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.