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A comment on High refined sugar intake linked to a 23% higher risk of mental disorders. Parent comment
Let group S be sugar eaters.
Let group A be all people w/o mental disorders.
Let group B be all people w/ mental disorders.
We have the main correlation between sugar and mental disorder:
p[A/S] <= p[B/S]
Using bayes rule:
p[A]p[S/A] <= p[B]p[S/B]
We also have "men and women with mental disorders were not more likely to consume more sugar":
p[S/A] >= p[S/B]
Comparing the inequalities gives us:
p[A] <= p[B]
So you're more likely to have a mental dissorder than not according to this study???
This doesn't follow. Just because mental disorders are correlated with sugar doesn't mean that most sugar eaters have mental disorders.
Let group S be sugar eaters.
Let group A be all people w/o mental disorders.
Let group B be all people w/ mental disorders.
We have the main correlation between sugar and mental disorder:
p[A/S] <= p[B/S]
Using bayes rule:
p[A]p[S/A] <= p[B]p[S/B]
We also have "men and women with mental disorders were not more likely to consume more sugar":
p[S/A] >= p[S/B]
Comparing the inequalities gives us:
p[A] <= p[B]
So you're more likely to have a mental dissorder than not according to this study???