## 1.1 Assumptions: Independent samples $$t$$-test

In addition to the three assumptions we saw last week for the one-sample $$t$$-test, there is one more assumption required for the independent samples $$t$$-test: equal variances between groups. This assumption is often also called homogeneity of variance. The assumptions of the independent samples $$t$$-test can therefore be summarised as follows:

Independent samples $$t$$-test Assumptions:

1. The data are numeric
2. Observations are independent of one another (that is, the sample is a simple random sample and each individual within the population has an equal chance of being selected)
3. The sample mean, $$\overline{X}$$, is normally distributed
4. Equal variances between groups.

Normally, if the standard deviation of one group is more than twice the standard deviation of the other group, then the equal variance assumption has been violated. There is also a statistical test we can use to help us check this assumption. In the following section, we will see how this can be done, and what we can do if it is determined that this assumption has been violated.