Maybe. It depends on the distributions over programming ability that the test and color, respectively, provide. [ETA1: I should have written, “the test and the conjunction of test and color, respectively...”. The point is that, conditioned on test results, color could be independent of ability.] [ETA2: Though, if your “further conclusions” was meant to include things beyond what the test tests for, but which correlate with color, then you’re definitely right.]
The test’s being colorblind doesn’t mean that its results don’t correlate with color in the population of subjects. It means that, were you to fix a test subject and vary its color while holding everything else constant, its test results wouldn’t correlate with the color change.
Learning the color means you can make further predictions about the general distribution of ability over the general populace—not over the populace you have already selected/hired.
You didn’t give a reason for your wrong claim, so it’s hard to guess why you held it.
Maybe this will help: only if the test is infinitely long (produces an infinite amount of evidence as to the actual skill of the tested subject) will the prior evidence be completely irrelevant.
Ok, but I had the sense that, one you’ve already hired, based on skill, learning the colour will no longer give you any help in determining the skills of the people you have already hired… but will only give an indication of what percentage of each colour in the general population has the level of skill you hired-for.
Um—I’m not sure how this relates to what I said… can you please expand/clarify? :)
What I mean is: once you learn the colour, you can reason backwards that “oh, given we have X people with a skill roughly between 13 and 15… 90% of them are blue… this must imply that in the general population, blue weasels are more likely than red weasels to score roughly between 13 and 15 on skill tests at a ratio of roughly 9 to 1”
I don’t know that you can prove much else base don just that data alone.
But if you then additionally learn the color, you can make further conclusions which the test failed to deliver because of the color blindness.
Maybe. It depends on the distributions over programming ability that the test and color, respectively, provide. [ETA1: I should have written, “the test and the conjunction of test and color, respectively...”. The point is that, conditioned on test results, color could be independent of ability.] [ETA2: Though, if your “further conclusions” was meant to include things beyond what the test tests for, but which correlate with color, then you’re definitely right.]
The test’s being colorblind doesn’t mean that its results don’t correlate with color in the population of subjects. It means that, were you to fix a test subject and vary its color while holding everything else constant, its test results wouldn’t correlate with the color change.
Learning the color means you can make further predictions about the general distribution of ability over the general populace—not over the populace you have already selected/hired.
I have no problem with being wrong… but I do like to know why :)
You didn’t give a reason for your wrong claim, so it’s hard to guess why you held it.
Maybe this will help: only if the test is infinitely long (produces an infinite amount of evidence as to the actual skill of the tested subject) will the prior evidence be completely irrelevant.
Ok, but I had the sense that, one you’ve already hired, based on skill, learning the colour will no longer give you any help in determining the skills of the people you have already hired… but will only give an indication of what percentage of each colour in the general population has the level of skill you hired-for.
Instead of thinking “I perfectly measured his skill level; it’s 14”, think “I obtained X bits of evidence that his skill is between 13 and 15″.
Um—I’m not sure how this relates to what I said… can you please expand/clarify? :)
What I mean is: once you learn the colour, you can reason backwards that “oh, given we have X people with a skill roughly between 13 and 15… 90% of them are blue… this must imply that in the general population, blue weasels are more likely than red weasels to score roughly between 13 and 15 on skill tests at a ratio of roughly 9 to 1”
I don’t know that you can prove much else base don just that data alone.