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# Free statistical calculators

## Comparison of means calculator

## 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*:

where *s*_{1} and *s*_{2} are the standard deviations of the two samples with sample sizes *n*_{1} and *n*_{2}.

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

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

The P-value is the area of the *t* distribution with *n*_{1} + *n*_{2} − 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.
- Kirkwood BR, Sterne JAC (2003) Essential medical statistics, 2
^{nd}ed. Oxford: Blackwell Science.

## How to cite this page

- MedCalc Software Ltd. Comparison of means calculator. https://www.medcalc.org/calc/comparison_of_means.php (Version 22.026; accessed June 24, 2024)