# Method to detect statistical differences between populations [on hold]

I would like to detect if two populations are the same between two time points and given several attributes.

Imagine a population at day 1, with these characteristics:

population total N = 10000
Gardening
gardeners: 6000 (60%)
non-gardeners: 4000 (40%)

Walk
walker: 8000 (80%)
hikers: 1000 (10%)
no_walk: 1000 (10%)


The next year, I get new data:

N = 11000
Gardening
gardener: 7000 (64%)
non-gardener: 4000 (36%)

Walk
walker: 8500 (77%)
hiker: 1500 (13%)
no_walk: 1000 (10%)


Now, statistically, I want to calculate a p-value to assess whether the population at 2 points in time are the same or not. I would compare each category together (gardener at day 1 with gardener next year, etc.).

For example, I can use a 2 proportion z test to compare the same attribute pairwise from one year to the next. In the case of gardener, I can use the information: Day 1: 0.6, 10000 One year: 0.64, 11000 And detect if there is a significant different with the 2 proportion z test.

Note 1: the populations are different since there is an increase in people, but I want to understand if the new population has the same proportions in terms of attributes of "Gardening" and "Walk" in my example. So I am more interested in looking at proportions.

Note 2: I have a subset sample of the population with weights representing the full population

I was thinking about using the chi-squared metric, taking the expected counts from day 1 (renormalized to account for population increase). However, the usage of the chi square I saw was being done on only one category (Walk, for example) or across categories (Gardening and Walk, so I would need the joint distribution -> gardeners and walkers for example).

The chi square definitively gives me a result, but I am not sure if it is valid, since I have several categories, each representing the total population, instead of one category with several segments adding up to the population total.

## put on hold as unclear what you're asking by StatsStudent, user158565, Michael Chernick, Siong Thye Goh, mktJun 16 at 11:19

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• Are these samples from the population, or the full populations at each time point? – jsk Jun 13 at 4:54
• Since you have complete data from the population, it is not appropriate to do a hypothesis test to detect statistical differences in the populations. You already know the populations have changed. The question now is whether the differences are large or small, but that's not a statistical question. – jsk Jun 13 at 5:35
• The populations obviously are different: one has 10,000 people and the other has 11,000! This trivial observation points out how important it is to state how you want to compare the populations. It's unlikely you want to treat either group as the entire "population," BTW, because that would preclude being able to extend your observations or conclusions to any other set of people. – whuber Jun 13 at 12:51
• Are you measuring some of the same people at time 1 and time 2? – jsk Jun 13 at 16:14
• @StatsStudent I really have a subset of the population, used to represent the full population with weights. Sorry, I was not clear, and I did not know it would cause confusion. – Damien Jun 13 at 16:24