Does a correlation go both ways?

Comments

• inactive Alum Member

  May 2017 12637 karma

  Bumping so more people can see this!
• jknauf Alum Member

  May 2017 edited May 2017 1741 karma

  Hmm, I'm completely unsure. But I'll throw in some ideas which hopefully gets the conversation going.

  I don't think we can logically conclude much from a correlation. We can find a correlation with anything. For example, there is a correlation between the average growth of a 7th graders big toe and how well that 7th grader is able to spell. Is this correlation positive or negative? We don't know. If the 7th graders big toe is growing rapidly, can we conclude that they must be good at spelling? If the 7th grader is good at spelling, can we conclude he must have a good size toe?
  (what is considered a good sized toe anyways?) We can't conclude either of those two ideas. The only thing we can conclude is that there is a correlation.

  So lets try and think through another example somewhat analogous to your question above. "The longer duration a person can run, the farther away from a starting point that person will be after ten minutes."

  So now can we conclude "The farther away from a starting point one person is after ten minutes, the longer duration one person can run."?

  No! What if we have one person who can run full sprint for 2 minutes and make it 1 mile from a starting point, and another person who can run for 10 minutes and only make it 1 mile from the starting point?

  I think the only idea we can conclude is what the LSAT authors gave us. I believe reversing the relationship would be an unwarranted assumption.

  But seeing how the rebuttal example I came up with, would also destroy the idea of The farther away from the starting point one person is after ten minutes, the longer a person can run I'm now beating my head on the computer desk thinking in circles.
• CinnamonTea Member

  May 2017 550 karma

  Thanks @jkanuf. Does anyone else know the answer to my question above (as related to the LSAT?)
• AllezAllez21 Member Inactive Sage Inactive ⭐

  May 2017 edited May 2017 1917 karma

  I believe you can conclude both 1 and 2 based on context and how we know the world works. I think the statement you give hints at the duration one can remain submerged as a necessary condition for the depth to which one can dive (to an unknown extent).

  So for the second statement, if an animal can dive deeper and deeper, it necessarily must be able to be submerged for a longer duration. I would add the important caveat that this only works within an individual, possibly within a species. So maybe there is some dolphin that cannot be submerged for all that long, but it's super fast so it can dive deep. Compare that to some other creature who is super slow at diving so they don't go as deep but can stay submerged for much longer. However, all other things being equal, the longer a particular individual can stay submerged, the deeper it can dive.

  I guess all that is to say that you just have to be aware of the context and circumstances being given in the stimulus.

  Does a correlation go both ways? I think it does by definition. A correlation is a description of how two things relate to one another. You cannot have one without the other.

  Think of a positive correlation scatter plot, like this one: http://www.shmoop.com/images/algebra/alg_probstat_bivar_narr_graphik_14.png

  As you get more Y, you get more X. As you get more X, you get more Y. This is unavoidable. If this relationship did not hold, then X and Y would not be positively correlated.

  Edit: so I think the issue here is really more about what is a correlation, how will the LSAT try to imply correlation or trick you with something that sounds like a correlation but really isn't.
• jknauf Alum Member

  May 2017 1741 karma

  @AllezAllez21 said:

  As you get more Y, you get more X. As you get more X, you get more Y. This is unavoidable. If this relationship did not hold, then X and Y would not be positively correlated.
  
  Edit: so I think the issue here is really more about what is a correlation, how will the LSAT try to imply correlation or trick you with something that sounds like a correlation but really isn't.

  Yeah I agree with this
• xtrfalcon Alum Member

  May 2017 148 karma

  @AllezAllez21 said:
  As you get more Y, you get more X. As you get more X, you get more Y. This is unavoidable. If this relationship did not hold, then X and Y would not be positively correlated.
  
  Edit: so I think the issue here is really more about what is a correlation, how will the LSAT try to imply correlation or trick you with something that sounds like a correlation but really isn't.

  This was a nice way of putting it. Pay attention as to whether the premises gloss over the fact that they are indeed, correlated (by saying they are, or are inversely so) versus providing you with two events that have happened (that lead us to believe they may or may not be correlated). Just want to emphasize what Allez said when it's probably more important to understand whether they are tricking you with something that isn't actually correlated.

  As to your other thoughts, you seem to have a solid understanding that I can't add much value to. I would be keen on seeing similar examples that have prompted your cause/effect relationship reversal issue to come to the forefront.
• CinnamonTea Member

  May 2017 550 karma

  Thank you so much @AllezAllez21