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CONFIDENCE.T Function (LibreOffice Calc)

Math Intermediate LibreOffice Calc LibreOffice 4.0

The CONFIDENCE.T function in LibreOffice Calc returns the margin of error for a confidence interval using the Student t-distribution. This guide explains syntax, interpretation, examples, errors, and best practices.

The **CONFIDENCE.T** function returns the **margin of error** for a confidence interval around a sample mean using the **Student t-distribution**. This is the correct method when the population standard deviation is unknown or the sample size is small.

This guide provides syntax, interpretation rules, examples, common errors, and best practices, making it one of the most complete CONFIDENCE.T references available for LibreOffice Calc.

What the CONFIDENCE.T Function Does

  • Computes the margin of error using the t-distribution
  • Correct for small samples or unknown population SD
  • Uses sample standard deviation
  • Works across sheets

The confidence interval is:

[ \bar{x} \pm \text{CONFIDENCE.T} ]

Syntax

CONFIDENCE.T(alpha; standard_dev; size)

Where:

  • alpha — significance level (e.g., 0.05 for 95% confidence)
  • standard_dev — sample standard deviation (STDEV.S)
  • size — sample size
Use CONFIDENCE.NORM only when population SD is known or sample size is large.

Interpretation of Alpha

Alpha Confidence Level
0.10 90%
0.05 95%
0.01 99%

Basic Examples

95% confidence interval margin of error

=CONFIDENCE.T(0.05; STDEV.S(A1:A30); COUNT(A1:A30))

99% confidence interval

=CONFIDENCE.T(0.01; STDEV.S(A1:A20); COUNT(A1:A20))

Across sheets

=CONFIDENCE.T(0.05; Sheet1.B1; Sheet2.C1)

Advanced Examples

Full confidence interval (lower and upper bounds)

Lower bound:

=AVERAGE(A1:A30) - CONFIDENCE.T(0.05; STDEV.S(A1:A30); COUNT(A1:A30))

Upper bound:

=AVERAGE(A1:A30) + CONFIDENCE.T(0.05; STDEV.S(A1:A30); COUNT(A1:A30))

Confidence interval ignoring errors

=CONFIDENCE.T(0.05; STDEV.S(IF(ISNUMBER(A1:A100); A1:A100)); COUNT(IF(ISNUMBER(A1:A100); A1:A100)))

(Confirm with Ctrl+Shift+Enter in older Calc.)

Confidence interval after removing outliers

=CONFIDENCE.T(0.05; STDEV.S(FILTER(A1:A100; A1:A100<1000)); COUNT(FILTER(A1:A100; A1:A100<1000)))

Confidence interval for small-sample experiments

=CONFIDENCE.T(0.05; STDEV.S(ExperimentData); COUNT(ExperimentData))

Confidence interval for standardized data

=CONFIDENCE.T(0.05; 1; COUNT(A1:A30))

(Standardized SD = 1)

How CONFIDENCE.T Calculates Margin of Error

  1. Compute t-critical value:

[ t = t^{-1}(1 - \alpha/2, , n - 1) ]

  1. Compute standard error:

[ SE = \frac{s}{\sqrt{n}} ]

  1. Compute margin of error:

[ ME = t \cdot SE ]

Where:

  • ( s ) = sample standard deviation
  • ( n ) = sample size

Common Errors and Fixes

Err:502 — Invalid argument

Occurs when:

  • Alpha ≤ 0 or ≥ 1
  • Standard deviation ≤ 0
  • Sample size < 2

Err:504 — Parameter error

Occurs when:

  • Semicolons are incorrect
  • Range references malformed

Margin of error seems too large

Possible causes:

  • Very small sample size
  • Large sample SD
  • High confidence level (small alpha)

Best Practices

  • Use CONFIDENCE.T for small samples or unknown population SD
  • Use CONFIDENCE.NORM only for large samples or known SD
  • Remove outliers before computing SD
  • Use named ranges for cleaner formulas
  • Report both margin of error and interval bounds
  • Use T.TEST and T.DIST for deeper inferential analysis
CONFIDENCE.T gives you the statistically correct margin of error for real-world data — where population standard deviation is almost never known.