BINOMTEST

Overview

The BINOMTEST function performs a test that the probability of success in a Bernoulli experiment is equal to a specified value. It is used to determine whether the observed number of successes in a fixed number of independent trials is consistent with a hypothesized probability of success. This function is commonly used in quality control, clinical trials, and other applications where binary outcomes are observed. For more details, see the scipy.stats.binomtest documentation .

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

Usage

To use the function in Excel:


=BINOMTEST(k, n, [p])

k (int, required): Number of successes observed.
n (int, required): Number of trials.
p (float, optional, default=0.5): Hypothesized probability of success.

The function returns a 2D list with two elements: the test statistic (number of successes) and the p-value (float), or an error message (string) if the input is invalid.

Examples

Example 1: Fair Coin Test

Test if 5 heads in 10 coin flips is consistent with a fair coin (p=0.5).

Inputs:

k	n	p
5	10	0.5

Excel formula:


=BINOMTEST(5, 10, 0.5)

Expected output:

Test Statistic	p-value
5	1.0

Example 2: Biased Coin

Test if 8 heads in 10 flips is consistent with a fair coin.

Inputs:

k	n	p
8	10	0.5

Excel formula:


=BINOMTEST(8, 10, 0.5)

Expected output:

Test Statistic	p-value
8	0.109375

Example 3: Custom Probability

Test if 7 successes in 12 trials is consistent with p=0.6.

Inputs:

k	n	p
7	12	0.6

Excel formula:


=BINOMTEST(7, 12, 0.6)

Expected output:

Test Statistic	p-value
7	1.0

Example 4: Default Probability

Test if 3 successes in 6 trials is consistent with the default p=0.5.

Inputs:

k	n	p
3	6	0.5

Excel formula:


=BINOMTEST(3, 6)

Expected output:

Test Statistic	p-value
3	1.0

Python Code


from scipy.stats import binomtest as scipy_binomtest
 
def binomtest(k, n, p=0.5):
    """
    Perform a binomial test for the probability of success in a Bernoulli experiment.
 
    Args:
        k: Number of successes (int).
        n: Number of trials (int).
        p: Hypothesized probability of success (float, default 0.5).
 
    Returns:
        2D list: [[test statistic (int), p-value (float)]], or error message (str) if input is invalid.
 
    This example function is provided as-is without any representation of accuracy.
    """
    # Validate inputs
    try:
        k_int = int(k)
        n_int = int(n)
        p_float = float(p)
    except Exception:
        return "Invalid input: k, n must be integers and p must be a float."
    if n_int <= 0:
        return "Invalid input: n must be positive."
    if not (0 <= k_int <= n_int):
        return "Invalid input: k must be between 0 and n."
    if not (0 <= p_float <= 1):
        return "Invalid input: p must be between 0 and 1."
    try:
        result = scipy_binomtest(k_int, n_int, p_float)
        stat = k_int
        pval = float(result.pvalue)
        # Disallow nan/inf
        if not (pval == pval and pval != float('inf') and pval != float('-inf')):
            return "Invalid output: p-value is not finite."
        return [[stat, pval]]
    except Exception as e:
        return f"scipy.stats.binomtest error: {e}"

Example Workbook

Link to Workbook