Comparing two sets of data over time to infer correlation or imply causation

I have two data sets, over a period of time that I would like to compare. I am very unfamiliar with statistics so sorry if this is simple. I need to use SPSS.

I am comparing the number of journal articles published relating to a two different disciplines, over a period of 40 or so years.

Is it possible to statistically compare these two 'lines' to give more argument to the trends?

Based on the data collected, the current trend is they are both very similar, and then in the last 10 years, one rises substantially, and the other begins to fall. Is there a way I can statistically infer a relationship between them, especially the part where one begings to rise and one begins to fall?

Do I need to standardise my data to account for the fact one of the lines has a smaller sample size? Edit: the sample sizes are taken over the same amount of years, but see below, one has considerably more hits than the other - would standardising make the relationship clearer?

I hope this makes sense.

Edit: this is how my data appears already. I'm not sure if anyone knows a better way of representing it, I know the large time frame makes it quite hard to see what is going on until the huge spike

What I would like to infer, if possible, that there may be a relationship between the green line substantially rising, and the black line starting to fall off

First thing, I would probably forget about causation. The number of articles published in one discipline is pretty independent from the number of articles published in another, at least from a causal standpoint.

Second, you can't analyze the relationship between those two variables before fully detrending them. I recommend you look at percentage change from one year to the next (or whatever the frequency your data has). Once, you detrend those two variables as suggested you could simply calculate the correlation between the two over let's say 10 periods. And, next observe how those correlations (based on 10 periods) move and even flip signs. This type of testing will be indicative of the relationship between those two variables. By just looking at the graph, I suspect those correlations will be very volatile indicating that there is no stable relationship between the two.

Visually alone, you can observe how unstable this relationship is between the two variables. Between 1992-2009, the correlation between the two looks reasonably positive. However, between 2009-2016 the correlation is very negative.

• Detrending and differencing are assumed filters. The preferred approach is to build an ARMA model for the stationary X series and use that filter to pre-whiten the stationary Y and X . Your suggestion can be right BUT not in general. See onlinecourses.science.psu.edu/stat510/node/75 for more. Jan 20, 2017 at 15:20

I am not familiar with SPSS, but for the linear trends that are very similar as you said, you could do a test for coincidence and parallelism of them. This method will test, in a given probability level, those two behaviors.

If coincidence is not verified, parallelism will answer you if the growing rates are the same also in a given probability level.

Let me know if it helped or if you need more information on these tests.

• Hi, thank you for this, unfortunately I am completely unfamiliar with stats so if you could give me some more information that would be great. Apr 11, 2015 at 14:19
• I will edit my original post to show the data graph so far Apr 11, 2015 at 14:19
• @Rebecca, I think you should give a little more think on what you do need or want from the data. Actually, this is the most important question before choosing any kind of analysis. Saying that you want to compare those lines is pretty vague, since you could do this using only the graphic you showed. Apr 12, 2015 at 21:07