# Comparison of means

## Description

Performs a t-test for the comparison of the means of two independent samples.

## 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.

## Results

The program calculates:

- the difference between the two means, the standard error and 95% confidence interval for this difference
- t-statistic, degrees of freedom (DF) and P value.

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

## Computational notes

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.

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).

## Literature

- Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.

## Link

Go to Comparison of means.