By definition a confounder skews in one direction, otherwise it does not confound the relationship and is not a confounder
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Replying to @GidMK @K_Sheldrick
A confounder skews in one direction *internally* to a single study, but those wash out at high numbers of studies/coin flips. What you need are global confounders to make the argument.
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Replying to @GidMK @K_Sheldrick
It's provably correct. May I invite you to walk through the math with me on camera?
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Replying to @EduEngineer @K_Sheldrick
It has very little to do with maths actually. The maths of meta-analysis is really quite simple, it's just a weighted average, if the included studies all make the same errors in terms of confounding than by definition the weighted average will also have this error
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Replying to @GidMK @K_Sheldrick
"if the included studies all make the same errors in terms of confounding than by definition the weighted average will also have this error" That assumes there is a confounder that is global in bias. Otherwise, it's random. It's a coinflip embedded in a coinflip that...
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Replying to @EduEngineer @K_Sheldrick
Nonsense. That's just a misunderstanding of confounding
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Replying to @GidMK @K_Sheldrick
Saying that there is a difference in kind between the effects of local and global confounders is a misunderstanding? Wow. This is truly amazing.
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Replying to @EduEngineer
Nope, just that you've totally misunderstood and misdefined confounding at a very basic level
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Replying to @GidMK
I've never defined confounder, but the point is *a local effect that doesn't affect every study, vs. *a global effect that affects every study. The first kind has no expected effect on the outcome of the p-value. The second does. I can prove it, and will do so live with you.
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You said that confounders affect results randomly. That's by definition incorrect
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