Experimental
Research question: Are songs effective to teach listening comprehension?
Design:

You draw the sample randomly from the population.
Then you assign the sample into an experimental and control groups also randomly.
You give a treatment to the experimental group, but not to the control one.
Ex-post Facto
Research question: Does learning English in elementary school affect the university students’ speaking ability?
Design:

There is no randomization here.
You select the subjects on the basis of a certain existing condition.
You do not give treatment to any group because:
1. the “treatment” already happened in the past and you can no longer do anything about it, or
2. it is unethical to give a treatment to the ex-post facto group.
We will discuss more about the above designs near the end of this semester.