Independent samples t test

Introduction

Independent samples t test is used to compare the means of two unrelated groups of samples. The aim of this article is to show you an example.

The independent t-test formula is :

\[ t = \frac{m_1 - m_2}{\sqrt{ \frac{S^2}{n_1} + \frac{S^2}{n_2} }} \]

  • \(m_1\) and \(m_2\) are the means of the two groups being compared.
  • \(n_1\) and \(n_2\) are the sizes of the two groups, respectively.
  • \(S^2\) is the common variance of the two samples.

The degrees of freedom are :

\[ df = n_1 + n_2 -2 \]

Once the t test value has been calculated, you have to use t test table to determine the level of significance.

The t-test formula is described in details here and an online t-test calculator is available here.

Example of data

As an example, we have a population of 20 people selected randomly (10 women and 10 men). We want to know whether women’s average weight is significantly different from men’s average weight.

In this typical example the two samples being compared are completely unrelated and you have to use independent samples t test.

Online independent samples t-test calculator

The best free statistics calculator software can be used to calculate t-test statistics online.

If you want to do it with R, follow this link : **independent t test.


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