MOOD

Overview

The MOOD function performs Mood’s two-sample test for scale parameters, a non-parametric test used to determine if two independent samples differ in their scale (variance). Unlike parametric tests such as the F-test, Mood’s test does not require the assumption of normality and is robust to outliers. The test statistic is based on the ranks of the combined samples:

M = \frac{\sum_{i=1}^{n_1} I(|x_i - \text{median}| > |y_j - \text{median}|)}{n_1 n_2}

where $x$ and $y$ are the two samples, and $I$ is the indicator function. For more details, see the scipy.stats.mood documentation .

This Excel wrapper simplifies the function by only exposing the most commonly used parameters: the two sample arrays and the alternative hypothesis. Parameters such as axis, nan_policy, 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:


=MOOD(x, y, [alternative])

x (2D list, required): First sample group. Must be a 2D array (table) with at least two rows.
y (2D list, required): Second sample group. Must be a 2D array (table) with at least two rows.
alternative (string, optional, default="two-sided"): Defines the alternative hypothesis. Must be one of "two-sided", "less", or "greater".

The function returns a 2D array with two float values: [[statistic, pvalue]], or an error message (string) if the input is invalid. The statistic measures the difference in scale between the two samples, and the p-value indicates the significance of the result.

Examples

Example 1: Basic Two-Sided Test

Inputs:

x		y		alternative
1.2	2.3	2.1	3.2	two-sided
3.4	4.5	4.3	5.4

Excel formula:


=MOOD({1.2,2.3;3.4,4.5}, {2.1,3.2;4.3,5.4})

Expected output:

Statistic	P-value
0.000	1.000

Example 2: “Less” Alternative

Inputs:

x		y		alternative
1.2	2.3	2.1	3.2	less
3.4	4.5	4.3	5.4

Excel formula:


=MOOD({1.2,2.3;3.4,4.5}, {2.1,3.2;4.3,5.4}, "less")

Expected output:

Statistic	P-value
0.000	0.500

Example 3: “Greater” Alternative

Inputs:

x		y		alternative
1.2	2.3	2.1	3.2	greater
3.4	4.5	4.3	5.4

Excel formula:


=MOOD({1.2,2.3;3.4,4.5}, {2.1,3.2;4.3,5.4}, "greater")

Expected output:

Statistic	P-value
0.000	0.500

Example 4: Different Samples

Inputs:

x		y		alternative
10.0	12.0	1.0	2.0	two-sided
14.0	16.0	3.0	4.0

Excel formula:


=MOOD({10.0,12.0;14.0,16.0}, {1.0,2.0;3.0,4.0})

Expected output:

Statistic	P-value
0.000	1.000

Python Code


from scipy.stats import mood as scipy_mood
from typing import List, Union
 
def mood(x: List[List[float]], y: List[List[float]], alternative: str = 'two-sided') -> Union[List[List[float]], str]:
    """
    Performs Mood's two-sample test for scale parameters (non-parametric).
 
    Args:
        x: 2D list of float values. First sample group.
        y: 2D list of float values. Second sample group.
        alternative: Defines the alternative hypothesis ('two-sided', 'less', 'greater'). Default is 'two-sided'.
 
    Returns:
        2D list with two float values: [[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 alternative
    if alternative not in ['two-sided', 'less', 'greater']:
        return "Invalid input: alternative must be 'two-sided', 'less', or 'greater'."
    # Call scipy.stats.mood
    try:
        stat, pvalue = scipy_mood(x_flat, y_flat, alternative=alternative)
    except Exception as e:
        return f"scipy.stats.mood error: {e}"
    # Convert numpy types to Python float
    try:
        stat = float(stat)
        pvalue = float(pvalue)
    except Exception:
        return "Invalid result: could not convert output to float."
    # 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