Meaningful statistic measure of data pairs I have a dilemma. I have pairwise data, (a,b), that rep

Zeihergp

Zeihergp

Answered question

2022-05-26

Meaningful statistic measure of data pairs
I have a dilemma.
I have pairwise data, (a,b), that represents some form of speed, whether it's miles/hour or megabits/second. Let's say that we have the following set of data from measuring the "speed" of the same "car" on two different "courses" A and B under different conditions (say weather), ignoring the unit for now, and with apologies for my notations.
{(a,b)} = {(1, 4), (1, 2), (1, 1), (2, 1), (4, 1)}
There are a few ways to interpret the data:
1) If one believes that the "car" runs faster on "course" A and calculates the average of speed-up (a/b):
average speedup = (1/4 + 1/2 + 1/1 + 2/1 + 4/1)/5 = 1.55
Voila, "course" A makes the "car" go 55% faster than "course" B!
2) If one believes that the "car" runs faster on "course" B and calculates the average of speed-up (b/a):
average speedup = (4/1 + 2/1 + 1/1 + 1/2 + 1/4)/5 = 1.55
Voila, "course" B makes the "car" go 55% faster than "course" A!
3) If one believes say CDF is the right way to compare the data set, then it will be something like:
A: 1, 1, 1, 2, 4
B: 1, 1, 1, 2, 4
Voila, "courses" A and B are more or less identical.
Obviously, all three interpretations mask out important details, but at the same time, I am not able to come up with a good statistical measure to describe this set of data. This is clearly just a toy example, but I am facing similar dilemmas interpreting real data.
Thanks!

Answer & Explanation

Porter Cohen

Porter Cohen

Beginner2022-05-27Added 7 answers

You have to decide what is important for your situation. Let's say the average speed is important. Then you do a hypothesis test on the means. In this case a paired t-test might be appropriate. Or maybe a permutation test.
Maybe it's important to know if the speeds for A and B have the same distribution or not. Then a two-sample Kolmogorov-Smirnov test could be applied.
A single metric could work for you. It just depends on what you really need to know.

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