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I feel like all the mucking about with Bayes' Theorem, while technically correct, is completely missing the point. 100 people getting a color wrong seems imposs

I feel like all the mucking about with Bayes' Theorem, while technically correct, is completely missing the point. 100 people getting a color wrong seems impossible, so if it were to happen, I would look for deeper explanations rather than jumping to probabilities. Perhaps it's because those people are from a country/culture that doesn't distinguish blue and green (many don't, see https://en.wikipedia.org/wiki/Blue%E2%80%93green_distinction_in_language https://en.wikipedia.org/wiki/Blue%E2%80%93green_distinction...). While this particular example is unimportant, I think it illustrates a point that just paving over statistical oddities can cause you to skip important investigations.

cortesoft 9y ago
It also is really important how the question is asked.. if people are asked to say what the color is, then many people might say 'blue', but others might say a more specific shade of blue (navy, periwinkle, turquoise, etc). That is very different than if they were asked the yes/no question of 'is this car blue?'
Bartweiss 9y ago
I think we can go a step further and say that the basic Bayes treatment shown is mathematically incorrect. It assumes conditional independence and equal accuracy between judges, which is almost certainly not the case here. If a full 10% of people who observe a car say that it is not blue, I strongly doubt their evaluations are independent. Rather, I would guess that most of them are making the same assessment, like "my culture doesn't distinguish blue and green" or "I am a person who does not consider cyan to be blue". So simply calculating odds based on 1000 conditionally-independent assessments isn't a valid approach. Less formally: I expect a car with 900 votes for 'blue' to be a different color than a car with 999 votes for 'blue'. Is each car blue in the binary sense we're talking about? Well, for that we'd need an objective standard of blue, which the problem quietly failed to set.
ebola1717 9y ago
Or said another way, their analysis is assuming each person's answer is statistically independent, which it's not!
em500 9y ago
> 100 people getting a color wrong seems impossible, so if it were to happen, I would look for deeper explanations rather than jumping to probabilities. Everyone already forgot this? https://en.wikipedia.org/wiki/The_dress https://en.wikipedia.org/wiki/The_dress

cortesoft 9y ago

It also is really important how the question is asked.. if people are asked to say what the color is, then many people might say 'blue', but others might say a more specific shade of blue (navy, periwinkle, turquoise, etc). That is very different than if they were asked the yes/no question of 'is this car blue?'

Bartweiss 9y ago

I think we can go a step further and say that the basic Bayes treatment shown is mathematically incorrect. It assumes conditional independence and equal accuracy between judges, which is almost certainly not the case here. If a full 10% of people who observe a car say that it is not blue, I strongly doubt their evaluations are independent. Rather, I would guess that most of them are making the same assessment, like "my culture doesn't distinguish blue and green" or "I am a person who does not consider cyan to be blue". So simply calculating odds based on 1000 conditionally-independent assessments isn't a valid approach. Less formally: I expect a car with 900 votes for 'blue' to be a different color than a car with 999 votes for 'blue'. Is each car blue in the binary sense we're talking about? Well, for that we'd need an objective standard of blue, which the problem quietly failed to set.

ebola1717 9y ago

Or said another way, their analysis is assuming each person's answer is statistically independent, which it's not!

em500 9y ago

> 100 people getting a color wrong seems impossible, so if it were to happen, I would look for deeper explanations rather than jumping to probabilities. Everyone already forgot this? https://en.wikipedia.org/wiki/The_dress https://en.wikipedia.org/wiki/The_dress