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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No, that's not a misunderstanding. Study 1 made mistake A that skewed in direction X. Study 2 made a mistake B that skewed in direction Y. Either X and Y are the same direction (hence local skew becomes the same as global skew) or (assuming X and Y are not orthogonal) they'll
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Correct. As an expected value, non-correlating confounders have a neutral result. That he doesn't seem to understand this is pretty damning for a person in his position, trying to appear as an authority on statistics.
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I'm not an authority in statistics, happy to clarify
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