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Comparison of means calculator

Sample 1

Sample 2

Description

This procedure calculates the difference between the observed means in two independent samples. A significance value (P-value) and 95% Confidence Interval (CI) of the difference is reported. The P-value is the probability of obtaining the observed difference between the samples if the null hypothesis were true. The null hypothesis is the hypothesis that the difference is 0.

Required input

For both samples, you enter:

  • Mean: the observed arithmetic mean.
  • Standard deviation: the observed standard deviation.
  • Sample size: the number of observations in the sample.

Computational notes

The program first calculates the pooled standard deviation s:

Comparison of means: pooled standard deviation

where s1 and s2 are the standard deviations of the two samples with sample sizes n1 and n2.

The standard error se of the difference between the two means is calculated as:

Comparison of means: standard error of the difference between two means

The significance level, or P-value, is calculated using the t-test, with the value t calculated as:

Comparison of means: t-value

The P-value is the area of the t distribution with n1 + n2 − 2 degrees of freedom, that falls outside ± t (see Values of the t distribution table).

When the P-value is less than 0.05 (P<0.05), the conclusion is that the two means are significantly different. Note that in MedCalc P-values are always two-sided (or two-tailed).

Literature

  • 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

How to cite this page

  • MedCalc Software Ltd. Comparison of means calculator. https://www.medcalc.org/calc/comparison_of_means.php (Version 20.009; accessed August 3, 2021)

See also

Recommended book

Essentials of Medical Statistics
Betty Kirkwood, Jonathan Sterne

Buy from Amazon US - CA - UK - DE - FR - ES - IT

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.