Does the Correlation works both ways?

[smtq123]

Q1: Given that "As A increases, B increases". Then is it true to say that "As B increases, A increases"?
Q2: Given that "A tends to be B". Then is it true to say that "As B increases, A increases"?

Reposting it after amending it. Please disregard the below query and answer this one. Thanks.

Hi,

Please answer the following query:
Q1: Given that A increases as B increases. Then is it true to say that as B increases A increases?
Q2: Given that A tends to be B. Then is it true to say that as B increases A increases?

Many thanks in advance.

Regards.

[Beth Hayden]

Hi SMTQ,

Remember that and are different and have different implications. A B does not necessarily mean that B A.

If as A increases, B increases, that doesn't mean that A and B always increase together. There may be times that B increases but A stays the same. Consider this example: whenever I get a raise at work and my salary increases, I buy more shoes. This year I didn't get a raise and my salary stayed the same, but I nevertheless still bought more shoes. An increase in B tells you nothing about whether or not A also increased.

Now let's look at your second question--this would be the same as saying that most As are Bs. That doesn't tell you anything about what happens when there are more Bs. To make this clearer, let's use some numbers. Imagine that "most" means 75%, so for every 4 As, 3 of them are also Bs. But maybe there are also 100 Bs that are not As, they are just lonely Bs. Well if I add 4 more As, I will also necessarily add 3 more Bs. But it doesn't work the other way! I might add 100 more Bs, but they are lonely Bs, they have no effect on the number of As.

From A B you can infer ~B ~A, but you can't just reverse the arrow!

Hope that helps!
Beth

[smtq123]

Many thanks for clearing it for me.

Regards.

[smtq123]

Hi,

I have a follow up questions:
Q1. Given that "As A increases, B increases"; Can we say that conditionality exist between A & B in the form A ---> B, i.e. If A, then B.
Q2. Given that "A tends to be B"; Can we say that conditionality exist between A & B in the form A ---> B, i.e. If A, then B.
Q3. More generally, can we say if correlation is present then we also have conditionality? If NOT, then how these two are connected to each other?

Many thanks for your support in answering my queries.

Regards.

[Adam Tyson]

Q1. Given that "As A increases, B increases"; Can we say that conditionality exist between A & B in the form A ---> B, i.e. If A, then B.

Sort of. We can say that MORE A requires MORE B, but it leaves open the possibility of some base amount of A for which there is no B at all. Thus, A may not require B. Conditional relationships aren't generally expressed in terms of positive or negative correlations., and you would be better served on the LSAT to treat correlations as just that. Don't try to force them into a conditional framework.

Q2. Given that "A tends to be B"; Can we say that conditionality exist between A & B in the form A ---> B, i.e. If A, then B.

No, because "tends to" does not guarantee or require anything. It just means "usually" or "most of the time," which is an expression not of a conditional relationship but of Formal Logic. Conditional reasoning is about 100% guarantees. The necessary condition is more than probable or usual, but is certain to occur.

Q3. More generally, can we say if correlation is present then we also have conditionality? If NOT, then how these two are connected to each other?

No, which goes back to the first question. Correlations need not be perfect or guaranteed, but can be more along the lines of what is usual or typical. When faced with a correlation, treat it as just a correlation and not as a conditional relationship. Leave conditional analysis for true conditional claims, most of which will use the language commonly associated with conditionality (if...then and other similar forms). On the LSAT, correlation is usually (but not always) coupled with some sort of causal claim, and those need to be handled differently than conditional claims. Many wrong answers will mix those two up, so you should avoid going down that path yourself.

There CAN be conditional claims with correlations involved, but they are the exception rather than the norm on the LSAT. "Whenever I eat more than one helping of lasagna I get heartburn" is a conditional relationship ("whenever" indicates a Sufficient Condition) and a correlation (more than one helping correlates with heartburn). Faced with statement, though, I would ignore the correlation and focus on the conditionality, because that is what the LSAT would be likely to test in this case (unless the argument concluded with a causal claim, in which case my analysis would shift away from conditional reasoning and towards causal reasoning, as it is the more active and powerful reasoning type and generally takes precedence when the two are mixed).

In short, correlations are not conditional, and you shouldn't treat them as such. Confusion and wrong answers will await you if you do.