CRAMERVONMISES_2SAMP

Overview

The CRAMERVONMISES_2SAMP function performs the two-sample Cramér-von Mises test for goodness of fit between two independent samples. This test evaluates whether two samples come from the same continuous distribution, providing a statistic and p-value. It is more sensitive to differences in the tails of distributions than the Kolmogorov-Smirnov test. The test statistic is computed as:

W^2 = \frac{nm}{(n+m)^2} \sum_{i=1}^{n+m} \left[ F_n(X_i) - G_m(X_i) \right]^2

where $F_n$ and $G_m$ are the empirical distribution functions of the two samples, and $n$ , $m$ are their sizes. For more details, see the scipy.stats.cramervonmises_2samp documentation .

This wrapper exposes only the most commonly used parameters: the two samples and the method for p-value calculation. Parameters related to array axis, NaN handling, and broadcasting are omitted for Excel compatibility. This example function is provided as-is without any representation of accuracy.

Usage

To use the function in Excel:


=CRAMERVONMISES_2SAMP(x, y, [method])

x (2D list, required): First sample data. Must be a table with at least two rows, each containing one or more numeric values.
y (2D list, required): Second sample data. Must be a table with at least two rows, each containing one or more numeric values.
method (string, optional, default='auto'): Method to compute p-value. Allowed values: 'auto', 'asymptotic', 'exact'.

The function returns a single-row 2D array: [statistic, pvalue], or an error message (string) if the input is invalid. The statistic quantifies the difference between distributions; the p-value indicates the probability of observing such a difference under the null hypothesis.

Examples

Example 1: Basic Case (auto method)

Inputs:

x	y
1.0	1.5
2.0	2.5
3.0	3.5
4.0	4.5

Excel formula:


=CRAMERVONMISES_2SAMP({1.0;2.0;3.0;4.0}, {1.5;2.5;3.5;4.5})

Expected output:

statistic	pvalue
0.063	1.000

Example 2: Asymptotic Method

Inputs:

x	y	method
1.0	1.5	asymptotic
2.0	2.5
3.0	3.5
4.0	4.5

Excel formula:


=CRAMERVONMISES_2SAMP({1.0;2.0;3.0;4.0}, {1.5;2.5;3.5;4.5}, "asymptotic")

Expected output:

statistic	pvalue
0.063	0.974

Example 3: Exact Method

Inputs:

x	y	method
1.0	1.5	exact
2.0	2.5
3.0	3.5
4.0	4.5

Excel formula:


=CRAMERVONMISES_2SAMP({1.0;2.0;3.0;4.0}, {1.5;2.5;3.5;4.5}, "exact")

Expected output:

statistic	pvalue
0.063	1.000

Example 4: Different Samples

Inputs:

x	y
1.0	10.0
2.0	20.0
3.0	30.0
4.0	40.0

Excel formula:


=CRAMERVONMISES_2SAMP({1.0;2.0;3.0;4.0}, {10.0;20.0;30.0;40.0})

Expected output:

statistic	pvalue
0.688	0.029

Python Code


from scipy.stats import cramervonmises_2samp as scipy_cramervonmises_2samp
from typing import List, Union
 
def cramervonmises_2samp(x: List[List[float]], y: List[List[float]], method: str = 'auto') -> Union[List[List[float]], str]:
    """
    Performs the two-sample Cramér-von Mises test for goodness of fit between two independent samples.
 
    Args:
        x: 2D list of float values. First sample data.
        y: 2D list of float values. Second sample data.
        method: Method to compute p-value ('auto', 'asymptotic', 'exact'). Default is 'auto'.
 
    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 x and y are 2D lists with at least two rows
    if not (isinstance(x, list) and all(isinstance(row, list) for row in x) and len(x) >= 2):
        return "Invalid input: x must be a 2D list with at least two rows."
    if not (isinstance(y, list) and all(isinstance(row, list) for row in y) and len(y) >= 2):
        return "Invalid input: y must be a 2D list with at least two rows."
    # Flatten x and y
    try:
        x_flat = [float(item) for row in x for item in row]
        y_flat = [float(item) for row in y for item in row]
    except Exception:
        return "Invalid input: x and y must contain only numeric values."
    if len(x_flat) < 2 or len(y_flat) < 2:
        return "Invalid input: each sample must contain at least two values."
    # Validate method
    if method not in ['auto', 'asymptotic', 'exact']:
        return "Invalid input: method must be 'auto', 'asymptotic', or 'exact'."
    # Call scipy.stats.cramervonmises_2samp
    try:
        result = scipy_cramervonmises_2samp(x_flat, y_flat, method=method)
        stat = float(result.statistic)
        pvalue = float(result.pvalue)
    except Exception as e:
        return f"scipy.stats.cramervonmises_2samp error: {e}"
    # Check for nan/inf
    if any([isinstance(val, float) and (val != val or val in [float('inf'), float('-inf')]) for val in [stat, pvalue]]):
        return "Invalid result: statistic or pvalue is nan or inf."
    return [[stat, pvalue]]

Example Workbook

Link to Workbook