Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: jinjon on 24/05/2022 16:36:47
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Hi,
I am wondering if it is a mistake to write the results of linear regression and logistic regression analysis as that the variables that you have analysed: do or do not correlate with each other.
Or is it wrong to say that they are correlated to each other and you should say that there is an association ( or no association) between the variables?
For example a is the independent variable, b is the dependent variable. You apply linear regression or logistic regression and report the results as:
a is correlatad with b or not correlated with b...
Hope you understand what I mean.
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a is the independent variable, b is the dependent variable
I know that this is normal terminology, but it implies a causal direction.
- If there is some variable in your experiment that you can easily control, and another variable that you can easily measure, then it is fair to say that "when I changed variable x, variable y changed in a (linear/parabolic/exponential) manner"
However, when it comes to complex things like the impact of obesity in a human population on heart attacks:
- There is no easy way to control obesity in a whole population
- There is no easy way to control heart attacks in a whole population
- There are many factors which can cause heart attacks (eg genetics, congenital problems, education on exercise, stress)
- There are many factors which can cause obesity (eg genetics, income, education on healthy diet, stress)
- So the easiest thing to do is to do some sort of scatterplot of obesity vs age of first heart attack
- Then do a regression line through it, to conclude that "with increased variable x, variable y changes in a (linear/parabolic/exponential) manner"
- You could hypothesize that obesity contributes to heart attacks (since the obesity was present before the first heart attack), but it's not guaranteed: Someone who has an underlying heart condition may be predisposed to a sedentary lifestyle, which may make them obese.
- You could make comments like "For patients with BMI > 30, a weight reduction of 1 kg is associated with a delay of z years in age of first heart attack."
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Hi.
Good general discussion from @evan_au above.
is it wrong to say that they are correlated to each other
No it's not "wrong" it's just a bit dangerous or could be misunderstood.
Essentially it depends on your target audience - the people who you expect to read your statements.
The phrase "X and Y are uncorrelated" has a precise meaning to a Statistician or Mathematician. It means precisely r(X,Y) = 0 (the correlation coefficient = 0) and nothing more. They won't jump to any other conclusions, in particular they won't assume that X and Y are completely unrelated or independent variables. They know that X could still be entirely determined by Y, they just aren't linearly related.
The phrase "X and Y are correlated" would just mean that r(x,Y) equals anything else other than 0. To be honest, that's a rare phrase to use for statisticians. It would be more common to take more lines and state that r(X,Y) cannot be zero but its not clear that a linear relationship exists or else just leave it written in symbols r(X,Y) ≠ 0. If you did leave that phrase "X and Y are correlated" as if it was some sort of final conclusion then they might reasonably assume you meant that X and Y are strongly correlated, or that |r(x,Y)| ≈ 1. To say that in plain English - they might assume that X is (or is almost entirely explained by) a linear function of Y.
If your target audience is not a group of statisticians, then you "know" that when people hear the words "correlated" or "uncorrelated" they will jump to conclusions about whether X and Y are independent or unrelated. They might make even bigger jumps than that and assume one thing is actually the cause of the other. So if your target audience isn't a group of statisticians, then you really must do as @evan_au suggested and choose your phrases more carefully.
Best Wishes.
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Thank you guys for the help!