Post Hoc, Ergo Propter Hoc
Translation: After this, therefore because of this.

When I drank Budweiser I would always get a headache. When I woke up the next day I would always have a blinding sinus headache hangover. I would look in the mirror and always see a bunch of shiney silver hairs popping up on my head. After a couple of days they would go away. It doesn't happen when I drink other beer. My older brothers are twins of each other. They drink more than I. They drink Budweiser all the time. They have totally silver hair. They have had silver hair for over ten years. They are only 1 and a half years older than me.
Budweiser causes sinus headaches and silver hair.
Is this Post Hoc, Ergo Propter Hoc?

I don't drink Budweiser anymore and I don't have silver hair.

A somewhat more understandable translation is: "because one event happens after another event, the second is necessarily caused by the first."

Yes.

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Ach, mein Sinn, wo willst du endlich hin, wo soll ich mich erquicken? Bleib' ich hier, oder wünsch' ich mir Berg und Hügel auf den Rücken?
Bei der Welt ist gar kein Rat, und im Herzen steh'n die Schmerzen meiner Missetat, weil der Knecht den Herrn verleugnet hat.

The term is often used to denote a logical fallacy, mistaking correlation with causation, but with the addition of a time element. Is it possible that the Bud could be causing your symptoms?

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"What you think you thought you saw you did not see." Agent J, MiB - Manhatten Bureau

You've made two statements above that can be separated:

(1) Budweiser causes sinus headaches
(2) Budweiser causes grey hair

Both can be in the form of post hoc, ergo propter hoc. And by themselves as statements they are both logical fallacies. Just because the result is because of the Bud, doesn't mean the statement isn't still a logical fallacy when it stands alone. The truth isn't the point, rather the logic of the statement is. Without evidence, both are logical fallacies. Now ... when you bring evidence (as you have with a time frame for the headaches and I'm sure could bring many others such as dehydration, body effects of Bud ingredients, etc), the statement is no longer a post hoc, ergo propter hoc statement because you can define all the steps in between the drinking .. and the headache ... and each step logically follows the other.

The grey hair example only works if they weren't grey before starting to drink Bud, because the assumed effect has to have come after the assumed cause (which I'm sure you knew I'm just saying it for clarity). When it comes to the grey hair example, I think you'd be hard pressed to find logical, scientific steps connecting the two and therefore noticing that people who drink Bud ended up with grey hair ... remains a logical fallacy.

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I seem to recall that alcohol affects DHT levels in the blood. DHT is also related to hair growth.

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"What you think you thought you saw you did not see." Agent J, MiB - Manhatten Bureau

Budwiser? Silver hairs? Hair doesn't grow fast enough for you to see "a bunch of shiny silver hairs popping up" the next morning. Perhaps three mornings later...

Are you sure you didn't grab a can of silver Halloween hair spray, by mistake?

I think it's an issue of pigmentation not hair growth. It doesn't happen after drinking other beers or wine so alcohol alone isn't the causative factor. Also the repeating pattern and the time element establishes the causative case. So the proper phrasing would be usually after Bud therefore because of Bud.

Gray hair is hereditary. You get it from your children.

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Later . . .

Probably, but someone asked for some sort of scientific link and that's what I recalled.

It's more likely to be due to mental state in the morning allowing one to distinguish the gray hairs that are already there. That doesn't rule out biochemical causation, but it might suggest that possibly caused by the same source, are merely correlated in the timeframe described.

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"What you think you thought you saw you did not see." Agent J, MiB - Manhatten Bureau

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