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Related Discussions
Inferrences based on "the more Xs, the more Ys"
Rev_Lefe
Member
Hi All,
My question is: from "the more Xs, the more Ys", could I infer "the less Xs, the less Ys"?
This inference seems neither a valid nor a strongly supported inference to me, because we can't infer a negative corelation from a positive correlation. Still, I am very unsure. Anyone can share your thoughts?
Thanks a lot.
Leon
Comments
Unless you know if there’s a cause in the relationship, you cannot make an inference on a correlation statement.
If you’re given a correlation (the more A, the more B ), it gives rise to four possibilities:
1. A causes B
2. B causes A
3. C causes both A and B
4. No relationship
For example: The more money I have, the more things I can buy.
If I tell you that money determines how many things that I buy (A causes B ), then yes, you can say that the less money I have, the less things that I can buy.
Here, you can make an inference because I’m telling you that A causes B. But if you were only given the correlation statement, then you wouldn’t be able to make further inferences because you wouldn’t know which of the four possibilities it would fall into.
Hey Leon!
In essence, the answer is going to be yes.
"The more Xs, the more Ys" inherently also means if you have less Xs, you will also have less Ys. These are both considered a positive correlation.
A negative correlation is when one property increases, another property decreases.
This would be if the statement said "the more X, the less Y". With this, you can also infer that the less X you have, the more Y you will have.
Yeah, these can get really complicated. You can actually graph them on an x and y axis, and you'll see that "the more . . . the more . . ." does indeed result in an inference of "the less . . . the less . . . ."
One thing the test writers sometimes do here to really complicate it is that they'll introduce a threshold. So they might say something like, "happiness tends to increase with household income levels until incomes reach $80,000." Now we know that from $0 to $80,000 we have this relationship, but past the $80k threshold, the relationship breaks. (We should also be sensitive here to the word "tends" here, which could become really important depending on the specific direction of the question.)
This is particularly tricky when it's the AC that introduces the threshold rather than the stimulus. Maybe we're asked to weaken an argument that claims that job performance increases with the number of hours worked per week. An answer introducing a threshold may say, "past 70 hours a week, workers begin facing burnout which may have a negative impact on their job performance." This only impacts the end of the spectrum, but it's enough. If the relationship doesn't hold across the full range of possibilities, it doesn't hold for a universal conclusion like in the example here.
In addition to the points made earlier, I'd add that you should be careful not to assume that "the more X, the more Y" implies a proportional relationship. A doubling in the amount of X implies an increase in the amount of Y, but it doesn't have to correspond to a doubling of Y.
@"Chris Nguyen" @"Cant Get Right"
Does a “the more A, the more B” statement always imply that there is a relationship between A and B (meaning, A affects B )?
I think of arguments such as:
There’s been an increase in ice cream sales this summer. There has also been an increase in swimming pool drownings. Therefore, if we want less people to drown, we should lessen the ice cream sales.
If we break this argument down, the premise is implying that the more ice cream sales, the more swimming pool drownings and then it’s further inferring in the conclusion that the less ice cream sales, the less swimming pool drownings.
If this was a flaw question, we would say the the conclusion doesn’t follow because it’s making a correlation-causation error.
Is the error because it’s inferring a false “the more A, the more B” statement, or because there is no known causal relationship between A and B, so you can’t say “the less we have of A, the less we have of B”?
Also, "the more X, the more Y": This is not a correlation.
Absolutely it does. It's just a relationship which doesn't require causation. Whether A causes B or not doesn't matter. Certainly if more A caused more B that would explain the relationship, but with or without the underlying cause, the statement establishes the relationship just the same.
Despite the flawed causation, isn't it likely true that "the more ice cream that gets sold, the more swimming pool drowning deaths that are reported." Doesn't this strike your intuition as likely true? We know ice cream isn't causing drowning deaths, but the statement isn't making any claims as to the underlying cause. It is simply saying that an increase in one phenomenon corresponds to an increase in another. With C causing A and B style causation flaws, the flaw is mistaking correlation for causation. But the correlation is very much there in these types of things, and correlations are relationships.
In your example, the flaw is making a leap from correlation to causation. You're absolutely right about that. But a "the more . . . the more . . ." statement on its own is not flawed at all. It's not asserting any inferences or conclusions, so it is merely serving as an observation. It's role in the argument is just a premise, so we need to accept it as true. Unless it's given as a conclusion, of course, then that's a whole other issue!
@"Cant Get Right"
Ohhh, I think I understand. So, if we look at these two arguments:
1) The more ice cream sales, the more swimming pool drownings. Therefore, the less ice cream sales, the less swimming pool drownings.
2) The more ice cream sales, the more swimming pool drownings. The less ice cream sales, the less swimming pool drownings. Therefore, we should lessen ice cream sales if we want to prevent people from drowning.
Both arguments are making a correlation-causation error, right?
I thought OP’s argument was in reference to arguments like (1), which is why I was so confused.
But, in (1) the “less A, less B” statement is used to infer a causal relationship because it’s in the conclusion. Whereas in (2), the “less A, less B” is in the premise, so that observation/statement is valid.
This is a valid argument. If we were to map it out, it would look like this:
https://study.com/cimages/multimages/16/screen_shot_2017-06-01_at_7.21.45_pm.png
The further along we move along the x axis, the further up we move on the y axis.
If you look at it on a graph. The more you have of x, the more you get of y. If this holds true, then the reverse is also true. There's nowhere to move along the line so that you get less of x and not also less of y.
@bananabo
Is it possible you're confusing (1) "The less X, the less Y" with (2) "If we reduce X, we will reduce Y"?
Statement (1) is not making a causal claim. Statement (2) is, however, based on a causal assumption (that X causes Y).
Using your ice cream example:
Statistics show that the more ice cream sales in a month, the more drownings that month. Therefore, since May had fewer ice cream sales than June, we can infer that May had fewer drownings than June.
Statistics show that the more ice cream sales in a month, the more drownings that month. Therefore, if we can reduce ice cream sales next month, we will help decrease the number of drownings that occur.
The first argument is valid and is not asserting any kind of causal relationship. The second argument is invalid and is assuming that the ice cream sales play a causal role in the drownings.
Ahhhh, yes! I was interpreting (1) to mean (2), but now I understand the difference haha
Thank you!
Really great thread. This is exactly the kind of thing we’re looking for in diagnosing our errors. Things like question type can be helpful early in prep, but in more advanced stages, it’s this type of underlying reasoning that we are trying to get at in review and analysis. This is one I’d identified in my own prep and kept a careful eye out for. Once I’d done the hard work of figuring out the nuances to the relationship in review, then anytime I’d come across it again I’d already done 80% of the work for solving future questions. And that’s how you get these right and get them fast.
For anyone wanting to dig deeper, here are a few questions I had compiled which utilize this type of relationship in some way:
PT.Section.Question
46.2.10
51.3.9
57.2.6
78.1.11
85.3.17