TTEST_1SAMP

Overview

The TTEST_1SAMP function performs a one-sample t-test for the mean of a group of scores, testing the null hypothesis that the expected value (mean) of a sample is equal to a specified population mean. This is commonly used to determine if a sample mean significantly differs from a known or hypothesized value. The function returns the test statistic, p-value, and degrees of freedom. For more details, see the scipy.stats.ttest_1samp documentation .

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

Usage

To use the function in Excel:


=TTEST_1SAMP(data, popmean)

data (2D list, required): Table or column vector of sample observations (must contain two or more elements).
popmean (float, required): Expected value in the null hypothesis.

The function returns a 2D list with three values: test statistic (float), p-value (float), and degrees of freedom (float), or an error message (string) if the input is invalid.

Examples

Example 1: Sample mean greater than population mean

Inputs:

data	popmean
2.3	2.0
2.7
2.9
3.1
2.8

Excel formula:


=TTEST_1SAMP({2.3;2.7;2.9;3.1;2.8}, 2.0)

Expected output:

Test Statistic	P-value	Degrees of Freedom
5.7287	0.0046	4

Example 2: Sample mean less than population mean

Inputs:

data	popmean
1.2	2.0
1.5
1.7
1.9
2.1

Excel formula:


=TTEST_1SAMP({1.2;1.5;1.7;1.9;2.1}, 2.0)

Expected output:

Test Statistic	P-value	Degrees of Freedom
-2.0486	0.1099	4

Example 3: Sample mean equals population mean

Inputs:

data	popmean
2.0	2.0
2.0
2.0
2.0
2.0

Excel formula:


=TTEST_1SAMP({2.0;2.0;2.0;2.0;2.0}, 2.0)

Expected output:

Test Statistic	P-value	Degrees of Freedom
nan	nan	nan

Example 4: Larger sample size

Inputs:

data	popmean
5.1	5.0
5.3
5.2
5.4
5.0
5.5
5.3
5.2
5.1
5.4

Excel formula:


=TTEST_1SAMP({5.1;5.3;5.2;5.4;5.0;5.5;5.3;5.2;5.1;5.4}, 5.0)

Expected output:

Test Statistic	P-value	Degrees of Freedom
5.0000	0.0007	9

Python Code


from scipy.stats import ttest_1samp as scipy_ttest_1samp
 
def ttest_1samp(data, popmean):
    """
    Perform a one-sample t-test for the mean of a group of scores.
 
    Args:
        data: 2D list. Sample observations (must contain two or more elements).
        popmean: float. Expected value in null hypothesis.
 
    Returns:
        2D list. Test statistic, p-value, and degrees of freedom.
 
    This example function is provided as-is without any representation of accuracy.
    """
    # Validate data
    if not isinstance(data, list) or len(data) < 2:
        return "Invalid input: data must be a 2D list with at least two rows."
    # Flatten data to 1D list
    try:
        flat = []
        for row in data:
            if isinstance(row, list):
                flat.extend(row)
            else:
                flat.append(row)
        flat = [float(x) for x in flat]
    except Exception:
        return "Invalid input: data must contain numeric values."
    if len(flat) < 2:
        return "Invalid input: data must contain at least two values."
    try:
        popmean = float(popmean)
    except Exception:
        return "Invalid input: popmean must be a number."
    try:
        stat, pval = scipy_ttest_1samp(flat, popmean)[:2]
        df = len(flat) - 1
        # Disallow nan/inf
        if any([
            isinstance(x, float) and (x != x or x == float('inf') or x == float('-inf'))
            for x in [stat, pval, df]
        ]):
            return [["nan", "nan", "nan"]]
        return [[stat, pval, df]]
    except Exception as e:
        return f"scipy.stats.ttest_1samp error: {e}"

Example Workbook

Link to Workbook