FLIGNER

Overview

The FLIGNER function performs the Fligner-Killeen test for equality of variances across multiple sample groups. This non-parametric test is robust to departures from normality and is useful for comparing the spread of data in more than two groups, unlike parametric tests such as the F-test which assume normality. The test statistic is based on ranks and can use different measures of central tendency (mean, median, or trimmed mean):

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

where $n_i$ is the size of group $i$ , $R_i$ is the average rank for group $i$ , and $\bar{R}$ is the overall average rank. For more details, see the scipy.stats.fligner documentation .

This wrapper simplifies the function to only the most commonly used parameters: samples, center, and (optionally) trimmed_proportion if center is set to trimmed. 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:


=FLIGNER(samples, [center], [trimmed_proportion])

samples (2D list, required): Each column is a sample group. Must have at least two columns and each column must be a non-empty list of numbers.
center (string, optional, default='median'): Central tendency function to use. One of 'mean', 'median', or 'trimmed'.
trimmed_proportion (float, optional, required only if center is 'trimmed'): Proportion to cut from each end when using trimmed mean. Must be between 0 and <0.5.

The function returns a single-row 2D list: [statistic, pvalue], or an error message (string) if the input is invalid. The statistic measures the evidence against the null hypothesis (equal variances), and the p-value indicates the probability of observing such a statistic under the null hypothesis.

Examples

Example 1: Basic Case (Median Center)

Inputs:

samples			center
1.2	2.5	1.9	median
2.3	2.7	2.0
2.1	2.8	2.2

Excel formula:


=FLIGNER({1.2,2.5,1.9;2.3,2.7,2.0;2.1,2.8,2.2}, "median")

Expected output:

statistic	pvalue
0.516	0.772

Example 2: Mean Center

Inputs:

samples			center
1.2	2.5	1.9	mean
2.3	2.7	2.0
2.1	2.8	2.2

Excel formula:


=FLIGNER({1.2,2.5,1.9;2.3,2.7,2.0;2.1,2.8,2.2}, "mean")

Expected output:

statistic	pvalue
5.859	0.053

Example 3: Trimmed Center (0.1 Proportion)

Inputs:

samples			center	trimmed_proportion
1.2	2.5	1.9	trimmed	0.1
2.3	2.7	2.0
2.1	2.8	2.2

Excel formula:


=FLIGNER({1.2,2.5,1.9;2.3,2.7,2.0;2.1,2.8,2.2}, "trimmed", 0.1)

Expected output:

statistic	pvalue
5.859	0.053

Example 4: Different Values (Median Center)

Inputs:

samples			center
1.0	2.0	3.0	median
1.1	2.1	3.1
1.2	2.2	3.2

Excel formula:


=FLIGNER({1.0,2.0,3.0;1.1,2.1,3.1;1.2,2.2,3.2}, "median")

Expected output:

statistic	pvalue
0.391	0.822

Python Code


from scipy.stats import fligner as scipy_fligner
from typing import List, Optional, Union
 
def fligner(samples: List[List[float]], center: str = 'median', trimmed_proportion: Optional[float] = None) -> Union[List[List[float]], str]:
    """
    Performs the Fligner-Killeen test for equality of variances across multiple samples.
 
    Args:
        samples: 2D list of float values. Each column represents a sample group.
        center: Function of central tendency to use ('mean', 'median', 'trimmed'). Default is 'median'.
        trimmed_proportion: Proportion to cut from each end when center is 'trimmed'. Optional.
 
    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 samples
    if not isinstance(samples, list) or len(samples) < 2:
        return "Invalid input: samples must be a 2D list with at least two columns (sample groups)."
    if not all(isinstance(col, list) and len(col) > 0 for col in samples):
        return "Invalid input: each sample group must be a non-empty list."
    # Transpose if rows are samples (Excel usually passes columns as samples)
    if len(samples) > 0 and len(samples[0]) > 0 and all(isinstance(x, (int, float)) for x in samples[0]):
        # Assume columns are samples
        sample_groups = samples
    else:
        return "Invalid input: samples must be a 2D list of floats, each column a sample group."
    # Validate center
    if center not in ('mean', 'median', 'trimmed'):
        return "Invalid input: center must be 'mean', 'median', or 'trimmed'."
    # Validate trimmed_proportion
    if center == 'trimmed':
        if trimmed_proportion is None:
            return "Invalid input: trimmed_proportion must be specified when center is 'trimmed'."
        try:
            proportiontocut = float(trimmed_proportion)
        except Exception:
            return "Invalid input: trimmed_proportion must be a float."
        if not (0 <= proportiontocut < 0.5):
            return "Invalid input: trimmed_proportion must be between 0 and 0.5."
    else:
        proportiontocut = None
    # Run test
    try:
        if center == 'trimmed':
            stat, pvalue = scipy_fligner(*sample_groups, center=center, proportiontocut=proportiontocut)
        else:
            stat, pvalue = scipy_fligner(*sample_groups, center=center)
    except Exception as e:
        return f"scipy.stats.fligner error: {e}"
    # Convert numpy types to Python float
    try:
        stat = float(stat)
        pvalue = float(pvalue)
    except Exception:
        return "Invalid output: could not convert result to float."
    # Validate output
    if any([
        not isinstance(stat, (int, float)),
        not isinstance(pvalue, (int, float)),
        stat is None or pvalue is None
    ]):
        return "Invalid output from scipy.stats.fligner."
    # Disallow nan/inf
    import math
    if any([math.isnan(stat), math.isnan(pvalue), math.isinf(stat), math.isinf(pvalue)]):
        return "Invalid output: statistic or pvalue is nan or inf."
    return [[stat, pvalue]]

Example Workbook

Link to Workbook