Whether the population exists in an experimental study? In my oral exam one of my teachers asked whether the population exists in an experimental study. 
I answered: "Yes. the population exists in an experimental study. And I will get it from my interested subject."
But he rejected the answer and told me that the population does not exist in an experimental study but exists in an observational study.
I have not understood it. If the population does not exist in an experimental study, then how can I get my sample ?
 A: I found the best answer (IMO) in a dated but wonderful book: Arthur S. Goldberger, A Course in Econometrics, 1991, Chapter 16.
In experimental studies the $\mathbf{x}_i$ define $n$ "subpopulations", or strata. A random drawing is made for each stratum, that is, $y_1$ is drawn from stratum 1, $y_2$ is drawn from stratum 2, and so on. In this scheme, the sampled $y$'s are not identically distributed; they are drawn from different strata. The researcher controls the $\mathbf{x}$ values and imposes them on the subjects; he defines (we could say: he creates) the relevant "subpopulations", or strata. Furthermore, the list of $n$ selected $\mathbf{x}$ vectors and their values is maintained in repeated sampling, so:


*

*the expectations of the successive $y$'s will depend only on $i$, and one can then write $E(y_i)$ instead of $E(y_i\mid\mathbf{x}_i)$ (the $\mathbf{X}$ matrix is typically nonstochastic);

*it does not make sense to use the sample to estimate the population means and variances of the $x$'s and $y$; the sample on $\mathbf{x}$ is not randomly drawn from the population joint distribution of $\mathbf{x}$ (is controlled by the researcher), and consequently the sample on $y$ is not randomly drawn from the population marginal distribution of $y$.

A: Can it be explained like the following so that I can say the population is non-existing ?
suppose we are interested about a new drug whether it removes headache or not. A sample of 50 people who have headache are being taken and the new drug and placebo are randomly given to the units. Here  we didn't take the sample from the population that have headache and take the drugsince we couldn’t identified the population physically , rather we randomly gave the  new drug to the 25 people who have headache. and after test procedure based on this 25 peolple we are talking about the whole population that if the population have headache and they were given the drug,then the result would like that at $alpha=0.5$ level of significance.
If the population do exist here than we would first identified the population here that have headache and take the drug ; and then we would take a random sample of $25$  and based on the sample we would draw the inference here.
The only difference I am getting here is that :
$\bullet$In sampling design, we first identify the population and randomly select our sample. We didn't apply here any treatment and this is observational study.So here population is existing here.
But
$\bullet$In experimental design we first draw our sample and think that if my population would fulfill the condition like my sample, then it would also produce the result at $\alpha$ level of significance. So here population is non-existing here.
