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Test for one mean calculator

Observed mean

Null hypothesis value


The Test for one mean can be used to test the hypothesis that a sample mean is equal to a given mean (with unknown standard deviation) or certified value.

Required input

  • The observed sample mean, standard deviation and sample size (n).
  • Test mean is equal to: enter the value to compare the mean to.

Computational notes

This procedure calculates the difference of an observed mean with a hypothesized value. A significance value (P-value) and 95% Confidence Interval (CI) of the observed mean is reported. The P-value is the probability of obtaining the observed mean in the sample if the null hypothesis value were the true value.

The P-value is calculated using the one sample t-test, with the value t calculated as:

General formula for t-value$$ t = \frac {sample\ mean\ -\ hypothesized\ mean} {standard\ error\ of\ sample\ mean } $$

or when the hypothesized mean is k and the standard deviation is s:

Formula for t-value$$ t = \frac {\bar{x} - k} { s / \sqrt{n} } $$

The P-value is the area of the t distribution with n−1 degrees of freedom, that falls outside ± t (see Values of the t distribution table).

How to cite this page

  • MedCalc Software Ltd. Test for one mean calculator. (Version 22.021; accessed February 27, 2024)


  • Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall. Buy from Amazon
  • Kirkwood BR, Sterne JAC (2003) Essential medical statistics, 2nd ed. Oxford: Blackwell Science. Buy from Amazon

See also

Recommended book

Book cover

Essentials of Medical Statistics
Betty Kirkwood, Jonathan Sterne

Buy from Amazon

Essential Medical Statistics is a classic amongst medical statisticians. An introductory textbook, it presents statistics with a clarity and logic that demystifies the subject, while providing a comprehensive coverage of advanced as well as basic methods. The second edition of Essential Medical Statistics has been comprehensively revised and updated to include modern statistical methods and modern approaches to statistical analysis, while retaining the approachable and non-mathematical style of the first edition. The book now includes full coverage of the most commonly used regression models, multiple linear regression, logistic regression, Poisson regression and Cox regression, as well as a chapter on general issues in regression modelling. In addition, new chapters introduce more advanced topics such as meta-analysis, likelihood, bootstrapping and robust standard errors, and analysis of clustered data.