SOMERSD

Overview

The SOMERSD function calculates Somers’ D, an asymmetric measure of ordinal association between two variables. Like Kendall’s tau, Somers’ D measures the correspondence between two rankings, but it is normalized differently and is asymmetric: in general, $D(Y|X) \neq D(X|Y)$ . Somers’ D is useful for analyzing the strength and direction of association between an independent (row) variable and a dependent (column) variable, especially for ordinal data or contingency tables. The calculation can be performed on two lists of rankings or on a 2D contingency table. For more details, see the scipy.stats.somersd documentation .

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

Usage

To use the function in Excel:


=SOMERSD(x, [y], [alternative])

x (2D list, required): Either a 2D list of rankings (as a column vector) or a 2D contingency table. If a 2D list of rankings, must have at least two rows.
y (2D list, optional): 2D list of rankings (as a column vector), same number of rows as x. Ignored if x is a contingency table.
alternative (str, optional, default=“two-sided”): Defines the alternative hypothesis. One of “two-sided”, “less”, or “greater”.

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

Examples

Example 1: Contingency Table (Hotel Cleanliness and Satisfaction)

Inputs:

x
27	25	14	7	0
7	14	18	35	12
1	3	2	7	17

Excel formula:


=SOMERSD({27,25,14,7,0;7,14,18,35,12;1,3,2,7,17})

Expected output:

Statistic	P-value
0.603277	1.00071E-27

Example 2: Two Rankings (Perfect Agreement)

Inputs:

x	y
1	1
2	2
3	3
4	4
5	5

Excel formula:


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

Expected output:

Statistic	P-value
1	0

Example 3: Two Rankings (Perfect Disagreement)

Inputs:

x	y
1	5
2	4
3	3
4	2
5	1

Excel formula:


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

Expected output:

Statistic	P-value
-1	0

Example 4: Two Rankings (Random Association)

Inputs:

x	y
1	3
2	1
3	5
4	2
5	4

Excel formula:


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

Expected output:

Statistic	P-value
0.2	0.3613104285261787

Python Code


from scipy.stats import somersd as scipy_somersd
 
def somersd(x, y=None, alternative="two-sided"):
    """
    Calculate Somers' D, an asymmetric measure of ordinal association between two variables.
 
    Args:
        x: 2D list, either a column vector of rankings or a 2D contingency table. If rankings, must have at least two rows.
        y: 2D list, optional. Column vector of rankings, same number of rows as x. Ignored if x is a contingency table.
        alternative: str, optional. Defines the alternative hypothesis. One of "two-sided", "less", or "greater" (default: "two-sided").
 
    Returns:
        2D list: [[statistic, pvalue]], or an error message (str) if input is invalid.
 
    This example function is provided as-is without any representation of accuracy.
    """
    # Validate x
    if not isinstance(x, list) or len(x) < 2:
        return "Invalid input: x must be a 2D list with at least two rows."
    # Check if x is a contingency table (2D matrix) or a column vector
    is_contingency = all(isinstance(row, list) and len(row) > 1 for row in x)
    try:
        if is_contingency:
            # Validate all elements are numbers
            for row in x:
                for val in row:
                    float(val)
            result = scipy_somersd(x, alternative=alternative)
        else:
            # x and y must be column vectors
            x_vec = [float(row[0]) if isinstance(row, list) else float(row) for row in x]
            if y is None:
                return "Invalid input: y must be provided when x is a vector."
            if not isinstance(y, list) or len(y) != len(x):
                return "Invalid input: y must be a 2D list with the same number of rows as x."
            y_vec = [float(row[0]) if isinstance(row, list) else float(row) for row in y]
            result = scipy_somersd(x_vec, y_vec, alternative=alternative)
        stat = result.statistic
        pval = result.pvalue
        # Disallow nan/inf
        if any([stat is None, pval is None]):
            return "Invalid result: statistic or pvalue is None."
        if hasattr(stat, 'is_integer') and (stat != stat or abs(stat) == float('inf')):
            return "Invalid result: statistic is NaN or infinite."
        if hasattr(pval, 'is_integer') and (pval != pval or abs(pval) == float('inf')):
            return "Invalid result: pvalue is NaN or infinite."
        return [[stat, pval]]
    except Exception as e:
        return f"Error: {e}"

Example Workbook

Link to Workbook