T-Test Essentials: Definition, Formula and Calculation

One Sample T-Test Formula

This article describes the one sample t-test formula, which is used to compare the mean of one sample to a known standard mean. This is also referred as:

  • single sample t-test formula and
  • one sample t-test equation


Related Book

Practical Statistics in R II - Comparing Groups: Numerical Variables


The the one-sample t-test formula can be written as follow:

t = \frac{m-\mu}{s/\sqrt{n}}


  • \(m\) is the sample mean
  • \(n\) is the sample size
  • \(s\) is the sample standard deviation with \(n-1\) degrees of freedom
  • \(\mu\) is the theoretical mean

The p-value, corresponding to the absolute value of the t-test statistics (|t|), is computed for the degrees of freedom (df): df = n - 1.

How to interpret the one-sample t-test results?

If the p-value is inferior or equal to the significance level 0.05, we can reject the null hypothesis and accept the alternative hypothesis. In other words, we conclude that the sample mean is significantly different from the theoretical mean.

Related article

T-test in R

Version: Français

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