What statistical test to compare two variables' growth?

Question

I'll be really grateful to anyone who can help with this!

I have two time series representing an index of average house prices in area A and area B, for each month over several years. Example data look like this:

Area A B

Jan 00 100 100

Feb 00 104 105

Mar 00 105 105

Apr 00 106 105

..and so on

I wish to test if area A has a different rate of growth to area B. The

null hypothesis is that there is no difference. I have tested this by

calculating the difference between area A and area B for each month (i.e. A-B), and then performing a paired-values t-test. My concern with this is that because these indices represent average house prices in two separate areas we shouldn't really use a paired t-test: this isn't data from the same sample before and after a treatment, it's data from two different groups.

Really what I'm trying to do is say "do the line graphs of these two areas, when we plot index against time, look similar enough", but with a statistical test.

Many, many thanks!

Answer 1

You're right, a paired t-test would not be the right thing to do, as this assumes independence between months, which is clearly not the case here.

You could try fitting a regression where Y = difference in growth between the areas for each month (i.e. the same as you do above, A-B) and X = time.

Then test whether the slope is different from zero or not.

HTH

Answer 2

Instead of a paired t-test, why not do a t-test for independent samples? Sample A versus Sample B? Because you're interested in the rate growth and not the means, consider taking the logarithms of each sample and do an independent 2-sample t-test.

Answer 3

If you are looking for a difference that is statistically significant then you do need to use a t-test

but is is matched pairs so t test related is correct