Captain Bluetooth is confused about the consensus
Arg, me hearties, I’ve been learnin’ me numbers. Need to divvy up the booty fair ‘n square. Burden of bein’ a cap’n, an all.
A week past I got cut in a fight with Leftie Jake. So I got to wonderin’, what proportion of sailor dogs are right handed?
So I calls the crew on deck, all three ‘undred men, and I asks ‘em “Which hand do you dogs like to use yer cutlass in?”.
[100 CUTLASSES FIGURE]
Ninety seven of them says “Right”. Two says “Left”. Roberts says “Both”, the blaggard [PRINCESS BRIDE LINK].
The other two hundred? They’re cussin’ me and yelling “I’ve only got one ‘and”. Except for two-hooks Jim who fixes me a stare that’s blacker ‘n pitch.
So this is what’s puzzlin’ me. Is the proportion of sailor dogs that’s right ‘anded 97% (ninety seven of an ‘undred), or 32% (ninety seven of three ‘undred).
The captain’s problem is that he is confused over a distinction between what he is trying to measue and the data he is using to measure it. The number he is trying to determine is the proportion of sailors which are right handed. The observations are the count of pirates in his crew who use their cutlass in their right hand by preference.
The captain’s best guess at the proportion of right handers is clearly 97%. Why? Because only 100 of the crew give him an answer which is relevent to determining handedness, and of them 97 are right handed. He has no information about the handedness of the remainder, or indeed the crews of other ships, and so has to infer their handedness from the sample he knows about. However to conclude that only 32% are right handed would be nonsense.
[STUFF ON WHY THIS IS LIKE TCP, INCLUDING BARREL FIGURE]