ALEXANDERGOVERN

Overview

The ALEXANDERGOVERN function performs the Alexander-Govern test for equality of means across multiple independent groups, allowing for heterogeneity of variance. This robust alternative to one-way ANOVA is useful when the assumption of equal variances is violated. The test statistic is computed as described in the SciPy documentation :

AG = \frac{\sum_{j=1}^k w_j (\bar{x}_j - \bar{x})^2}{\sum_{j=1}^k w_j s_j^2 / n_j}

where $w_j$ is the weight for group $j$ , $\bar{x}_j$ is the mean of group $j$ , $\bar{x}$ is the overall mean, $s_j^2$ is the variance of group $j$ , and $n_j$ is the sample size of group $j$ .

This wrapper exposes only the most commonly used parameter: a 2D array of samples, where each column is a group and each row is an observation. Parameters such as nan_policy, axis, and keepdims are omitted for Excel compatibility. This example function is provided as-is without any representation of accuracy.

Usage

To use the function in Excel:


=ALEXANDERGOVERN(samples)

samples (2D list, required): Table of numeric values. Each column represents a group/sample; each row an observation. Must have at least two columns and two rows.

The function returns a single-row 2D array: [statistic, pvalue] (both floats), or an error message (string) if the input is invalid. The statistic quantifies the difference in means across groups, and the p-value indicates the probability of observing such a difference under the null hypothesis of equal means.

Examples

Example 1: Two Groups, Basic

Inputs:

samples
1.2	2.3
1.5	2.1
1.3	2.2
1.4	2.4

Excel formula:


=ALEXANDERGOVERN({1.2,2.3;1.5,2.1;1.3,2.2;1.4,2.4})

Expected output:

statistic	pvalue
15.074	0.000

Example 2: Three Groups

Inputs:

samples
1.2	2.3	3.1
1.5	2.1	3.2
1.3	2.2	3.0
1.4	2.4	3.3

Excel formula:


=ALEXANDERGOVERN({1.2,2.3,3.1;1.5,2.1,3.2;1.3,2.2,3.0;1.4,2.4,3.3})

Expected output:

statistic	pvalue
22.510	0.000

Example 3: Groups with Close Means

Inputs:

samples
10.0	10.1
10.2	10.0
10.1	10.2
10.0	10.1

Excel formula:


=ALEXANDERGOVERN({10.0,10.1;10.2,10.0;10.1,10.2;10.0,10.1})

Expected output:

statistic	pvalue
0.132	0.716

Example 4: Groups with Different Variance

Inputs:

samples
1.0	10.0
1.1	10.1
0.9	9.9
1.2	10.2

Excel formula:


=ALEXANDERGOVERN({1.0,10.0;1.1,10.1;0.9,9.9;1.2,10.2})

Expected output:

statistic	pvalue
40.811	0.000

Python Code


from scipy.stats import alexandergovern as scipy_alexandergovern
from typing import List, Union
 
def alexandergovern(samples: List[List[float]]) -> Union[List[List[float]], str]:
    """
    Performs the Alexander-Govern test for equality of means across multiple independent samples with possible heterogeneity of variance.
 
    Args:
        samples: 2D list of float values. Each column represents a group/sample; each row an observation.
 
    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 and shape
    if not isinstance(samples, list) or len(samples) < 2:
        return "Invalid input: samples must be a 2D list with at least two rows."
    if not all(isinstance(row, list) for row in samples):
        return "Invalid input: samples must be a 2D list."
    n_cols = len(samples[0])
    if n_cols < 2:
        return "Invalid input: samples must have at least two columns (groups)."
    for row in samples:
        if len(row) != n_cols:
            return "Invalid input: all rows must have the same number of columns."
        for val in row:
            if not isinstance(val, (int, float)):
                return "Invalid input: all values must be numeric."
    # Transpose to columns as groups
    groups = [ [row[col] for row in samples] for col in range(n_cols) ]
    try:
        result = scipy_alexandergovern(*groups)
    except Exception as e:
        return f"scipy.stats.alexandergovern error: {e}"
    stat, pvalue = float(result.statistic), float(result.pvalue)
    # Check for nan/inf
    if any([isinstance(x, float) and (x != x or x == float('inf') or x == float('-inf')) for x in [stat, pvalue]]):
        return "Invalid result: statistic or pvalue is nan or inf."
    return [[stat, pvalue]]

Example Workbook

Link to Workbook