I have four datasets: A1, A2, B1, B2. Every dataset has between 100-300 items.
Every item in every dataset has two values: x, y
- Find what datasets have similar x values.
- If the datasets have similar x values, are their correlations between x and y similar? And vice-versa.
With t-test for x values I found out, that A1 and A2 are not too different (mean value is not significantly different). The same thing stands for B1, B2. But every of A datasets is significantly different than any of B datasets. In list
- A1.x and A2.x - similar
- B1.x and B2.x - similar
- A1.x and (B1.x or B2.x) - different
- A2.x and (B1.x or B2.x) - different
Now I am interested, if the correlation between x and y in dataset, is the same for A1 and A2, while it is different for correlation of B1 and B2 (what should be the same again). I calculated this correlations and I got:
- correlation of A1.x and A1.y = 0.487
- correlation of A2.x and A2.y = 0.460
- correlation of B1.x and B1.y = 0.598
- correlation of B2.x and B2.y = 0.610
Main question: What test I should use, to measure how significant is this similarity / difference in the correlations? Because it probably still could be just coincidence.
Other question: Is the t-test good way how to estimate if two datasets comes from the same precess? Should I do it also for y values in this case?
I hope it is clear what I need. If not, please comment what is unclear, I will do my best to explain.