# Confusion between sample and population

A team has conducted a study in which an introductory class was randomly divided into two groups. Group 1 was administered a dosage of alcohol. Group 2 was given an equvialent dosage of marijuana. Fifteen minutes after administration, both groups were asked to solve a puzzle. The experimenter recorded the amount of time in seconds it took for each subject to solve the puzzle.

Now, in this case, will the given data for each group be considered as sample or population?

• "equivalent dosage" seems a bit suspect. Off the topic of your question but saying in case this is your research project.
– user14281
Commented Oct 2, 2012 at 5:24

It depends on to whom you wish to generalize your final results. If your sole interest was just to see how these people react and you don't care about inference, they are your population. If you wish to use the results to somehow infer how other similar people may behave under influence, then they are samples. Most studies tend to do the latter.

Also, for the inference to be valid, the sample should be drawn from the population with a known probability. The more the sampling deviated from the being probability-based, the shakier the inference will become.

It may also be worth mentioning that attributing exposure such as alcohol or marijuana to human subjects probably will not pass through ethical review process. Don't jump into answering the design feature before making sure that it's not a trick question.

As @Michael said, this would be considered a sample. One additional question is "from what population"? That is harder to say, but this is a problem that bedevils many studies. Often researchers will assume that a sample like this is "almost random" or something like that. What is the population, though? All college students? All students in this particular university? All students taking this type of class? All humans?

To consider these two groups as populations would be to say that you aren't interested in generalizing the study at all.

This is tricky stuff that often gets little attention.

For the purposes of statistical tests, this would be considered a sample. For example the average time for group 1 to complete puzzle is $\bar X_1$ and not $\mu_1$ the population mean.

Using a small group (or even large group) to determine effect of alcohol on 'completion time' of puzzle, cannot give you $\mu_1$. The population mean is usually something 'imaginary' (unless we know the exact distribution) often approximated by $\bar X$.

• I agree. The population is often a construct representing abstractly an infinite number of in your case two populations of students, one that is treated with alcohol and the other that is treated with marijuana. Statistical inference is made by assuming a parametric or nonparametric model for this population and the test subjects are viewed as though they are a randomly selected sample from this population. In other situations such as with survey sampling, the population is a finite sampling from from which an actual random sample is selected. Commented Oct 2, 2012 at 10:29