Independence of two data sets? I have a task where a human subject uses a joystick to move a dot on the screen according to a desired trajectory for 5 minutes. During this experiment I record the joystick data; let's call it data1. The same human subject again performs the same task for the same desired trajectory for 5 minutes on a different day, and let's call that data data2. Can we say that data1 and data2 are independent since they were recorder from two different trial runs on two different day and time? And why if yes or no?
 A: No, we cannot say they're independent.
The trajectories are recorded by the same individual, and so there's no reason to believe they're independent, and instead, we would expect they're dependent.
If the trajectories were recorded by different people then such an assumption would be justified.
A: If there is a correlation between the single trajectory and each of the two tracking records for two trials, it does not matter who did them, and when they were done; the two tracking records will also be correlated, although likely less so than either tracing record correlates with the trajectory. Thus, there is no independence. Notice, significance has nothing to do with it. That is, a significance of correlation of one tracking record with another would be irrelevant; they are not independent.
A: I also would say there dependent because the human subject already played with the joystick so he in some way knows the rules of the experiment, next time he plays again, he will incorporate this knowledge in the trial, making it conditioned. 
