NORMALTEST

Overview

The NORMALTEST function tests whether a sample differs from a normal distribution using D’Agostino and Pearson’s omnibus test. This test combines measures of skewness and kurtosis to determine if the data significantly deviates from normality. It is commonly used in statistics to check the normality assumption before applying parametric tests. For more details, see the scipy.stats.normaltest documentation .

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

Usage

To use the function in Excel:


=NORMALTEST(data)

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

The function returns a 2D list with two values: the test statistic and the p-value. If the input is invalid, it returns a string error message.

Examples

Example 1: Normal Data

Inputs:

data
0.1
0.2
0.0
-0.1
0.05
-0.05
0.15
-0.2

Excel formula:


=NORMALTEST({0.1;0.2;0.0;-0.1;0.05;-0.05;0.15;-0.2})

Expected output:

Statistic	P-value
0.2669	0.8751

Example 2: Non-Normal Data (Bimodal)

Inputs:

data
1.0
1.1
1.2
1.3
5.0
5.1
5.2
5.3

Excel formula:


=NORMALTEST({1.0;1.1;1.2;1.3;5.0;5.1;5.2;5.3})

Expected output:

Statistic	P-value
8.3802	0.0151

Example 3: Slightly Skewed Data

Inputs:

data
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2

Excel formula:


=NORMALTEST({0.5;0.6;0.7;0.8;0.9;1.0;1.1;1.2})

Expected output:

Statistic	P-value
0.6787	0.7122

Example 4: Uniform Data

Inputs:

data
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5

Excel formula:


=NORMALTEST({0.1;0.3;0.5;0.7;0.9;1.1;1.3;1.5})

Expected output:

Statistic	P-value
0.6787	0.7122

Python Code


from scipy.stats import normaltest as scipy_normaltest
 
def normaltest(data):
    """
    Test whether a sample differs from a normal distribution (omnibus test).
 
    Args:
        data: 2D list. Sample data (must contain at least 8 elements).
 
    Returns:
        2D list. Test statistic and p-value, or a string error message if input is invalid.
 
    This example function is provided as-is without any representation of accuracy.
    """
    # Validate input is a list
    if not isinstance(data, list):
        return "Invalid input: data must be a 2D list."
    # Flatten if 2D list
    try:
        flat = []
        for row in data:
            if isinstance(row, list):
                flat.extend(row)
            else:
                flat.append(row)
        arr = [float(x) for x in flat]
    except Exception:
        return "Invalid input: data must be numeric."
    if len(arr) < 8:
        return "Invalid input: data must contain at least 8 elements."
    try:
        stat, pval = scipy_normaltest(arr)
    except Exception as e:
        return f"scipy.stats.normaltest error: {e}"
    # Check for nan/inf
    if any([x is None or isinstance(x, str) for x in [stat, pval]]):
        return "Invalid output: statistic or p-value is not a number."
    if hasattr(stat, 'tolist'):
        stat = float(stat)
    if hasattr(pval, 'tolist'):
        pval = float(pval)
    if not (isinstance(stat, (int, float)) and isinstance(pval, (int, float))):
        return "Invalid output: statistic or p-value is not a number."
    if stat != stat or pval != pval or stat == float('inf') or pval == float('inf') or stat == float('-inf') or pval == float('-inf'):
        return "Invalid output: statistic or p-value is nan or inf."
    return [[stat, pval]]

Example Workbook

Link to Workbook