I'm quite stumped as to how to answer the question because it would be rather difficult to correct the interpretations of others...
The best model of the data will be like this:
It is plausible. That means that there isn't something mistaken about the explanation.
It has the best explanatory scope. That means very few data points need to be called 'outliers'.
It has the best explanatory power. That means that the data fit the model very well.
It is less ad-hoc. That means that the model only needs a few equations, and there are very few data points that require extra explanation.
Here's a example:
We do an experiment and get valid results. We say X causes A to happen. We do another experiment and get valid results. We say Y causes A to happen.
In both cases, we have math and observations backing up our claims.
But X and Y are self-exclusive (a xor if you will). So what can we do in this case ?
We can do experiments of another nature and see what was actually correct. But if that's not possible, we should select the cause that actually can explain more.
I encountered this in physics many times, where theories were validated both by observation and math and in the math part we had a constant "c" and a variable "v" because in this manner the observations could be explained. But re-thinking everything, one could see that in the math formulas, the same valid result is obtained if "c" varies and "v" is declared a constant. Both cannot be variable or constant in the same time because it would invalidate the math part supporting the theory. So we got 2 options leading to the same result, confirming the same theory but we do not know which is a variable and which is a constant and we have no observable/experimental way to determine this.
What did in such a case was choosing the option that can explain more. In the current example, let's say if we had a constant "c" and a variable "v" we can perfectly explain how a car engine works, but cannot determine anything related to the car wheels. If "c" varies and "v" is constant and we explain how the engine works just as in the 1st theory but we can also explain how the wheels work, we select the second option as the valid one.
Different interpretations of data involve different philosophical ideas about how to conduct discussion and different explanations of what is happening in reality to bring about that data.
Different explanations can be tested by looking for cases in which they differ and performing tests in those cases. You can also consider different explanations by looking at whether they are consistent, whether they are ad hoc and that sort of thing.
Philosophical ideas can be discussed critically too. If you're discussing epistemology, then you can consider issues like the following. Do idea X and idea Y contradict the laws of logic? Do idea X and idea Y make any clear recommendations for action? Do these recommendations have anything to do with the rest of the content of the theory or do they completely divorced from reality? Is it possible to implement the measures recommended by idea X or idea Y?
Is there any way disputes over a knowledge claim due to different interpretations of data can be resolved?
The answer is always maybe. This is the whole basis of science. If you cannot follow these steps, then the dispute is always subjective.
- You create a hypothesis that explains the data.
- You create an experiment that will confirm or deny the hypothesis.
- You perform the experiment and look at the data.
What has been discovered is our experiments exclude options, but can only say a particular effect happens, not absolutely what that effect is. So the resolution of a dispute relies on the creation of a hypothesis which is linked to an experiment that will show the outcomes.
Now some issues are unresolvable, because no such hypothesis and experiment is possible to create. Dark matter is such an issue.