KRUSKAL

Overview

The KRUSKAL function performs the Kruskal-Wallis H-test for independent samples, a non-parametric statistical test used to determine whether there are statistically significant differences between the medians of two or more groups. Unlike one-way ANOVA, Kruskal-Wallis does not assume normality or equal variances, making it suitable for ordinal or non-normally distributed data. The test statistic is calculated as:

H = \frac{12}{N(N+1)} \sum_{i=1}^k n_i (R_i - \bar{R})^2

where $N$ is the total number of observations, $k$ is the number of groups, $n_i$ is the number of observations in group $i$ , $R_i$ is the average rank of group $i$ , and $\bar{R}$ is the overall average rank. For more details, see the scipy.stats.kruskal documentation .

This wrapper simplifies the function to accept only the most commonly used parameter: a 2D list of samples, with each column representing a group. Parameters such as nan_policy, axis, and keepdims are excluded for Excel compatibility. This example function is provided as-is without any representation of accuracy.

Usage

To use the function in Excel:


=KRUSKAL(samples)

samples (2D list, required): Table where each column is a sample group and each row is an observation. Each group must have at least two values, and all groups must have the same number of values.

The function returns a single row with two values: the Kruskal-Wallis test statistic and the p-value, both as floats. If the input is invalid, it returns an error message (string).

Examples

Example 1: Basic Two Groups

Inputs:

samples
1.2	1.1
2.1	1.4
2.3	1.2

Excel formula:


=KRUSKAL({1.2,1.1;2.1,1.4;2.3,1.2})

Expected output:

Statistic	p-value
1.765	0.184

Example 2: Three Groups

Inputs:

samples
1.2	1.1	2.0
2.1	1.4	2.2
2.3	1.2	2.4

Excel formula:


=KRUSKAL({1.2,1.1,2.0;2.1,1.4,2.2;2.3,1.2,2.4})

Expected output:

Statistic	p-value
4.235	0.120

Example 3: All Arguments Typical

Inputs:

samples
10	15	12
20	25	22
30	35	32

Excel formula:


=KRUSKAL({10,15,12;20,25,22;30,35,32})

Expected output:

Statistic	p-value
0.800	0.670

Example 4: Groups with Ties

Inputs:

samples
1	2	1
2	2	1
2	3	1

Excel formula:


=KRUSKAL({1,2,1;2,2,1;2,3,1})

Expected output:

Statistic	p-value
5.627	0.060

Python Code


from scipy.stats import kruskal as scipy_kruskal
from typing import List, Union
 
def kruskal(samples: List[List[float]]) -> Union[List[List[float]], str]:
    """
    Computes the Kruskal-Wallis H-test for independent samples.
 
    Args:
        samples: 2D list of float values. Each column represents a sample group.
 
    Returns:
        2D list with a single row: [statistic, pvalue], or an error message (str) if input is invalid.
 
    This example function is provided as-is without any representation of accuracy.
    """
    # Validate input type
    if not isinstance(samples, list) or len(samples) < 2:
        return "Invalid input: samples must be a 2D list with at least two columns (groups)."
    # Check each column is a list with at least two elements
    try:
        columns = []
        n_rows = None
        for col in samples:
            if not isinstance(col, list) or len(col) < 2:
                return "Invalid input: each sample group must be a list with at least two values."
            # Check all elements are float/int
            for v in col:
                if not isinstance(v, (int, float)):
                    return "Invalid input: all sample values must be numeric."
            if n_rows is None:
                n_rows = len(col)
            elif n_rows != len(col):
                return "Invalid input: all sample groups must have the same number of values."
            columns.append([float(x) for x in col])
    except Exception:
        return "Invalid input: samples must be a 2D list of numeric values."
    # Run test
    try:
        result = scipy_kruskal(*columns)
    except Exception as e:
        return f"scipy.stats.kruskal error: {e}"
    # Convert np.float64 to float for output
    stat = float(result.statistic)
    pval = float(result.pvalue)
    if any([x is None or not isinstance(x, (int, float)) for x in [stat, pval]]):
        return "Invalid output from scipy.stats.kruskal."
    return [[stat, pval]]

Example Workbook

Link to Workbook