Wilcoxon Rank Sum

Calculate a two-group Wilcoxon rank-sum statistic with averaged tied ranks.

Description

The Wilcoxon rank-sum statistic compares two groups by ranks rather than raw magnitudes.

The Wilcoxon rank-sum statistic compares two groups by ranks rather than raw magnitudes. Equal observations share the average of their occupied ranks.^[1]

Calculate a two-group Wilcoxon rank-sum statistic with averaged tied ranks.

When to use Wilcoxon Rank Sum

Use this tool to calculate a two-group Wilcoxon rank-sum statistic with averaged tied ranks.

Prepare the upstream counts, expression values, sequences or record lists requested by this tool. Keep corresponding features in the same order and confirm count units, transformations and caller-selected criteria.

How to use Wilcoxon Rank Sum and understand its results

Prepare the upstream counts, expression values, sequences or record lists requested by this tool. Keep corresponding features in the same order and confirm count units, transformations and caller-selected criteria.
Enter groupOne, groupTwo using the field table and calculation rules, then run the tool.
Read rankSum, uStatistic, groupOneSize, groupTwoSize. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
groupOne	Group one	list of number	Required
groupTwo	Group two	list of number	Required

Enter two nonempty finite observation lists; their lengths need not match. Pool and sort values, assign average tied ranks and sum ranks for group one. Return that rank sum, its U statistic and both sizes.

U₁=rankSum₁−n₁(n₁+1)/2

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
rankSum	Rank sum	number
uStatistic	U statistic	number
groupOneSize	Group one size	number
groupTwoSize	Group two size	number

json

{
  "input": {
    "groupOne": [
      1,
      2
    ],
    "groupTwo": [
      3,
      4
    ]
  },
  "output": {
    "rankSum": 3,
    "uStatistic": 0,
    "groupOneSize": 2,
    "groupTwoSize": 2
  }
}

Limitations and assumptions

No exact or approximate p-value, tie correction for variance or effect-size inference is computed. Independent observations and the scientific interpretation remain caller responsibilities.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Dye Swap Correlation: Correlate forward dye ratios with sign-reversed dye-swap replicates. For a complementary task, use Batch Effect Screen: Screen batch-level mean shifts relative to within-batch variation.

References

Wilcoxon Rank Sum — tool.io

Similar or alternative tools

Dye Swap Correlation
Correlate forward dye ratios with sign-reversed dye-swap replicates.
Batch Effect Screen
Screen batch-level mean shifts relative to within-batch variation.