Given a table as below:
It was obtained when several respondents were asked to look at a given picture(stimulus) and then press a button depending on what was seen by them. The column reaction time denotes the time between the moment the image was shown and the button is pressed. The data obtained from the 4 pictures(stimulus) is recorded in a table shown above. Let the values under column reaction time be represented as $x_{1},x_{2},x_{3},...,x_{n}$ in the order represented in the above table.
How to make a conclusion that whether $x_{1}$ and $x_{2}$ can be independent or $x_{1}$ and $x_{5}$ are independent or $x_{1},x_{2},x_{3},...,x_{n}$ are independent and identically distributed sample of some random variable?
I tried by using the correlation approach to check if the two rows are correlated or not. Based on that, i came up to the conclusion that it is not independent. But am not sure if the above approach is correct for the given formulation.
Can you please let me know if the correlation approach is correct for the above formulation?