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I have two sets of monthly Consumer Price Index (CPI) values for the period January 2014 through April 2017. One set is the national monthly CPI for Canada and the second is the provincial monthly CPI for Alberta (a province of Canada).
The CPI values for both Canada and Alberta represent a mean value calculated during the period by randomly sampling values within the geographic region in question. Alberta is part of Canada so there is necessarily some Alberta data being used to contribute to the Canadian CPI mean.
It is clear enough from the data that some months Alberta CPI is higher than the national value and some months it is lower but I want to be able to determine if the overall difference during the study period is statistically significant.
My current approach is to use a T-test and compare the two sets of data to see if there is a significant difference between their means. My concerns are:
A) is there an issue with this approach because the data is temporal? i.e. does the time series nature of the data preclude the use of a T-test?
B) is there an issue with independence given the fact that the Alberta data is a subset of the national data?
C) is there an issue with using a T-test to treat the monthly CPIs as point data given that they themselves are means? I don't have access to the raw data that was used to calculate the monthly CPIs and I am concerned with the validity of taking the mean of mean data to perform the statistical test.
Finally, if a T-test is out as an option, is there another statistical test that is appropriate?