You don't really.

But assuming the FB/Google reported numbers are accurate, would you pay for them and just convince yourself they are actually increasing your sales?

You should be able to at least plot sales numbers against ad spending per week over a year.

Facebook also "should" be able to report numbers in a way that isn't misleading to their customers.

Inputs are not good or bad, they are better or worse.

In the 1300s, feedback to the advertiser took years.

In the 1900s, months.

In the 1960s, you could now measure the effect of blanketing a MMR with ads, and see how sales there compared to nationally.

This century, you have still-imperfect, yet much better than before, attribution.

Good analysis in the 1930s was different than now. Good marketing was the same, but with cruder tools.

Ah, classic courtroom fraud defense. "Feel fortunate you even caught me; that would've been impossible a century ago!"

Having wiggle room on numbers isn't a bad thing. Lying about the amount of wiggle room on said numbers is.

You can do the analysis that you want, there's no proof that advertising increase something. They are bad and should be banned from our live.