An independent samples are those samples which are taken or selected randomly and thus the values of the observations does not depend on the values of the other observations. In order to obtain independent samples, the experimenter or the researcher needs to select random samples from the group.
In this the selection process of the samples may not be the same for the other processes.
In the context, the analyst selecting random samples from the registered Democrats and comparing the observations with the observations of the random samples selected from the registered Republicans is an example of Independent samples.
