# Determining significant (or otherwise) difference between 2 rates of change

#### Axial

##### New Member
Dear Users,

I am trying to determine the statistical significant difference (or otherwise) between 2 series of data and am unsure how to proceed. It is rates of admission for arthritis between 2 countries.

Country A the average rate of increase per year is 8.1%, and for Country B the average rate of increase is 8.7% (both over 10 years). What test do I apply to determine whether this difference in rates is statistically significant?

#### trinker

##### ggplot2orBust
This is fairly straight forward answer but I'm going to direct you to a resource we have compiled by a moderator (TheEcologist) that will enable you to determine which test to use (LINK). In this thread (which is located in the FAQ forum of our website) you'll see links to various resources to help you make this determination.

I think that this could best be analyzed with a test of proportions but you need to have an n for group 1 and 2

#### Axial

##### New Member
Many thanks, this is a brilliant link

#### Axial

##### New Member
The page seems to suggest (from my reading) that I use an ancova. My understanding is that I am not trying to test a proportion, it is a rate, and I don't have a "n" for each group as such so I am worried this will be the wrong test. My data looks like this (These are my actual numbers):

Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10
Country E 705 817 907 917 954 1026 1065 1225 1276 1449 average rate of increase = 8.3%
Country N 1724 1875 1771 1805 1945 2085 2422 2614 3042 3118 average rate of increase = 6.5%

#### kabooze

##### New Member
The data doesn't seem to come from samples (rather from a census or register)? If that's the case, it's not meaningful to look for "statistical significance".. because the differnces are the truth differences and can't suffer from any sampling error.

#### Dason

The data doesn't seem to come from samples (rather from a census or register)? If that's the case, it's not meaningful to look for "statistical significance".. because the differnces are the truth differences and can't suffer from any sampling error.
This isn't exactly true. I know we've discussed this in another thread but just because you have one population of interest doesn't mean that significance testing is meaningless.

#### Karabiner

##### TS Contributor
The data doesn't seem to come from samples (rather from a census or register)? If that's the case, it's not meaningful to look for "statistical significance".. because the differnces are the truth differences and can't suffer from any sampling error.
As soon as you want to go beyond the data at hand, the data here and now,
and want to make general statements instead, then inferential statistics is an issue.
What one has measured are realizations of variables, and those realizations
are always subject to chance variation.

Kind regards

K.

#### kabooze

##### New Member
You have to specify your research question and your population first. If the data isn't a sample from the specified population I disagree with you on this point (what would the finite correction cause with the CI:s?).