CRONBACH_ALPHA

This function estimates internal consistency reliability across multiple items intended to measure the same latent construct.

For k items with item variances \sigma_i^2 and total score variance \sigma_T^2, Cronbach’s alpha is:

\alpha = \frac{k}{k-1}\left(1 - \frac{\sum_{i=1}^{k}\sigma_i^2}{\sigma_T^2}\right)

Higher values indicate stronger internal consistency among items, subject to assumptions about dimensionality and measurement scale.

Excel Usage

=CRONBACH_ALPHA(data, items, scores, subject, cronbach_nan_policy)

data (list[list], required): Input table as a 2D range with a header row followed by data rows.
items (str, optional, default: null): Optional item identifier column for long-format data.
scores (str, optional, default: null): Optional score/value column for long-format data.
subject (str, optional, default: null): Optional subject identifier column for long-format data.
cronbach_nan_policy (str, optional, default: “pairwise”): Missing value handling strategy.

Returns (float): Cronbach’s alpha coefficient.

Example 1: Cronbach alpha from wide-format item matrix

Inputs:

data
i_one	i_two	i_three
3	4	3
4	4	5
2	3	2
5	5	4
4	3	4

Excel formula:

=CRONBACH_ALPHA({"i_one","i_two","i_three";3,4,3;4,4,5;2,3,2;5,5,4;4,3,4})

Expected output:

0.84

Example 2: Pairwise handling with missing cell in wide data

Inputs:

data			cronbach_nan_policy
i_one	i_two	i_three	pairwise
3	4	3
4		5
2	3	2
5	5	4
4	3	4

Excel formula:

=CRONBACH_ALPHA({"i_one","i_two","i_three";3,4,3;4,,5;2,3,2;5,5,4;4,3,4}, "pairwise")

Expected output:

0.850103

Example 3: Long-format table using subject, items, and scores

Inputs:

data			items	scores	subject
subj	item	score	item	score	subj
1	A	3
1	B	4
1	C	3
2	A	4
2	B	4
2	C	5
3	A	2
3	B	3
3	C	2
4	A	5
4	B	5
4	C	4

Excel formula:

=CRONBACH_ALPHA({"subj","item","score";1,"A",3;1,"B",4;1,"C",3;2,"A",4;2,"B",4;2,"C",5;3,"A",2;3,"B",3;3,"C",2;4,"A",5;4,"B",5;4,"C",4}, "item", "score", "subj")

Expected output:

0.9

Example 4: Long-format reliability with listwise policy

Inputs:

data			items	scores	subject	cronbach_nan_policy
subj	item	score	item	score	subj	listwise
1	A	3
1	B	4
1	C	3
2	A	4
2	B
2	C	5
3	A	2
3	B	3
3	C	2
4	A	5
4	B	5
4	C	4

Excel formula:

=CRONBACH_ALPHA({"subj","item","score";1,"A",3;1,"B",4;1,"C",3;2,"A",4;2,"B",;2,"C",5;3,"A",2;3,"B",3;3,"C",2;4,"A",5;4,"B",5;4,"C",4}, "item", "score", "subj", "listwise")

Expected output:

0.972973

Python Code

import pandas as pd
import pingouin as pg

def cronbach_alpha(data, items=None, scores=None, subject=None, cronbach_nan_policy='pairwise'):
    """
    Compute Cronbach's alpha reliability coefficient for a set of items.

    See: https://pingouin-stats.org/generated/pingouin.cronbach_alpha.html

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

    Args:
        data (list[list]): Input table as a 2D range with a header row followed by data rows.
        items (str, optional): Optional item identifier column for long-format data. Default is None.
        scores (str, optional): Optional score/value column for long-format data. Default is None.
        subject (str, optional): Optional subject identifier column for long-format data. Default is None.
        cronbach_nan_policy (str, optional): Missing value handling strategy. Valid options: Pairwise, Listwise. Default is 'pairwise'.

    Returns:
        float: Cronbach's alpha coefficient.
    """
    try:
        def to2d(value):
            return [[value]] if not isinstance(value, list) else value

        matrix = to2d(data)
        if not isinstance(matrix, list) or len(matrix) < 2 or not all(isinstance(row, list) for row in matrix):
            return "Error: Invalid input - data must be a 2D list with header and rows"

        headers = [str(col).strip() for col in matrix[0]]
        if len(headers) == 0 or any(col == "" for col in headers):
            return "Error: Invalid input - header row must contain non-empty column names"

        width = len(headers)
        records = []
        for row in matrix[1:]:
            values = list(row)
            if len(values) < width:
                values = values + [None] * (width - len(values))
            elif len(values) > width:
                values = values[:width]
            records.append(values)

        frame = pd.DataFrame(records, columns=headers)

        items_arg = None if items is None or str(items).strip() == "" else str(items)
        scores_arg = None if scores is None or str(scores).strip() == "" else str(scores)
        subject_arg = None if subject is None or str(subject).strip() == "" else str(subject)

        if (items_arg is None) != (scores_arg is None) or (items_arg is None) != (subject_arg is None):
            return "Error: Invalid input - items, scores, and subject must be provided together for long-format data"

        alpha_result = pg.cronbach_alpha(
            data=frame,
            items=items_arg,
            scores=scores_arg,
            subject=subject_arg,
            nan_policy=str(cronbach_nan_policy),
        )

        alpha_value = alpha_result[0] if isinstance(alpha_result, (list, tuple)) else alpha_result
        return float(alpha_value)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

data *

Input table as a 2D range with a header row followed by data rows.

items

Optional item identifier column for long-format data.

scores

Optional score/value column for long-format data.

subject

Optional subject identifier column for long-format data.

cronbach_nan_policy

Missing value handling strategy.