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Assume that somebody claims that driving a car or being an airplane pilot is just like riding a bike and anybody can do it with just a little practice and therefore it is unnecessary to have a license. He says that unlicensed car drivers and unlicensed airplane pilots are at least as good as "real" licensed vehicle operators because if you don't have a license then you are more careful not to get caught (hypothetical argument by myself) and therefore they are careful. So his argument would be that unlawful vehicle drivers are at least as safe as drivers who have a license.

Can I test or contradict such a claim when I can't know and can't estimate how many drivers or pilots there are in the population who don't have a license? We will know who had a license only if the driver was actually caught.

Is it possible or must I make additional assumptions and/or extrapolate?

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    Well, it seems like you'd need a prior of some sort. That is, if you knew that $10\%$ of the total driving population was unlicensed, you could compare that to the unlicensed percent of drivers who are caught driving unsafely. Absent that sort of knowledge, I can't see anything you could say.... – 2017-01-13
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    @lulu I suppose I could say that the claim is not scientific or non-falsifiable. There is a word in my native language "mörkertal" literally meaning "number in the darkness" about such percentages that you can't measure for different reasons but you know that they exist, mainly used about crime statistics. – 2017-01-13
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    Well, it's not untestable in principle. That is to say, I'd imagine that there are ways of estimating the unlicensed population. But, yes...some approach to the prior probability is needed. – 2017-01-13
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    One method of estimating the size of the population of unlicensed drivers might be 'capture-recapture' (AKA 'mark-recapture'). Googleable. The capture phase is licensing, the recapture phase might use data from random stops (e.g., at holiday time) to screen for drunk drivers. Some of these stops are set up so drivers cannot anticipate them and turn out of the way to avoid them. (Although I'm a fan if Bayesian statistics, I feel the term 'prior' is being tossed about carelessly, vaguely and uselessly--"slarvigt"-- here.) – 2017-01-13

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