## Two Sample t-Test

### Purpose

To compare responses from two groups. These two groups can come from different experimental treatments, or different natural "populations".

### Assumptions

- each group is considered to be a sample from a distinct population
- the responses in each group are independent of those in the other group
- the distributions of the variable of interest are normal

### How It Works

- The null hypothesis is that the two population means are equal to each other.
To test the null hypothesis, you need to calculate the following values:
(the
means of the two samples),
*s*_{1}^{2},*s*_{2}^{2}(the variances of the two samples),*n*_{1},*n*_{2}(the sample sizes of the two samples), and*k*(the degrees of freedom).

- Compute the
*t*-statistic.

- Compare the calculated
*t*-value, with*k*degrees of freedom, to the critical*t*value from the*t*distribution table at the chosen confidence level and decide whether to accept or reject the null hypothesis.

*Reject the null hypothesis when: calculated *t*-value > critical *t*-value

- Note: This procedure can be used when the distribution variances from the two populations are not equal, and the sample sizes are not equal.