SKEWTEST

Overview

The SKEWTEST function tests whether the skewness of a sample is different from that of a normal distribution. This is useful for assessing the symmetry of a dataset and determining if it deviates from normality. The test computes a z-score for the skewness and a corresponding p-value, based on the D’Agostino test:

z = \frac{\sqrt{n(n-1)}}{n-2} \cdot \frac{m_3}{m_2^{3/2}}

where $m_3$ is the third central moment and $m_2$ is the second central moment (variance). For more details, see the scipy.stats.skewtest documentation .

This example function is provided as-is without any representation of accuracy.

Usage

To use the function in Excel:


=SKEWTEST(data)

data (2D list, required): Sample data. Must contain at least 8 elements (as a column or row vector).

The function returns a 2D list with two values: the test statistic (z-score) and the p-value. If the input is invalid, an error message is returned as a string.

Examples

Example 1: Symmetric Data

Inputs:

data
1
2
3
4
5
6
7
8

Excel formula:


=SKEWTEST({1;2;3;4;5;6;7;8})

Expected output:

Statistic	P-value
1.010805	0.312110

Example 2: Skewed Data

Inputs:

data
1
2
3
4
5
6
7
8000

Excel formula:


=SKEWTEST({1;2;3;4;5;6;7;8000})

Expected output:

Statistic	P-value
3.571774	0.000355

Example 3: Repeated Values

Inputs:

data
100
100
100
100
100
100
100
101

Excel formula:


=SKEWTEST({100;100;100;100;100;100;100;101})

Expected output:

Statistic	P-value
3.571777	0.000355

Example 4: Mixed Data

Inputs:

data
2
8
0
4
1
9
9
0

Excel formula:


=SKEWTEST({2;8;0;4;1;9;9;0})

Expected output:

Statistic	P-value
0.446264	0.655407

Python Code


from scipy.stats import skewtest as scipy_skewtest
 
def skewtest(data):
    """
    Test whether the skewness of a sample is different from that of a normal distribution.
 
    Args:
        data: 2D list. Sample data (must contain at least 8 elements).
 
    Returns:
        2D list. Test statistic and p-value, or an error message (str) if input is invalid.
 
    This example function is provided as-is without any representation of accuracy.
    """
    # Validate input is a 2D list with at least 8 elements
    if not isinstance(data, list) or len(data) < 8:
        return "Invalid input: data must be a 2D list with at least 8 elements."
    try:
        # Flatten 2D list to 1D
        flat = [float(row[0]) if isinstance(row, list) and len(row) == 1 else float(row) for row in data]
    except Exception:
        return "Invalid input: data must be numeric."
    if len(flat) < 8:
        return "Invalid input: data must contain at least 8 elements."
    try:
        result = scipy_skewtest(flat)
        stat = float(result.statistic)
        pval = float(result.pvalue)
        # Check for nan/inf
        if any([x != x or x == float('inf') or x == float('-inf') for x in [stat, pval]]):
            return "Invalid result: nan or inf encountered."
        return [[stat, pval]]
    except Exception as e:
        return f"scipy.stats.skewtest error: {e}"

Example Workbook

Link to Workbook