# Difference between superpopulation and infinite population

What is the difference between Superpopulation and Infinite population? Please explain this with examples.

## 3 Answers

In survey sampling you have a finite population. One modeling method envisions the finite population as coming from a theoretical infinite population. This imaginary population is called a superpopulation model. On the other hand when selecting a random sample (not from a finite population) is viewed as sampling at random from an infinite population. So the term infinite population is for ordinary sampling and superpopulation specifically refers to the situation when the sample is taken from a finite population.

In the field of ecological statistics (e.g. mark-recapture) we often have long time series of data, where any individuals may only be exposed to sampling for only a portion of the total time series. In this context we can consider every individual that was exposed to sampling during the course of the experiment, a measure we call the superpopulation. This is different from the population at any given time point, which is the total number of individuals exposed to sampling at that time point. Both of these definitions of a population are finite measures.

Aside - I used the term "exposed to sampling" as population heterogeneity is often the rule rather than the exception in ecology. Subpopulations may exist that behave differently and may completely avoid detection by our survey techniques. These individuals thus are not part of our statistical population definition.

A population which is uncountable (or at least, not countable on fingertips) is called an "infinite population" — such as the number of red cells in blood, or the number of infective bacteria in the body of a patient.

An imaginary or theoretical population is called a superpopulation, or hypothetical population.

• How does this add to the existing answers? – Andy May 22 '14 at 12:29
• @Andy The original question did ask for specific examples, which are in short supply in the other answers, so I actually thought this answer did provide something worthwhile. The last textbook definition I saw of "infinite population" actually gave "grains of sand on a beach" as its example, which technically speaking is countable from a mathematical point of view but which is nevertheless described as an "infinite population" - so I do rather like this answer's idiomatic phrase "not countable on fingertips". A good copy-edit would help though. – Silverfish Apr 9 '15 at 11:28