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I have two samples (both n > 1000) taken from the same population. The first sample is taken in one year, say at t0, and the the other sample is taken a year after, say at t1. There are different people in the different samples, i.e. I do not have two measurements from the same person at t0 and t1. How do I test whether some proportion in the population has changed from t0 to t1?

My initial thought was to do a chi-squared test for difference in proportion, but I am not sure whether this is valid when the two samples are not from two populations. I have also considered doing a one-way within groups ANOVA.

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If both samples come from the same population then they would have the same characteristics but since due to sampling there is randomness involved, we could not be able to measure it precisely and we could obtain different sample characteristics. Comparing two samples from the same population would only tell you something about how precise are your measurements.

If you are comparing individuals as measured on time $t$ to individuals as measured on time $t+k$, then you are dealing with two samples, each taken from the different population. Population in statistics is simply a group of cases sharing some property of interest.

Check this question for a discussion of a similar misconception. Check also here, here and here.

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    $\begingroup$ Thanks for the answer! Just to make sure that I understand: If I draw two samples from, say all people between 15 and 25 years in country X, at two different points in time (again given that the people in the samples are not the same individuals), then I have two samples from two populations, i.e. the group of people between 15 and 25 at t0 is a different population than at t1. $\endgroup$ – avriis Oct 27 '16 at 12:24
  • $\begingroup$ @dahved yes, this is how you would call it in statistics. $\endgroup$ – Tim Oct 27 '16 at 12:42
  • $\begingroup$ Brilliant, so I assume the implication is that a chi-squared test for difference in proportions between two populations would be correct. Also, I couldn't quite find any information on why the same group of people are considered as different populations at different times in the links you provided. Can you guide me to some other references or should I post another question regarding this? $\endgroup$ – avriis Oct 27 '16 at 12:51
  • $\begingroup$ @dahved this is basically because of the definition that is used: population is a group sharing some characteristic of interest (having blue eyes, eating candies, that solved your questionnaire on Monday morning etc.). $\endgroup$ – Tim Oct 27 '16 at 12:56

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