# Best test for comparison of temporal counts

I have a data set of 182 concurrent count observations using two different methods and I was wondering what would be the best test to evaluate how closely related they are to each other.

My data set looks like this:

Datetime Count1 Count2
2021-09-06 10:00:00 186 226
2021-09-08 09:00:00 154 124
2021-09-11 16:00:00 186 90
2021-09-18 13:00:00 399 393

• Welcome to CV. There are several possibilities, but it's going to partly depend on what exactly you mean by "related". Sep 22, 2023 at 18:57
• I guess better way to phrase it is are they statistically similar or different Sep 22, 2023 at 18:59

It very much depends on what exactly you mean by "closely related".

One fairly obvious choice is correlation. This can be dangerous with time-series type data and lead to odd findings (e.g. shark attacks are related to ice cream sales) but, here, you have two measures of the same thing, so that's probably not a problem. But two series can be correlated even if they are very far apart.

set.seed(1234)
x <- seq(1:10)
y <- x*5 + rnorm(10, 0, 2)
cor(x,y) #0.99


Another idea is to regress one on the other and add a covariate for time.

If you aren't interested in the temporal aspect (seems odd, but it could happen) then you could compare means with a t-test.

If your time periods vary in length, you might want to convert the data to rates.

You could look graphically (you've already started) by looking at a QQ plot, or a Tukey mean difference plot (aka a Bland Altman plot).

You could make an ARIMA model for each and compare the models.

And ... Probably more! Those are just what I thought of in 10 minutes.