BARNARD_EXACT

Overview

The BARNARD_EXACT function performs Barnard’s exact test on a 2x2 contingency table. This test is a more powerful alternative to Fisher’s exact test for 2x2 tables, as it does not condition on both marginal totals but instead maximizes over a nuisance parameter. The test uses the Wald statistic with pooled or unpooled variance to test the hypothesis that two binomial proportions are equal. The calculation involves quasi-Monte Carlo sampling to compute exact p-values, which is not possible with standard Excel functions. For more details, see the scipy.stats.barnard_exact documentation .

Excel has no equivalent to Barnard’s exact test. This advanced statistical test requires sophisticated algorithms for computing exact p-values by maximizing over nuisance parameters and using quasi-Monte Carlo sampling methods. The computational complexity and specialized statistical methodology make it impossible to implement with standard Excel functions.

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

Usage

To use the function in Excel:


=BARNARD_EXACT(table, [alternative], [pooled])

table (2D list, required): 2x2 contingency table with non-negative integer entries.
alternative (string, optional, default=“two-sided”): Defines the alternative hypothesis. Options are "two-sided", "less", or "greater".
pooled (bool, optional, default=TRUE): Whether to use pooled variance (TRUE) or unpooled variance (FALSE).

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

Examples

Example 1: Default two-sided test

Inputs:

table		alternative	pooled
7	12	two-sided	TRUE
8	3

Excel formula:


=BARNARD_EXACT({7,12;8,3})

Expected output:

Statistic	P-value
-1.894	0.06814

Example 2: One-sided test (less)

Inputs:

table		alternative	pooled
7	12	less	TRUE
8	3

Excel formula:


=BARNARD_EXACT({7,12;8,3}, "less")

Expected output:

Statistic	P-value
-1.894	0.03407

Example 3: One-sided test (greater)

Inputs:

table		alternative	pooled
7	12	greater	TRUE
8	3

Excel formula:


=BARNARD_EXACT({7,12;8,3}, "greater")

Expected output:

Statistic	P-value
-1.894	0.9659

Example 4: Unpooled variance

Inputs:

table		alternative	pooled
7	12	two-sided	FALSE
8	3

Excel formula:


=BARNARD_EXACT({7,12;8,3}, "two-sided", FALSE)

Expected output:

Statistic	P-value
-2.018932133	0.068153433

Python Code


from scipy.stats import barnard_exact as scipy_barnard_exact
 
def barnard_exact(table, alternative='two-sided', pooled=True):
    """
    Perform Barnard's exact test on a 2x2 contingency table.
 
    Args:
        table: 2D list (2x2) contingency table with non-negative integer entries.
        alternative: Defines the alternative hypothesis. Options are 'two-sided', 'less', 'greater'.
        pooled: Whether to use pooled variance (True) or unpooled variance (False).
 
    Returns:
        A 2D list containing the Wald statistic and p-value, each as a separate element in the first row.
 
    This example function is provided as-is without any representation of accuracy.
    """
    # Validate table
    if not isinstance(table, list) or len(table) != 2 or not all(isinstance(row, list) and len(row) == 2 for row in table):
        return "Invalid input: table must be a 2x2 list of non-negative integers."
    try:
        arr = [[int(x) for x in row] for row in table]
    except Exception:
        return "Invalid input: table must contain integers."
    if any(x < 0 for row in arr for x in row):
        return "Invalid input: table must contain non-negative integers."
    # Validate alternative
    if alternative not in ['two-sided', 'less', 'greater']:
        return "Invalid input: alternative must be 'two-sided', 'less', or 'greater'."
    # Validate pooled
    if not (pooled is True or pooled is False):
        return "Invalid input: pooled must be True or False."
    try:
        res = scipy_barnard_exact(arr, alternative=alternative, pooled=pooled)
        stat = float(res.statistic)
        pval = float(res.pvalue)
        # Disallow nan/inf
        if any([s in [float('inf'), float('-inf')] or s != s for s in [stat, pval]]):
            return "Invalid output: statistic or p-value is not finite."
        return [[stat, pval]]
    except Exception as e:
        return f"scipy.stats.barnard_exact error: {e}"

Example Workbook

Link to Workbook