KURTOSISTEST

Overview

The KURTOSISTEST function tests whether the kurtosis of a sample is different from that of a normal distribution. This is useful in statistics for assessing the “tailedness” of the probability distribution of a real-valued random variable. The test returns a z-score and a p-value, indicating whether the sample kurtosis significantly deviates from normality. For more details, see the scipy.stats.kurtosistest documentation .

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

Usage

To use the function in Excel:


=KURTOSISTEST(data)

data (2D list, required): Table or column vector of sample data (must contain at least 20 elements).

The function returns a 2D list: the first element is the z-score (float), and the second is the p-value (float), or an error message (string) if the input is invalid.

Examples

Example 1: Normal Data

Inputs:

data
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

Excel formula:


=KURTOSISTEST({1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20})

Expected output:

z-score	p-value
-1.7058	0.0880

Example 2: High Kurtosis Data

Inputs:

data
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
100

Excel formula:


=KURTOSISTEST({1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;100})

Expected output:

z-score	p-value
4.6940	0.0000

Example 3: Low Kurtosis Data

Inputs:

data
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
100

Excel formula:


=KURTOSISTEST({1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;100})

Expected output:

z-score	p-value
4.4793	0.0000

Example 4: All Same Value

Inputs:

data
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5

Excel formula:


=KURTOSISTEST({5;5;5;5;5;5;5;5;5;5;5;5;5;5;5;5;5;5;5;5})

Expected output:

z-score	p-value
nan	nan

Python Code


from scipy.stats import kurtosistest as scipy_kurtosistest
 
def kurtosistest(data):
    """
    Test whether the kurtosis of a sample is different from that of a normal distribution.
 
    Args:
        data: 2D list. Sample data (must contain at least 20 elements).
 
    Returns:
        2D list: [[z-score, 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
    if not isinstance(data, list) or len(data) < 20:
        return "Invalid input: data must be a 2D list with at least 20 elements."
    # Flatten 2D list to 1D
    try:
        flat = [float(row[0]) if isinstance(row, list) else float(row) for row in data]
    except Exception:
        return "Invalid input: data must contain numeric values."
    if len(flat) < 20:
        return "Invalid input: data must contain at least 20 numeric values."
    try:
        z, p = scipy_kurtosistest(flat)
    except Exception as e:
        return f"scipy.stats.kurtosistest error: {e}"
    # Check for nan/inf
    if any([x is None or isinstance(x, str) for x in [z, p]]):
        return "Invalid result: z-score or p-value is not a number."
    import math
    if any([math.isnan(z), math.isnan(p), math.isinf(z), math.isinf(p)]):
        return [["nan", "nan"]]
    return [[z, p]]

Example Workbook

Link to Workbook