in rank units.
While checking signed-rank sum, use before values observations from one defined analysis set rather than totals copied from incompatible groups.
Worked values for signed-rank sum
The default signed-rank sum condition is Before values = 20, 18, 25, 22, 19, 24, After values = 22, 19, 27, 21, 20, 26.
The example has a signed-rank sum of 17.
The live calculator reports Signed rank sum 17 · Nonzero differences 6. Repeating one intermediate step from W+−W− from nonzero paired differences provides a fixed signed-rank sum reference check for later code changes.
Statistical context for signed rank sum
Ties receive average ranks; the sign depends on the declared after-minus-before direction.
For signed rank sum, robust and rank-based methods reduce sensitivity to particular assumptions but do not make the sampling design, independence, ties, or missing values irrelevant.
A second check on signed-rank sum
When interpreting signed rank sum, document tie handling, score convention, and the population feature the method targets before comparing implementations.
As a second check for signed-rank sum, outliers, ties, ordering, and missing entries can affect signed-rank sum even when the number of observations stays unchanged.
Varying a single signed rank sum input at a time
Change before values while holding the remaining entries fixed, then state why the direction and size of the signed-rank sum change are plausible from W+−W− from nonzero paired differences.
Repeat the signed-rank sum exercise with after values. If a modest defensible change materially alters the interpretation, report both conditions rather than presenting that signed-rank sum scenario as exact.
Documenting the signed rank sum result
Report signed-rank sum using W+−W− from nonzero paired differences, followed by the entered values, units, exclusions, and analysis date. Name the signed-rank sum population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including Signed rank sum 17 · Nonzero differences 6. A later signed-rank sum review can then distinguish a changed input from a different convention or software implementation.
The surrounding workflow may also require rank sum and empirical cumulative probability.
Questions about signed-rank sum
Which input deserves the closest boundary check?
For signed-rank sum, start with after values and then before values. Confirm the signed-rank sum units and allowed domain because a valid-looking entry can still describe the wrong statistical setup.
Why could another program report a different signed-rank sum?
A different convention for rounding, tails, ties, interpolation, parameterization, or missing values can change signed-rank sum. Compare the printed signed-rank sum formula and its input definitions before treating either output as wrong.
What does signed-rank sum represent on this page?
It is the quantity produced by W+−W− from nonzero paired differences from the displayed before values, after values. This page calculates the signed rank sum after removing zero paired differences and ranking absolute differences.
What should be saved with signed-rank sum?
Save the entered values and units for before values, after values, along with the analysis date, exclusions, software or formula version, and the relationship W+−W− from nonzero paired differences. That record is sufficient to rebuild this specific signed-rank sum calculation.
Does signed-rank sum establish a causal or population conclusion?
No. The displayed signed rank sum value is conditional on the entered data and named method. The signed-rank sum design, measurement process, and assumptions determine what can be concluded beyond those values.
How should signed-rank sum be rounded?
Keep the unrounded signed-rank sum for subsequent arithmetic, then report only the precision supported by the source measurements and the decision context. Extra digits in signed-rank sum do not correct sampling or model error.