Ah, OK. Now I see what you meant. Then the second shooter wasn't perfect either. However, he still came closer to "perfection" than the first shooter did, because his shots landed closer to his intended targets (the first shooter's bullet holes) than her shots did to her intended target (the bullseye).
He hit dead center of the target no more accurately than she had.
But the center of the target isn't his standard for accuracy, becuase that's not what he aimed for.
Precision is about replication. But, you say, he replicated all of her shots. That is true, but in doing so he failed to replicate any of his own.
It doesn't matter, because it wasn't his goal to repeatedly hit a single point; he was trying to replicate HER shots, one by one. Again, I'm talking about the precision of his aim: The distribution of his shots is a measurement of that precision. But instead of comparing his bullet holes to the bullseye, we compare them to their intended targets, i.e. the first shooter's bullet holes.
A shot is accurate if it hits its mark, i.e. if it hits where the shooter wants it to. This depends on the precision of the shooter's aim, but is also affected by things like the calibration of certain parts of the gun. However, if the aim is imprecise, then the shots will tend to deviate from their intended marks (one may land a bit to the right, another up and to the left, etc.), and thus be inaccurate.
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All true, but you're just throwing extra noise at me. Accounting for the throw of the weapon makes attaining accuracy & precision more difficult, but we're only dealing with the end results here.
See post 91 for the analogy describing accuracy and precision in an empirical sense.
If you're talking about measuring many things, the precision of your standard wouldn't be knowable.
Not necassarily. Like I said above, for this current example we can compare the second shooter's bullet holes to to his intended targets (i.e. the bullet holes of the first shooter) to obtain a measurement of his precision and accuracy.
in logic, it is meaningless to say that a statement is accurate if it is not defined precisely.
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Meaningless or not knowable?
Perhaps not knowable, but also meaningless. We've switched to talking about logic now (instead of empiricism), and if a statement is not defined precisely enough then it is automatically false. Let's go back to your "The ball is round" statement and make it universal: "All balls are round." Now there are lots of round balls, but this statement is false due to its generality. On the other hand, if we've never seen anything like an American football, then we might not know that this statement is false, but then all we could say is "Every ball I know of is round."
The accuracy of something is unknowable unless tested against a precise standard, but something could be accurate without that test.
But I'm talking about the accuracy of the test itself. In the shooting example, we already know exactly where the bullseye is before shooting at it, but that's different than what I'm talking about. When making measurements, it's other way around: You're trying to find the bullseye by shooting at it! :)
Ah, OK. Now I see what you meant. Then the second shooter wasn't perfect either.
Whether he was "perfect" or not is an unknown. Measurements from the centers of her holes & his holes could possibly prove perfect, as her holes were only a "suggested" target for him. As I said, if he had put all of his bullets through the holes she had made, totally missing the target would have been a possible conclusion. His real targets were her holes + a distance of X from them.
However, he still came closer to "perfection" than the first shooter did, because his shots landed closer to his intended targets (the first shooter's bullet holes) than her shots did to her intended target (the bullseye).
Correct.
But the center of the target isn't his standard for accuracy, becuase that's not what he aimed for.
Doesn't matter what his standard was, as this is my hypothetical, not his. I set up the parameters in order to communicate a concept, not to discuss our shooters, their thinking or their skill. I think they used a target with a human form, so there wasn't actually a "center", but I needed a center for the purpose of my hypothetical, so I put one in.
I said, "Precision is about replication. But, you say, he replicated all of her shots. That is true, but in doing so he failed to replicate any of his own."
It doesn't matter, because it wasn't his goal to repeatedly hit a single point; he was trying to replicate HER shots, one by one.
Come up with your own hypothetical. This one's mine. Cue evil dictator laughter, "bwhahaha". Since he is my tool, I tell you his intent was exactly what I say it was, to hit the imaginary center of that target... man, did he get lucky, as he proved himself at least as good as the woman. ;o)
A graph for precision charts density. The more density you have, the more precise your standard. I was trying to get you unstuck from thinking it was only about spread by giving you an exception to that "rule", so I gave him an extra bullet. :o)
Again, I'm talking about the precision of his aim: The distribution of his shots is a measurement of that precision. But instead of comparing his bullet holes to the bullseye, we compare them to their intended targets, i.e. the first shooter's bullet holes.
I already told you that his true accuracy & the precision of his shots were better than hers. How would we know if his precision was better if she had not set standards for him first? His shots raised the shot density by each of her shots. Now, picture his shots without hers. His shot density could then be seen as the same as hers had been & we'd be talking about the spread of his shots.