Pearson R and range of data I have the following two lists:
x = [7,8, 9, 9, 9, 9, 10, 10, 10]
y = [9, 9, 10, 9, 8, 6, 10, 9, 8]
the Pearson r value is equal to 0 in this case.
However, the thing is, these numbers are from two parameters where we ask participants to select values for each parameter from a range of 0 to 10, and it just happens that all the participants rated high values.
If I add (0,0) as an extra point as follows to make it aware of the breadth of the range:
x = [7,8, 9, 9, 9, 9, 10, 10, 10, 0]
y = [9, 9, 10, 9, 8, 6, 10, 9, 8, 0]
the r value changes to 0.87.
I do know however that I cannot add (0,0) so how do I let it know that the range is from 0 to 10?
Adding more context to the question: The correlation was calculated for a test-retest reliability. I have the same set of users test a tool twice, and each time they would answer the same question. That's why their questions are close. So for example, person 1 answered 7/10 the first time and 9/10 the second. The 2nd person answered 8/9 first time and 9/10 the second time. Those seem to be highly correlated answers to me, they are consistingly high. What I don't understand is why the Pearson R is 0 here. I feel I'm doing something wrong.

Why do you want to "let it know that the range is from 0 to 10"? This of course depends on why you calculated the Pearson $r$ as you did.
If you are interested in the association between $x$ and $y$, I would recommend you also look at the corresponding confidence interval for $r$ (for example in R with the cor.test method). For the data you provided this confidence interval is $[-.66, .66]$. That is a lot of uncertainty!
Your data are consistent with both large positive and large negative correlations, so my advice would be to obtain more data!
