QUANTILE_TEST

Overview

The QUANTILE_TEST function performs a statistical test of the null hypothesis that a specified quantile of the population is equal to a given value, using the sample data provided. This is useful for determining whether the observed quantile (such as the median) of a dataset significantly differs from a hypothesized value. The function is based on the SciPy quantile_test method, which uses the binomial distribution to compute the p-value for the test statistic.

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

Usage

To use the function in Excel:


=QUANTILE_TEST(x, [q], [p])

x (2D list, required): Sample data. Must contain at least two elements (as a column or row vector).
q (float, optional, default=0): Hypothesized value of the quantile.
p (float, optional, default=0.5): Probability associated with the quantile (e.g., 0.5 for median).

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

Examples

Example 1: Median Test (default p=0.5)

Inputs:

x	q	p
1	0	0.5
2
3
4
5

Excel formula:


=QUANTILE_TEST({1;2;3;4;5})

Expected output:

Test Statistic	P-value
0.0	0.0625

Example 2: Test for quantile = 3

Inputs:

x	q	p
1	3	0.5
2
3
4
5

Excel formula:


=QUANTILE_TEST({1;2;3;4;5}, 3)

Expected output:

Test Statistic	P-value
3.0	1.0

Example 3: Lower quantile (p=0.25)

Inputs:

x	q	p
1	2	0.25
2
3
4
5

Excel formula:


=QUANTILE_TEST({1;2;3;4;5}, 2, 0.25)

Expected output:

Test Statistic	P-value
1.0	1.0

Example 4: Upper quantile (p=0.75)

Inputs:

x	q	p
1	4	0.75
2
3
4
5

Excel formula:


=QUANTILE_TEST({1;2;3;4;5}, 4, 0.75)

Expected output:

Test Statistic	P-value
4.0	1.0

Python Code


from scipy.stats import quantile_test as scipy_quantile_test
 
def quantile_test(x, q=0, p=0.5):
    """
    Perform a quantile test and compute a confidence interval of the quantile.
 
    Args:
        x: 2D list. Sample data (must contain two or more elements).
        q: float, optional. Hypothesized value of the quantile (default 0).
        p: float, optional. Probability associated with the quantile (default 0.5).
 
    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.
    """
    # Flatten x to 1D list
    try:
        if isinstance(x, (int, float)):
            return "Invalid input: x must be a 2D list with at least two elements."
        flat_x = []
        for row in x:
            if isinstance(row, list):
                flat_x.extend(row)
            else:
                flat_x.append(row)
        if len(flat_x) < 2:
            return "Invalid input: x must contain at least two elements."
        flat_x = [float(val) for val in flat_x]
    except Exception:
        return "Invalid input: x must be a 2D list of numbers."
    try:
        q_val = float(q)
        p_val = float(p)
    except Exception:
        return "Invalid input: q and p must be numbers."
    try:
        result = scipy_quantile_test(flat_x, q=q_val, p=p_val)
        # result.statistic, result.pvalue
        return [[float(result.statistic), float(result.pvalue)]]
    except Exception as e:
        return f"scipy.stats.quantile_test error: {e}"

Example Workbook

Link to Workbook